From d465ee3d0c6cb4056bbc271a2c49ab91f7308281 Mon Sep 17 00:00:00 2001 From: a_corni Date: Mon, 9 Dec 2024 11:41:24 +0100 Subject: [PATCH 01/19] Create initial notebook --- tutorials/creating_sequences.ipynb | 312 +++++++---------------------- 1 file changed, 76 insertions(+), 236 deletions(-) diff --git a/tutorials/creating_sequences.ipynb b/tutorials/creating_sequences.ipynb index ff9c86816..e496aefae 100644 --- a/tutorials/creating_sequences.ipynb +++ b/tutorials/creating_sequences.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# Pulse Sequence Creation" + "# Introduction to the Pulse Sequence: Exciting an atom in the Rydberg state" ] }, { @@ -15,43 +15,31 @@ "source": [ "import numpy as np\n", "import pulser\n", - "from pprint import pprint" + "from pprint import pprint\n", + "import pulser_simulation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## 1. Creating the `Register`" + "The `Sequence` is the core object in Pulser. It enables the manipulation of the state of the atoms by controlling their configuration in the `Register` and the application of `Pulses`. This tutorial illustrates the [Conventions page](https://pulser.readthedocs.io/en/stable/conventions.html). It shows the step-by-step creation of a simple Pulser Sequence that excites one atom to the Rydberg state, and how to simulate it using a backend." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The `Register` defines the positions of the atoms and their names of each one. There are multiple ways of defining a `Register`, the most customizable one being to create a dictionary that associates a name (the key) to a cooordinate (the value)." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "L = 4\n", - "square = np.array([[i, j] for i in range(L) for j in range(L)], dtype=float)\n", - "square -= np.mean(square, axis=0)\n", - "square *= 5\n", - "\n", - "qubits = dict(enumerate(square))\n", - "reg = pulser.Register(qubits)" + "## 1. Creating the `Register`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The `Register` class provides some useful features, like the ability to visualise the array and to make a rotated copy." + "The `Register` defines the positions of the atoms and their associated names. There are multiple ways of defining a `Register`, and they are further described in the [Register section](https://pulser.readthedocs.io/en/stable/tutorials/reg_layouts.html) of the fundamentals.\n", + "\n", + "Let's create a `Register` composed of only 1 atom placed at the coordinate `(0, 0)`, using the `Register.from_coordinates` class method: " ] }, { @@ -60,41 +48,28 @@ "metadata": {}, "outputs": [], "source": [ - "print(\"The original array:\")\n", - "reg.draw()\n", - "reg1 = reg.rotated(45) # Rotate by 45 degrees\n", - "print(\"The rotated array:\")\n", - "reg1.draw()" + "reg = pulser.Register.from_coordinates([(0, 0)], prefix=\"q\")\n", + "reg.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "If one doesn't particularly care about the name given to the qubits, one can also create a `Register` just from a list of coordinates (using the `Register.from_coordinates` class method). In this case, the qubit ID's are just numbered, starting from 0, in the order they are provided in, with the option of adding a common prefix before each number. Also, it automatically centers the entire array around the origin, an option that can be disabled if desired." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "reg2 = pulser.Register.from_coordinates(\n", - " square, prefix=\"q\"\n", - ") # All qubit IDs will start with 'q'\n", - "reg2.draw()" + "## 2. Initializing the Sequence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Furthermore, there are also built-in class methods from creation of common array patterns, namely:\n", - "- Square lattices in rectangular or square shapes\n", - "- Triangular lattices\n", + "To create a `Sequence`, one has to provide it with the `Register` instance and the `Device` in which the sequence will be executed. A `Device` object stores all the physical constraints the `Sequence` has to match. It will first check that the `Register` is valid, and will be used to validate each `Pulse` that will be added to the `Sequence`. For more information regarding the `Device`, you can check [its section in the Fundamentals](tobedetermined).\n", + "\n", + "Pulser provides some examples of `Device` in `pulser.devices` (find the list of these examples [in the API](https://pulser.readthedocs.io/en/stable/apidoc/core.html#physical-devices)).\n", + "\n", + "Each QPU has an associated `Device`. The available devices can be fetched using a `RemoteConnection`. Have a look to [the page on QPU Backend](https://pulser.readthedocs.io/en/stable/tutorials/backends.html) to see how to fetch the `Device` associated with the QPU.\n", "\n", - "We could, thus, create the same square array as before by doing:" + "Let's build our `Sequence` with the `Register` previously defined and the device `AnalogDevice` from `pulser.devices`. `AnalogDevice` is an example of the first generation of QPU developed at Pasqal:" ] }, { @@ -103,24 +78,7 @@ "metadata": {}, "outputs": [], "source": [ - "reg3 = pulser.Register.square(4, spacing=5) # 4x4 array with atoms 5 um apart\n", - "reg3.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 2. Initializing the Sequence" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "To create a `Sequence`, one has to provide it with the `Register` instance and the device in which the sequence will be executed. The chosen device will dictate whether the register is valid or not.\n", - "\n", - "We import the device (in this case, `DigitalAnalogDevice`) from `pulser.devices` and initialize our sequence with the freshly created register:" + "from pulser.devices import AnalogDevice" ] }, { @@ -129,23 +87,25 @@ "metadata": {}, "outputs": [], "source": [ - "from pulser.devices import DigitalAnalogDevice\n", - "\n", - "seq = pulser.Sequence(reg, DigitalAnalogDevice)" + "seq = pulser.Sequence(reg, AnalogDevice)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## 3. Declaring the channels that will be used" + "## 3. Declaring a Channel" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Inspecting what channels are available on this device:" + "A `Device` implements some `Channels`, that can be used to modify the state of the atoms via the application of `Pulses`. As presented in the [conventions page](https://pulser.readthedocs.io/en/stable/conventions.html), each channel implements a different Hamiltonian. A complete description of the components of a `Channel` is provided in [its section in the Fundamentals](tobedetermined).\n", + "\n", + "The `AnalogDevice` has only one `Channel`, a `Rydberg.Global` channel that can be used to perform the same single-qubit operation on all the atoms using the rydberg states.\n", + "\n", + "At the beginning of the `Sequence`, all the channels of the `Device` are availble:" ] }, { @@ -161,7 +121,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "We're going to choose the `'rydberg_local'` and `'raman_local'` channels. Note how a declared channel is no longer reported as available." + "We can see that we only have the `Rydberg.Global` channel available. To be used in the `Sequence`, we have to declare the channel and provide it a name. Note how a declared channel is no longer reported as available." ] }, { @@ -172,12 +132,8 @@ }, "outputs": [], "source": [ - "seq.declare_channel(\"ch0\", \"raman_local\")\n", + "seq.declare_channel(\"ch0\", \"rydberg_global\")\n", "print(\"Available channels after declaring 'ch0':\")\n", - "pprint(seq.available_channels)\n", - "\n", - "seq.declare_channel(\"ch1\", \"rydberg_local\", initial_target=4)\n", - "print(\"\\nAvailable channels after declaring 'ch1':\")\n", "pprint(seq.available_channels)" ] }, @@ -203,30 +159,27 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 4. Composing the Sequence" + "## 4. Adding a Pulse" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Every channel needs to start with a target. For `Global` channels this is predefined to be all qubits in the device, but for `Local` channels this has to be defined. This initial target can be set through at channel declaration (see how `'ch1'` was set to target qubit `4`), or it can be done through the standard `target` instruction." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seq.target(1, \"ch0\")" + "Now that we have declared a `Channel`, we can add `Pulses` to this channel. `Pulses` are defined by three quantities: the amplitude $\\Omega$ (in rad/µs), the detuning $\\delta$ (in rad/µs) and the phase $\\phi$ (in rad).\n", + "\n", + "With Pulser, we can define the value of the amplitude and detuning at each nanosecond using `Waveforms`, while the phase is constant within each pulse.\n", + "\n", + "The are many ways to define a `Pulse` and its `Waveforms`. Read the [Pulse section in the Fundamentals](tobedetermined) to learn more about these." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now both channels have an initial target, so we can start building the sequence. Let's start by creating a simple pulse with a constant Rabi frequency of 2 rad/µs and a constant detuning of -10 rad/µs that lasts 200 ns." + "Let's program a `Pulse` that excites the atom in the Rydberg state. As described in [the white paper of Pulser](https://quantum-journal.org/papers/q-2020-09-21-327/pdf/) (see figure 7 on the `NOT` gate), a `Pulse` with $\\int_0^{\\Delta t} \\Omega(u) du = \\pi$, $\\delta(t)=0$ and $\\phi=0$ will perform just that.\n", + "\n", + "Among the waveforms available in Pulser, the [`BlackmanWaveform`](https://pulser.readthedocs.io/en/stable/apidoc/core.html#pulser.waveforms.BlackmanWaveform) can be defined by its area under the curve. Let's define a Pulse having as amplitude a `BlackmanWaveform` of area under the curve `pi`, and having detuning and phase constant equal to 0." ] }, { @@ -235,7 +188,10 @@ "metadata": {}, "outputs": [], "source": [ - "simple_pulse = pulser.Pulse.ConstantPulse(200, 2, -10, 0)" + "pi_wvf = pulser.BlackmanWaveform(600, np.pi)\n", + "print(\"Integral of the waveform is:\", pi_wvf.integral)\n", + "pi_wvf.draw(ylabel=\"BlackmanWaveform of area $\\\\pi$\")\n", + "pi_pulse = pulser.Pulse.ConstantDetuning(pi_wvf, 0, 0)" ] }, { @@ -251,68 +207,14 @@ "metadata": {}, "outputs": [], "source": [ - "seq.add(simple_pulse, \"ch0\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Now, say we want to idle `'ch1'` for 100 ns while `'ch0'` is doing its pulse. We do that by calling: " - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seq.delay(100, \"ch1\")" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Next, we want to create a more complex pulse to add to `'ch1'`, where the amplitude and the detuning are not constant. To do that, we use `Waveform`s:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "duration = 1000\n", - "amp_wf = pulser.BlackmanWaveform(\n", - " duration, np.pi / 2\n", - ") # Duration: 1000 ns, Area: pi/2\n", - "detuning_wf = pulser.RampWaveform(\n", - " duration, -20, 20\n", - ") # Duration: 1000ns, linear sweep from -20 to 20 rad/µs" + "seq.add(pi_pulse, \"ch0\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can visualize a waveform by calling:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "amp_wf.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Also, it is often convenient to find the integral of a waveform, which can be obtain by calling:" + "The `Sequence` can be printed, and we can see that the Pulse has been added to it:" ] }, { @@ -323,14 +225,14 @@ }, "outputs": [], "source": [ - "amp_wf.integral # dimensionless" + "print(seq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We then create the pulse with the waveforms instead of fixed values and we can also visualize it:" + "We can also draw the sequence, for a more visual representation:" ] }, { @@ -339,49 +241,28 @@ "metadata": {}, "outputs": [], "source": [ - "complex_pulse = pulser.Pulse(amp_wf, detuning_wf, phase=0)\n", - "complex_pulse.draw()" + "seq.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "When we're satisfied, we can then add it to a channel:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seq.add(complex_pulse, \"ch1\")" + "After this, you could add multiple `Pulses` to this channel, or define other channels to target other transitions. But let's move on to the final step: the measurement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let's check the schedule to see how this is looking:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "print(seq)" + "## 5. Measurement" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can also draw the sequence, for a more visual representation:" + "To finish a sequence, we measure it. A measurement signals the end of a sequence, so after it no more changes are possible. We can measure a sequence by calling:" ] }, { @@ -390,14 +271,14 @@ "metadata": {}, "outputs": [], "source": [ - "seq.draw()" + "seq.measure(basis=\"ground-rydberg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now, let's see how the Sequence builder handles conflicts (i.e. two channels acting on the same qubit at once). We're going to add a `complex_pulse`to `'ch0'`, but now we want to target it to qubit `4`, which is the same target of `'ch1'`." + "When measuring, one has to select the desired measurement basis. The availabe options depend on the device and can be consulted by calling:" ] }, { @@ -406,28 +287,14 @@ "metadata": {}, "outputs": [], "source": [ - "seq.target(4, \"ch0\")\n", - "seq.add(complex_pulse, \"ch0\")\n", - "\n", - "print(\"Current Schedule:\")\n", - "print(seq)\n", - "seq.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": { - "scrolled": true - }, - "source": [ - "By looking at the current schedule, we can see that `'ch0'` was delayed from `ti=220` to `tf=1100`, and only then was the `complex_pulse` added. The reason for this is simple: it had to wait for the pulse on `ch1`, also targeted to qubit `4`, to finish before it could apply its own. It behaved this way because, in `Sequence.add` there is a default argument `protocol='min-delay`." + "AnalogDevice.supported_bases" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Another protocol for pulse addition is `wait-for-all`, which makes the new pulse wait even if there is no conflict. Let's remove the conflict and add two `simple_pulse`s to `ch1` with the different protocols to see how the compare." + "We've now obtained the final sequence!" ] }, { @@ -436,12 +303,6 @@ "metadata": {}, "outputs": [], "source": [ - "seq.target(0, \"ch1\")\n", - "seq.add(simple_pulse, \"ch1\", protocol=\"min-delay\")\n", - "seq.add(simple_pulse, \"ch1\", protocol=\"wait-for-all\")\n", - "\n", - "print(\"Current Schedule:\")\n", - "print(seq)\n", "seq.draw()" ] }, @@ -449,14 +310,15 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Because we removed the conflict by changing the target of `ch1` to qubit `0`, we see that the first pulse was added without delay from `ti=1100` to `tf=1300` (i.e. while `complex_pulse` is still running in `ch0`). However, once we changed to `protocol='wait-for-all'`, there is now a delay (from `ti=1300` to `tf=2100`) that idles `ch1` until `ch0`is finished with its pulse, even though there was no conflict." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The third protocol is called `'no-delay'` which, as the name implies, never delays the channel where the pulse is being added, even if that means introducing a conflict." + "## 6. Submit the `Sequence` to a `Backend`\n", + "\n", + "We have tailored the `Pulse` such that the atoms all go from the ground state (measurement outcome: 0) to the excited state (measurement outcome: 1) (see the [Measurement section in the \"Conventions\" page](https://pulser.readthedocs.io/en/stable/conventions.html#state-preparation-and-measurement)). But is it really happening ? The `Sequence` can be simulated using a [`Backend`](https://pulser.readthedocs.io/en/stable/apidoc/backend.html), a common interface for execution of Sequences using the QPU or emulators. More details about the backends are provided in [its Fundamental section](tobedetermined).\n", + "\n", + "Prior to submitting the `Sequence` to the QPU, it is of good practice (if the number of atoms is not too big) to use an emulator to simulate the outcome of the Sequence. A list of all the available emulators is given [in the API](https://pulser.readthedocs.io/en/stable/apidoc/backend.html). Let's start with emulating the `Sequence` locally.\n", + "\n", + "Pulser comes with `pulser-simulation`, a package to simulate pulser `Sequence` using the python library [**QuTip**](https://qutip.org/). It implements the `QutipBackend` class. The `Backend` is initialized with a `Sequence`, and the simulation in itself is performed when calling the method `run`.\n", + "\n", + "The outcome of the `QutipBackend` for this kind of simulation is a `CoherentResult`. It stores the state of each atom in the Register at each simulation time. The state of the system at the end of the simulation can be obtained with the method `get_final_state`:\n" ] }, { @@ -465,33 +327,18 @@ "metadata": {}, "outputs": [], "source": [ - "seq.target(0, \"ch0\")\n", - "seq.add(complex_pulse, \"ch0\", protocol=\"no-delay\")\n", - "\n", - "print(\"Current Schedule:\")\n", - "print(seq)\n", - "seq.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With this protocol, it is possible (though not advised), to create an overlap where multiple channels can be acting on the same qubit at the same time. Here, we can see that both act on qubit `0` from `ti=2100` to `tf=2300`." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## 5. Measurement" + "sim = pulser_simulation.QutipBackend(seq)\n", + "res = sim.run()\n", + "res.get_final_state()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "To finish a sequence, we measure it. A measurement signals the end of a sequence, so after it no more changes are possible. We can measure a sequence by calling:" + "The final state is the rydberg state, defined by $\\left|r\\right> = (1, 0)$ (see the [conventions page](https://pulser.readthedocs.io/en/stable/conventions.html) for details).\n", + "\n", + "On a QPU, this state cannot be accessed. We can only estimate the probability to measure the system in the ground state (measurement 0) and the excited state (measurement 1) by making multiple measurements. We can model the measurement by the QPU with the method `sample_final_state`:" ] }, { @@ -500,39 +347,32 @@ "metadata": {}, "outputs": [], "source": [ - "seq.measure(basis=\"ground-rydberg\")" + "res.sample_final_state(N_samples=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "When measuring, one has to select the desired measurement basis. The availabe options depend on the device and can be consulted by calling:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "DigitalAnalogDevice.supported_bases" + "In all the measurement outcomes, all the atoms are measured in the '1' state. This means they are all always measured in the excited state: the `Sequence` works as intended !" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "And so, we've obtained the final sequence!" + "## Follow up" ] }, { - "cell_type": "code", - "execution_count": null, + "cell_type": "markdown", "metadata": {}, - "outputs": [], "source": [ - "seq.draw()" + "- Check a detailed description of all the components of the `Sequence` introduced here in the [Fundamentals section](tobedetermined) !\n", + "\n", + "- In this `Sequence`, we only worked with 1 atom in the Register. Begin our tutorials with the same sequence of Pulses, applied on a Register of 2 atoms placed far appart !\n", + "\n", + "- To further study the influence of an amplitude Pulse on the state of the atoms, you can have a look at our tutorial where we excite the state of the atoms in a superposition state and perform a Rabi experiment." ] } ], From b3f0778d279f2b31773af4c3d3732572d369c148 Mon Sep 17 00:00:00 2001 From: a_corni Date: Mon, 9 Dec 2024 15:49:21 +0100 Subject: [PATCH 02/19] Add temporary links --- tutorials/creating_sequences.ipynb | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/tutorials/creating_sequences.ipynb b/tutorials/creating_sequences.ipynb index e496aefae..2faaa7547 100644 --- a/tutorials/creating_sequences.ipynb +++ b/tutorials/creating_sequences.ipynb @@ -63,7 +63,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "To create a `Sequence`, one has to provide it with the `Register` instance and the `Device` in which the sequence will be executed. A `Device` object stores all the physical constraints the `Sequence` has to match. It will first check that the `Register` is valid, and will be used to validate each `Pulse` that will be added to the `Sequence`. For more information regarding the `Device`, you can check [its section in the Fundamentals](tobedetermined).\n", + "To create a `Sequence`, one has to provide it with the `Register` instance and the `Device` in which the sequence will be executed. A `Device` object stores all the physical constraints the `Sequence` has to match. It will first check that the `Register` is valid, and will be used to validate each `Pulse` that will be added to the `Sequence`. For more information regarding the `Device`, you can check [its section in the Fundamentals](https://pulser.readthedocs.io/en/stable/tutorials/virtual_devices.html).\n", "\n", "Pulser provides some examples of `Device` in `pulser.devices` (find the list of these examples [in the API](https://pulser.readthedocs.io/en/stable/apidoc/core.html#physical-devices)).\n", "\n", @@ -101,7 +101,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "A `Device` implements some `Channels`, that can be used to modify the state of the atoms via the application of `Pulses`. As presented in the [conventions page](https://pulser.readthedocs.io/en/stable/conventions.html), each channel implements a different Hamiltonian. A complete description of the components of a `Channel` is provided in [its section in the Fundamentals](tobedetermined).\n", + "A `Device` implements some `Channels`, that can be used to modify the state of the atoms via the application of `Pulses`. As presented in the [conventions page](https://pulser.readthedocs.io/en/stable/conventions.html), each channel implements a different Hamiltonian. A complete description of the components of a `Channel` is provided in [its section in the Fundamentals](https://pulser.readthedocs.io/en/stable/apidoc/core.html#channels).\n", "\n", "The `AnalogDevice` has only one `Channel`, a `Rydberg.Global` channel that can be used to perform the same single-qubit operation on all the atoms using the rydberg states.\n", "\n", @@ -170,7 +170,7 @@ "\n", "With Pulser, we can define the value of the amplitude and detuning at each nanosecond using `Waveforms`, while the phase is constant within each pulse.\n", "\n", - "The are many ways to define a `Pulse` and its `Waveforms`. Read the [Pulse section in the Fundamentals](tobedetermined) to learn more about these." + "The are many ways to define a `Pulse` and its `Waveforms`. Read the [Pulse section in the Fundamentals](https://pulser.readthedocs.io/en/stable/apidoc/core.html#module-pulser.pulse) to learn more about these." ] }, { @@ -312,7 +312,7 @@ "source": [ "## 6. Submit the `Sequence` to a `Backend`\n", "\n", - "We have tailored the `Pulse` such that the atoms all go from the ground state (measurement outcome: 0) to the excited state (measurement outcome: 1) (see the [Measurement section in the \"Conventions\" page](https://pulser.readthedocs.io/en/stable/conventions.html#state-preparation-and-measurement)). But is it really happening ? The `Sequence` can be simulated using a [`Backend`](https://pulser.readthedocs.io/en/stable/apidoc/backend.html), a common interface for execution of Sequences using the QPU or emulators. More details about the backends are provided in [its Fundamental section](tobedetermined).\n", + "We have tailored the `Pulse` such that the atoms all go from the ground state (measurement outcome: 0) to the excited state (measurement outcome: 1) (see the [Measurement section in the \"Conventions\" page](https://pulser.readthedocs.io/en/stable/conventions.html#state-preparation-and-measurement)). But is it really happening ? The `Sequence` can be simulated using a [`Backend`](https://pulser.readthedocs.io/en/stable/apidoc/backend.html), a common interface for execution of Sequences using the QPU or emulators. More details about the backends are provided in [its Fundamental section](https://pulser.readthedocs.io/en/stable/tutorials/backends.html).\n", "\n", "Prior to submitting the `Sequence` to the QPU, it is of good practice (if the number of atoms is not too big) to use an emulator to simulate the outcome of the Sequence. A list of all the available emulators is given [in the API](https://pulser.readthedocs.io/en/stable/apidoc/backend.html). Let's start with emulating the `Sequence` locally.\n", "\n", @@ -368,7 +368,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "- Check a detailed description of all the components of the `Sequence` introduced here in the [Fundamentals section](tobedetermined) !\n", + "- Check a detailed description of all the components of the `Sequence` introduced here in the [Fundamentals section](https://pulser.readthedocs.io/en/stable/apidoc/pulser.html) !\n", "\n", "- In this `Sequence`, we only worked with 1 atom in the Register. Begin our tutorials with the same sequence of Pulses, applied on a Register of 2 atoms placed far appart !\n", "\n", From 6593e568dc2b8b321771808b823ec74080965a0e Mon Sep 17 00:00:00 2001 From: a_corni Date: Fri, 13 Dec 2024 18:04:12 +0100 Subject: [PATCH 03/19] Add programming section --- docs/source/conf.py | 1 + docs/source/index.rst | 1 + docs/source/programming.md | 105 +++++++++++++++++++++++++++++++++++++ 3 files changed, 107 insertions(+) create mode 100644 docs/source/programming.md diff --git a/docs/source/conf.py b/docs/source/conf.py index e40503e2a..23438f6be 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -41,6 +41,7 @@ "sphinx.ext.mathjax", "sphinx.ext.napoleon", "sphinx_autodoc_typehints", + 'sphinxcontrib.mermaid' ] myst_enable_extensions = [ diff --git a/docs/source/index.rst b/docs/source/index.rst index bdccc5b32..06fa2a7a4 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -51,6 +51,7 @@ computers and simulators, check the pages in :doc:`review`. :caption: Installation and First Steps installation + programming intro_rydberg_blockade tutorials/creating tutorials/simulating diff --git a/docs/source/programming.md b/docs/source/programming.md new file mode 100644 index 000000000..f46afea1b --- /dev/null +++ b/docs/source/programming.md @@ -0,0 +1,105 @@ +# Programming a neutral-atom Quantum Computer + +## Introduction + +1. Atoms encode the state + +Neutral atoms store the quantum information in thier energy levels. If only 2 energy levels of an atom are being used, the atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of the atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. + +When multiple atoms are used, the state describing this multi-atom system is the tensor network of the states. Say these atoms are labeled $\[1, 2, ..., N\]$, then the state of the system is $\left|\Psi\right> = \left|\psi_1\right> \otimes \left|\psi_2\right> \otimes ... \otimes \left|\psi_N\right>$. + +2. Hamiltonian evolves the state + +In quantum physics, the state of a system of atoms evolve along time following the Schrödinger equation: $i\frac{d\left|\Psi\right>(t)}{dt} = \frac{H(t)}{\hbar} \left|\Psi\right>(t)$. $H(t)$ is the Hamiltonian describing the evolution of the system. **Pulser provides you the tools to program this Hamiltonian**. + +2.1. The Hamiltonian + +The Hamiltonian describing the evolution of the system can be written as + +$$ +H(t) = \sum_i \left (H^D_i(t) + \sum_{j$ is involved in the computation, then $\hat{E}_{ij}(R_{ij}) = \frac{C_6}{R_{ij}^6} |r\rangle\langle r|_i |r\rangle\langle r|_j$, where the interaction strength is $\frac{C_6}{R_{ij}^6}$, with $C_6$ a coefficient that can be programmed using Pulser. The entangling operator between atom $i$ and $j$ is $\hat{n}_i\hat{n}_j = |r\rangle\langle r|_i |r\rangle\langle r|_j$. +- If the information is stored in the $\left|0\right>$ and $\left|1\right>$ states of the `XY` basis, $\hat{E}_{ij}(R_{ij}) =\frac{C_3}{R_{ij}^3} (|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j)$, where the interaction strength is $\frac{C_3}{R_{ij}^3}$, with $C_3$ a coefficient that can be programmed using Pulser. The entangling operator between atom $i$ and $j$ is $\hat{\sigma}_i^{+}\hat{\sigma}_j^{-} + \hat{\sigma}_i^{-}\hat{\sigma}_j^{+} = |1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. + +2.3. Evolution of the system's state + +For a system of atoms in the initial state $\left|\Psi_0\right>$, the final state of the system after a time $\Delta t$ is: +$$ \left|\Psi_f\right> = \exp\left(-\frac{i}{\hbar}\int_0^{\Delta t} H(t) dt\right)$$ + +## Recipe + +As underlined above, Pulser lets the user program an Hamiltonian to modify the state of a system of atoms, that encode the states. What do you define at each step of a quantum program in Pulser ? Let's go over these steps. + +1. Pick a Device + +```{mermaid} + +flowchart TB + A[Picking a Device] --> B{Do I want to run on a QPU} + B -->|Yes| C[Pick the Device from the [QPU backend](./tutorials/backends.nblink)] + B -->|No| D[Do I want to mimic all the QPU's constraints ?] + D -->|Yes| E[Use a `Device` (like `pulser.AnalogDevice`)] + D --> |No| F[Use a [`VirtualDevice`](./tutorials/virtual_devices.nblink) (like `pulser.MockDevice`)] + +``` + +The `Device` you select will dictate some parameters and constraint others. For instance, the value of the $C_6$ and $C_3$ coefficients of the Interaction Hamiltonian are defined by the device. For a complete description of the constraints introduced by the device, [check its description](./apidoc/core.rst). + +2. Create the Register + +The Register defines the position of the atoms. This determines: + +- the number of atoms to use in the quantum computation, i.e, the size of the system (let's note it $N$). +- the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the interaction Hamiltonian. + +At this stage, the interaction strength of the Hamiltonian is fully determined. + +3. Pick the Channels + +This defines the energy levels that will be used in the computation. A Channel targets the transition between two energy levels. The Channel must be picked from the `Device.channels`: select your device for it to have the channels you need. + +Picking the channel will initialize the state of the system, and fully determine the Interaction Hamiltonian: +- If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_6}{R_{ij}^6}|r\rangle\langle r|_i |r\rangle\langle r|_j$. +- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|11...1\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. + +Note: It is possible to pick a `Rydberg` and a `Raman` channel, the information will then be encoded in 3 energy levels $\left|r\right>$, $\left|g\right>$ and $\left|h\right>$: the atoms are no-longer qubits but qutrits. However, it is not possible to pick the `Microwave` channel and another channel. + +4. Add the Pulses + +By adding a pulse to a channel, one defines the Driving Hamiltonian: +- the pulse defines the rabi frequency $\Omega(t)$, the detuning $\delta(t)$ and the phase $\phi$ of the Driving Hamiltonian over a duration $\Delta t$. +- the channel defines the states $\left|a\right>$ and $\left|b\right>$ of the Driving Hamiltonian. + +By applying a serie of pulses and delays, one define the evolution of the Driving Hamiltonian for each atom over time. + +**Conclusion**: We have successfully defined the hamiltonian $H$ describing the evolution of the system over time. \ No newline at end of file From 73e6b991daee8206a635d61e43778293172c890c Mon Sep 17 00:00:00 2001 From: a_corni Date: Mon, 16 Dec 2024 09:07:53 +0100 Subject: [PATCH 04/19] Fix installation of mermaid --- docs/requirements.txt | 2 +- docs/source/conf.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/requirements.txt b/docs/requirements.txt index 5c9ef500f..659ac9810 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -6,6 +6,6 @@ nbsphinx nbsphinx-link ipython >= 8.10 # Avoids bug with code highlighting myst-parser - +sphinxcontrib-mermaid # Not on PyPI # pandoc diff --git a/docs/source/conf.py b/docs/source/conf.py index 23438f6be..2161345a9 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -41,7 +41,7 @@ "sphinx.ext.mathjax", "sphinx.ext.napoleon", "sphinx_autodoc_typehints", - 'sphinxcontrib.mermaid' + "sphinxcontrib.mermaid", ] myst_enable_extensions = [ From bb2ae3dd387ba00c081b3631b0814d9f20decaf0 Mon Sep 17 00:00:00 2001 From: a_corni Date: Mon, 16 Dec 2024 11:39:12 +0100 Subject: [PATCH 05/19] Fix figure caption --- docs/source/programming.md | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/docs/source/programming.md b/docs/source/programming.md index f46afea1b..86d70f99a 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -29,12 +29,15 @@ and $j$. The driving Hamiltonian describes the effect of a pulse of Rabi frequency $\Omega(t)$, detuning $\delta(t)$ and phase $\phi(t)$ on an individual atom, exciting the transition between two of its energies levels, $|a\rangle$ and $|b\rangle$. - :::{figure} files/two_level_ab.png :align: center :alt: The energy levels for the driving Hamiltonian. :width: 200 +The coherent excitation is driven between a lower energy level, $|a\rangle$, and a higher energy level, +$|b\rangle$, with Rabi frequency $\Omega(t)$ and detuning $\delta(t)$. +::: + $$ H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-i\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{i\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| $$ From c94d2d894ea5237f9eb1c34436e547d1af7a66ea Mon Sep 17 00:00:00 2001 From: a_corni Date: Wed, 18 Dec 2024 09:12:03 +0100 Subject: [PATCH 06/19] Taking into account review comments --- docs/source/programming.md | 85 ++++++++++++++++++++++---------------- 1 file changed, 50 insertions(+), 35 deletions(-) diff --git a/docs/source/programming.md b/docs/source/programming.md index 86d70f99a..153b61c9d 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -2,17 +2,19 @@ ## Introduction -1. Atoms encode the state +### 1. Atoms encode the state -Neutral atoms store the quantum information in thier energy levels. If only 2 energy levels of an atom are being used, the atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of the atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. +Neutral atoms store the quantum information in their energy levels (also known as [_eigenstates_](./conventions.md#Bases)). When only two eigenstates are used to encode information, each atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of an atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. -When multiple atoms are used, the state describing this multi-atom system is the tensor network of the states. Say these atoms are labeled $\[1, 2, ..., N\]$, then the state of the system is $\left|\Psi\right> = \left|\psi_1\right> \otimes \left|\psi_2\right> \otimes ... \otimes \left|\psi_N\right>$. +When multiple atoms are used, the state of the system is described by a linear combination of the _eigenstates_ of the multi-atom system, whose set is obtained by making the cross product of the set of eigenstate of each atom. If each atom is described by $d$ eigenstates labelled ${\left|a_1\right>, \left|a_2\right>...\left|a_d\right>}$ (each atom is a _qudit_), and if there are $N$ atoms in the system, then the state of the whole system is provided by $\left|\Psi\right> = \sum_{i_1, ..., i_N \in [1, ..., d]} c_{i_1, ..., i_N} \left|a_{i_1}...a_{i_N}\right>$, with $\sum_{i_1, ..., i_N \in [1, ..., d]} |c_{i_1, ..., i_N}|^2 = 1$. -2. Hamiltonian evolves the state +### 2. Hamiltonian evolves the state -In quantum physics, the state of a system of atoms evolve along time following the Schrödinger equation: $i\frac{d\left|\Psi\right>(t)}{dt} = \frac{H(t)}{\hbar} \left|\Psi\right>(t)$. $H(t)$ is the Hamiltonian describing the evolution of the system. **Pulser provides you the tools to program this Hamiltonian**. +In quantum physics, the state of a quantum system evolves along time following the Schrödinger equation: $i\frac{d\left|\Psi\right>(t)}{dt} = \frac{H(t)}{\hbar} \left|\Psi\right>(t)$, where $H(t)$ is the Hamiltonian describing the evolution of the system. -2.1. The Hamiltonian +**Pulser provides you the tools to program this Hamiltonian**. + +#### 2.1. The Hamiltonian The Hamiltonian describing the evolution of the system can be written as @@ -24,9 +26,9 @@ where $H^D_i$ is the driving Hamiltonian for atom $i$ and $H^\text{int}_{ij}$ is the interaction Hamiltonian between atoms $i$ and $j$. -2.1. Driving Hamiltonian +#### 2.2. Driving Hamiltonian -The driving Hamiltonian describes the effect of a pulse of Rabi frequency $\Omega(t)$, detuning $\delta(t)$ and phase $\phi(t)$ on an individual atom, exciting the transition +The driving Hamiltonian describes the effect of a pulse of Rabi frequency $\Omega(t)$, detuning $\delta(t)$ and phase $\phi(t)$ on an individual atom, driving the transition between two of its energies levels, $|a\rangle$ and $|b\rangle$. :::{figure} files/two_level_ab.png @@ -42,67 +44,80 @@ $$ H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-i\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{i\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| $$ -2.2. Interaction Hamiltonian +:::{important} +With Pulser, you program the driving Hamiltonian by setting $\Omega(t)$, $\delta(t)$ and $\phi(t)$, all the while Pulser ensures that you respect the constraints of your chosen device. +::: + +#### 2.3. Interaction Hamiltonian -The interaction Hamiltonian depends on the distance between the atoms $i$ and $j$, $R_{ij}$, and the energy levels in which the information is encoded in these atoms, that define the interaction between the atoms $\hat{E}_{ij}$ + +The interaction Hamiltonian depends on the distance between the atoms $i$ and $j$, $R_{ij}$, and the energy levels in which the information is encoded in these atoms, that define the interaction between the atoms $\hat{U}_{ij}$ $$ -H^\text{int}_{ij} = \hat{E}_{ij}(R_{ij}) +H^\text{int}_{ij} = \hat{U}_{ij}(R_{ij}) $$ -The interaction operator $\hat{E}_{ij}$ is composed of an entangling operator and an interaction strength: -- If the rydberg state $\left|r\right>$ is involved in the computation, then $\hat{E}_{ij}(R_{ij}) = \frac{C_6}{R_{ij}^6} |r\rangle\langle r|_i |r\rangle\langle r|_j$, where the interaction strength is $\frac{C_6}{R_{ij}^6}$, with $C_6$ a coefficient that can be programmed using Pulser. The entangling operator between atom $i$ and $j$ is $\hat{n}_i\hat{n}_j = |r\rangle\langle r|_i |r\rangle\langle r|_j$. -- If the information is stored in the $\left|0\right>$ and $\left|1\right>$ states of the `XY` basis, $\hat{E}_{ij}(R_{ij}) =\frac{C_3}{R_{ij}^3} (|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j)$, where the interaction strength is $\frac{C_3}{R_{ij}^3}$, with $C_3$ a coefficient that can be programmed using Pulser. The entangling operator between atom $i$ and $j$ is $\hat{\sigma}_i^{+}\hat{\sigma}_j^{-} + \hat{\sigma}_i^{-}\hat{\sigma}_j^{+} = |1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. +The interaction operator $\hat{U}_{ij}$ is composed of an entangling operator and an interaction strength: +- If the Rydberg state $\left|r\right>$ is involved in the computation, then $\hat{U}_{ij}(R_{ij}) = \frac{C_6}{R_{ij}^6} \hat{n}_i \hat{n}_j$, where the interaction strength is $\frac{C_6}{R_{ij}^6}$, with $C_6$ a coefficient that depends on the principal quantum number of the Rydberg state. The entangling operator between atom $i$ and $j$ is $\hat{n}_i\hat{n}_j = |r\rangle\langle r|_i |r\rangle\langle r|_j$. Together with the driving Hamiltonian, this interaction encodes the _Ising Hamiltonian_ and is the **most common choice in neutral-atom devices.** +- If the information is stored in the $\left|0\right>$ and $\left|1\right>$ states of the `XY` basis, $\hat{U}_{ij}(R_{ij}) =\frac{C_3}{R_{ij}^3} (|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j)$, where the interaction strength is $\frac{C_3}{R_{ij}^3}$, with $C_3$ a coefficient that depends on the energy levels used to encode $\left|0\right>$ and $\left|1\right>$. The entangling operator between atom $i$ and $j$ is $\hat{\sigma}_i^{+}\hat{\sigma}_j^{-} + \hat{\sigma}_i^{-}\hat{\sigma}_j^{+} = |1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. This interaction hamiltonian is associated with the _XY Hamiltonian_ and is a less common mode of operation, usually accessible only in select neutral-atom devices. + +:::{important} +With Pulser, you program the interaction Hamiltonian by setting the distance between atoms, $R_{ij}$, and the choice of eigenstates used in the computation and the Rydberg level(s) targeted by the device. Most commonly, the ground and Rydberg states ($\left|g\right>$ and $\left|r\right>$) are used, such that +$$ +H^\text{int}_{ij} = \frac{C_6}{R_{ij}^6} \hat{n}_i\hat{n}_j +$$ +When providing the distance between atoms, Pulser ensures that you respect the constraints of your chosen device. +::: -2.3. Evolution of the system's state +#### 2.4. Evolution of the system's state For a system of atoms in the initial state $\left|\Psi_0\right>$, the final state of the system after a time $\Delta t$ is: $$ \left|\Psi_f\right> = \exp\left(-\frac{i}{\hbar}\int_0^{\Delta t} H(t) dt\right)$$ -## Recipe +## Writing a Pulser program -As underlined above, Pulser lets the user program an Hamiltonian to modify the state of a system of atoms, that encode the states. What do you define at each step of a quantum program in Pulser ? Let's go over these steps. +As outlined above, Pulser lets you program an Hamiltonian so that you can manipulate the quantum state of a system of atoms, that encode the states. The series of necessary instructions is encapsulated in the so-called Pulser `Sequence`. Here is a step-by-step guide to create your own Pulser `Sequence`. -1. Pick a Device +### 1. Pick a Device ```{mermaid} flowchart TB A[Picking a Device] --> B{Do I want to run on a QPU} - B -->|Yes| C[Pick the Device from the [QPU backend](./tutorials/backends.nblink)] - B -->|No| D[Do I want to mimic all the QPU's constraints ?] + B -->|Yes| C[Pick the Device from the QPU backend] + B -->|No| D[Do I want to be constrained by all the QPU specs ?] D -->|Yes| E[Use a `Device` (like `pulser.AnalogDevice`)] - D --> |No| F[Use a [`VirtualDevice`](./tutorials/virtual_devices.nblink) (like `pulser.MockDevice`)] + D --> |No| F[Use a `VirtualDevice` (like `pulser.MockDevice`)] ``` -The `Device` you select will dictate some parameters and constraint others. For instance, the value of the $C_6$ and $C_3$ coefficients of the Interaction Hamiltonian are defined by the device. For a complete description of the constraints introduced by the device, [check its description](./apidoc/core.rst). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the interaction Hamiltonian are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst#structure-of-a-device). -2. Create the Register +### 2. Create the Register -The Register defines the position of the atoms. This determines: +The `Register` defines the position of the atoms. This determines: - the number of atoms to use in the quantum computation, i.e, the size of the system (let's note it $N$). - the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the interaction Hamiltonian. -At this stage, the interaction strength of the Hamiltonian is fully determined. - -3. Pick the Channels +### 3. Pick the Channels -This defines the energy levels that will be used in the computation. A Channel targets the transition between two energy levels. The Channel must be picked from the `Device.channels`: select your device for it to have the channels you need. +A `Channel` targets the transition between two energy levels. Therefore, picking channels defines the energy levels that will be used in the computation. The channels must be picked from the `Device.channels`, so your device selection should take into account the channels it supports. -Picking the channel will initialize the state of the system, and fully determine the Interaction Hamiltonian: +Picking the channel will initialize the state of the system, and fully determine the interaction Hamiltonian: - If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_6}{R_{ij}^6}|r\rangle\langle r|_i |r\rangle\langle r|_j$. -- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|11...1\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. +- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. Note: It is possible to pick a `Rydberg` and a `Raman` channel, the information will then be encoded in 3 energy levels $\left|r\right>$, $\left|g\right>$ and $\left|h\right>$: the atoms are no-longer qubits but qutrits. However, it is not possible to pick the `Microwave` channel and another channel. -4. Add the Pulses +At this stage, the interaction strength of the Hamiltonian is fully determined. + +### 4. Add the Pulses -By adding a pulse to a channel, one defines the Driving Hamiltonian: -- the pulse defines the rabi frequency $\Omega(t)$, the detuning $\delta(t)$ and the phase $\phi$ of the Driving Hamiltonian over a duration $\Delta t$. -- the channel defines the states $\left|a\right>$ and $\left|b\right>$ of the Driving Hamiltonian. +By adding pulses to a channel, we incrementally construct the driving Hamiltonian: +- Each `Pulse` defines the Rabi frequency $\Omega(t)$, the detuning $\delta(t)$ and the phase $\phi$ of the driving Hamiltonian over a duration $\Delta t$. Similarly, a delay sets all these parameters to zero for a given amount of time. +- The channel dictates the states $\left|a\right>$ and $\left|b\right>$ of the driving Hamiltonian. -By applying a serie of pulses and delays, one define the evolution of the Driving Hamiltonian for each atom over time. +By applying a series of pulses and delays, one defines the entire driving Hamiltonian of each atom over time. **Conclusion**: We have successfully defined the hamiltonian $H$ describing the evolution of the system over time. \ No newline at end of file From a0a95942fd44d5a68baaa0232e326327ceb776ad Mon Sep 17 00:00:00 2001 From: a_corni Date: Wed, 18 Dec 2024 09:38:30 +0100 Subject: [PATCH 07/19] Fix doc --- docs/source/programming.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/source/programming.md b/docs/source/programming.md index 153b61c9d..cb506a287 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -4,7 +4,7 @@ ### 1. Atoms encode the state -Neutral atoms store the quantum information in their energy levels (also known as [_eigenstates_](./conventions.md#Bases)). When only two eigenstates are used to encode information, each atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of an atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. +Neutral atoms store the quantum information in their energy levels (also known as [_eigenstates_](./conventions.md)). When only two eigenstates are used to encode information, each atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of an atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. When multiple atoms are used, the state of the system is described by a linear combination of the _eigenstates_ of the multi-atom system, whose set is obtained by making the cross product of the set of eigenstate of each atom. If each atom is described by $d$ eigenstates labelled ${\left|a_1\right>, \left|a_2\right>...\left|a_d\right>}$ (each atom is a _qudit_), and if there are $N$ atoms in the system, then the state of the whole system is provided by $\left|\Psi\right> = \sum_{i_1, ..., i_N \in [1, ..., d]} c_{i_1, ..., i_N} \left|a_{i_1}...a_{i_N}\right>$, with $\sum_{i_1, ..., i_N \in [1, ..., d]} |c_{i_1, ..., i_N}|^2 = 1$. @@ -91,7 +91,7 @@ flowchart TB ``` -The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the interaction Hamiltonian are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst#structure-of-a-device). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the interaction Hamiltonian are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. Create the Register From 7084d4c929fb915d87733515ec7163f7fb4b600e Mon Sep 17 00:00:00 2001 From: a_corni Date: Wed, 18 Dec 2024 10:50:52 +0100 Subject: [PATCH 08/19] Try mermaid with mkdown --- docs/source/programming.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/docs/source/programming.md b/docs/source/programming.md index cb506a287..d5da59bcc 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -83,11 +83,11 @@ As outlined above, Pulser lets you program an Hamiltonian so that you can manipu ```{mermaid} flowchart TB - A[Picking a Device] --> B{Do I want to run on a QPU} - B -->|Yes| C[Pick the Device from the QPU backend] - B -->|No| D[Do I want to be constrained by all the QPU specs ?] - D -->|Yes| E[Use a `Device` (like `pulser.AnalogDevice`)] - D --> |No| F[Use a `VirtualDevice` (like `pulser.MockDevice`)] + A[Picking a Device] --> B{Do I want to run on a QPU ?} + B -->|Yes| C["`Pick the Device from the [QPU backend](./tutorials/backends.nblink)`"] + B -->|No| D["`Do I want to be constrained by all the QPU specs ?`"] + D -->|Yes| E["`Use a Device (like _pulser.AnalogDevice_)`"] + D --> |No| F["`Use a [_VirtualDevice_](./tutorials/virtual_devices.nblink) (like _pulser.MockDevice_)`"] ``` From f9d478acfb134304a9ed930c7b678120dd21535c Mon Sep 17 00:00:00 2001 From: a_corni Date: Wed, 18 Dec 2024 18:46:16 +0100 Subject: [PATCH 09/19] Address review comments --- docs/source/files/bloch_rotation_a_b.png | Bin 0 -> 141886 bytes docs/source/programming.md | 127 ++++++++++++++++------- 2 files changed, 88 insertions(+), 39 deletions(-) create mode 100644 docs/source/files/bloch_rotation_a_b.png diff --git a/docs/source/files/bloch_rotation_a_b.png b/docs/source/files/bloch_rotation_a_b.png new file mode 100644 index 0000000000000000000000000000000000000000..85be7fcce0f630b3668a18f89cadc72077623d98 GIT binary patch literal 141886 zcmeFZXHb+`*EWj72#z8$GAgKmh>A*3eU!B*gsR8Z2_rBL&@mkl~{ufmhw{P9Mm4=39 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z$Ga&neRQ?lv&RFLCekk+84WLxqNy*T-oLUA~wnhPY=>JKcoR=moOqXMRB7F9)DqOQL-h6J}C#q%n?Z6?SPR7(yG!5)ryMcj$ zR>9om~!9{PHvp7?ne+$ndx4Z+Ft{<+`QEPV9-MXAob z`Z>!$?@%se-m`ZXr)R~O+NslmTg?_-eqMHX-Y2-rR4;w+{{u^E+44Vs{(pnOh3!dP ZsoNS~vDe!R`!%-x(Sygor?`h*`43@LTKWJ0 literal 0 HcmV?d00001 diff --git a/docs/source/programming.md b/docs/source/programming.md index d5da59bcc..838cfff93 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -1,4 +1,4 @@ -# Programming a neutral-atom Quantum Computer +# Programming a neutral-atom QPU ## Introduction @@ -6,15 +6,30 @@ Neutral atoms store the quantum information in their energy levels (also known as [_eigenstates_](./conventions.md)). When only two eigenstates are used to encode information, each atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of an atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. -When multiple atoms are used, the state of the system is described by a linear combination of the _eigenstates_ of the multi-atom system, whose set is obtained by making the cross product of the set of eigenstate of each atom. If each atom is described by $d$ eigenstates labelled ${\left|a_1\right>, \left|a_2\right>...\left|a_d\right>}$ (each atom is a _qudit_), and if there are $N$ atoms in the system, then the state of the whole system is provided by $\left|\Psi\right> = \sum_{i_1, ..., i_N \in [1, ..., d]} c_{i_1, ..., i_N} \left|a_{i_1}...a_{i_N}\right>$, with $\sum_{i_1, ..., i_N \in [1, ..., d]} |c_{i_1, ..., i_N}|^2 = 1$. +When multiple atoms are used, the state of the system is described by a linear combination of the _eigenstates_ of the multi-atom system, whose set is obtained by making the cross product of the set of eigenstate of each atom. If each atom is described by $d$ eigenstates labelled ${\left|a_1\right>, \left|a_2\right>...\left|a_d\right>}$ (each atom is a _qudit_), and if there are $N$ atoms in the system, then the state of the whole system is provided by + +$$ +\begin{align} +\left|\Psi\right> &= \sum_{i_1, ..., i_N \in [1, ..., d]} c_{i_1, ..., i_N} \left|a_{i_1}...a_{i_N}\right> \\ +&= c_{1, 1, ..., 1}\left|a_{1}a_{1}...a_{1}\right> + ... + c_{1, 1, ..., d}\left|a_{1}a_{1}...a_{d}\right> + ... + c_{d, d, ..., d}\left|a_{d}a_{d}...a_{d}\right> +\end{align} +$$ + +where $\sum_{i_1, ..., i_N \in [1, ..., d]} |c_{i_1, ..., i_N}|^2 = 1$. If $d=2$ and $N=1$, you have the state of a qubit as above. If $d=2$, then for any number of atoms $N$ this becomes + +$$ +\left|\Psi\right> = c_{1, 1, ..., 1}\left|a_{1}a_{1}...a_{1}\right> + c_{1, 1, ..., 2}\left|a_{1}a_{1}...a_{2}\right> + ... + c_{2, 2, ..., 2}\left|a_{2}a_{2}...a_{2}\right> +$$ ### 2. Hamiltonian evolves the state -In quantum physics, the state of a quantum system evolves along time following the Schrödinger equation: $i\frac{d\left|\Psi\right>(t)}{dt} = \frac{H(t)}{\hbar} \left|\Psi\right>(t)$, where $H(t)$ is the Hamiltonian describing the evolution of the system. +In quantum physics, the state of a quantum system evolves along time following the Schrödinger equation: -**Pulser provides you the tools to program this Hamiltonian**. +$$i\frac{d\left|\Psi\right>(t)}{dt} = \frac{H(t)}{\hbar} \left|\Psi\right>(t)$$ + +Here $H(t)$ is the Hamiltonian describing the evolution of the system. For a system of atoms in the initial state $\left|\Psi_0\right>$, the final state of the system after a time $\Delta t$ is: -#### 2.1. The Hamiltonian +$$ \left|\Psi_f\right> = \exp\left(-\frac{i}{\hbar}\int_0^{\Delta t} H(t) dt\right)\left|\Psi_0\right>$$ The Hamiltonian describing the evolution of the system can be written as @@ -26,30 +41,35 @@ where $H^D_i$ is the driving Hamiltonian for atom $i$ and $H^\text{int}_{ij}$ is the interaction Hamiltonian between atoms $i$ and $j$. -#### 2.2. Driving Hamiltonian +:::{important} +**Pulser provides you the tools to program this Hamiltonian**. +::: -The driving Hamiltonian describes the effect of a pulse of Rabi frequency $\Omega(t)$, detuning $\delta(t)$ and phase $\phi(t)$ on an individual atom, driving the transition -between two of its energies levels, $|a\rangle$ and $|b\rangle$. +#### 2.1. Driving Hamiltonian -:::{figure} files/two_level_ab.png +The driving Hamiltonian describes the effect of a pulse on two of energies levels of an individual atom, $|a\rangle$ and $|b\rangle$. A pulse is determined by its Rabi frequency $\Omega(t)$, its detuning $\delta(t)$ and its phase $\phi(t)$. + +$$ +H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-i\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{i\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| +$$ + +In the Bloch sphere representation, this Hamiltonian describes a rotation around the axis **$\Omega$**$(t) = (\Omega(t)\cos(\phi), -\Omega(t)\sin(\phi), -\delta(t))^T$, with angular velocity $\Omega_{eff}(t) = |$**$\Omega$**$(t)| = \sqrt{\Omega^2(t) + \delta^2(t)}$. + +:::{figure} files/bloch_rotation_a_b.png :align: center -:alt: The energy levels for the driving Hamiltonian. +:alt: Representation of the drive Hamiltonian's dynamics as a rotation in the Bloch sphere. :width: 200 -The coherent excitation is driven between a lower energy level, $|a\rangle$, and a higher energy level, +Representation of the drive Hamiltonian's dynamics as a rotation in the Bloch sphere. The coherent excitation is driven between a lower energy level, $|a\rangle$, and a higher energy level, $|b\rangle$, with Rabi frequency $\Omega(t)$ and detuning $\delta(t)$. ::: -$$ -H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-i\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{i\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| -$$ :::{important} With Pulser, you program the driving Hamiltonian by setting $\Omega(t)$, $\delta(t)$ and $\phi(t)$, all the while Pulser ensures that you respect the constraints of your chosen device. ::: -#### 2.3. Interaction Hamiltonian - +#### 2.2. Interaction Hamiltonian The interaction Hamiltonian depends on the distance between the atoms $i$ and $j$, $R_{ij}$, and the energy levels in which the information is encoded in these atoms, that define the interaction between the atoms $\hat{U}_{ij}$ @@ -57,26 +77,47 @@ $$ H^\text{int}_{ij} = \hat{U}_{ij}(R_{ij}) $$ -The interaction operator $\hat{U}_{ij}$ is composed of an entangling operator and an interaction strength: -- If the Rydberg state $\left|r\right>$ is involved in the computation, then $\hat{U}_{ij}(R_{ij}) = \frac{C_6}{R_{ij}^6} \hat{n}_i \hat{n}_j$, where the interaction strength is $\frac{C_6}{R_{ij}^6}$, with $C_6$ a coefficient that depends on the principal quantum number of the Rydberg state. The entangling operator between atom $i$ and $j$ is $\hat{n}_i\hat{n}_j = |r\rangle\langle r|_i |r\rangle\langle r|_j$. Together with the driving Hamiltonian, this interaction encodes the _Ising Hamiltonian_ and is the **most common choice in neutral-atom devices.** -- If the information is stored in the $\left|0\right>$ and $\left|1\right>$ states of the `XY` basis, $\hat{U}_{ij}(R_{ij}) =\frac{C_3}{R_{ij}^3} (|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j)$, where the interaction strength is $\frac{C_3}{R_{ij}^3}$, with $C_3$ a coefficient that depends on the energy levels used to encode $\left|0\right>$ and $\left|1\right>$. The entangling operator between atom $i$ and $j$ is $\hat{\sigma}_i^{+}\hat{\sigma}_j^{-} + \hat{\sigma}_i^{-}\hat{\sigma}_j^{+} = |1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. This interaction hamiltonian is associated with the _XY Hamiltonian_ and is a less common mode of operation, usually accessible only in select neutral-atom devices. +The interaction operator $\hat{U}_{ij}$ is composed of an entangling operator and an interaction strength. + +:::{note} +The interaction Hamiltonian is time-independent. It is always on, no matter the values of the drive Hamiltonian (even if the values of the parameters $\Omega$, $\delta$, $\phi$ are equal to $0$ over a time $\Delta t$). +::: + +##### Ising Hamiltonian + +If the Rydberg state $\left|r\right>$ is involved in the computation, then -:::{important} -With Pulser, you program the interaction Hamiltonian by setting the distance between atoms, $R_{ij}$, and the choice of eigenstates used in the computation and the Rydberg level(s) targeted by the device. Most commonly, the ground and Rydberg states ($\left|g\right>$ and $\left|r\right>$) are used, such that $$ -H^\text{int}_{ij} = \frac{C_6}{R_{ij}^6} \hat{n}_i\hat{n}_j +\hat{U}_{ij}(R_{ij}) = \frac{C_6}{R_{ij}^6} \hat{n}_i \hat{n}_j $$ -When providing the distance between atoms, Pulser ensures that you respect the constraints of your chosen device. -::: -#### 2.4. Evolution of the system's state +- The interaction strength is $\frac{C_6}{R_{ij}^6}$, with $C_6$ a coefficient that depends on the principal quantum number of the Rydberg state. +- The entangling operator between atom $i$ and $j$ is $\hat{n}_i\hat{n}_j = |r\rangle\langle r|_i |r\rangle\langle r|_j$. + +Together with the driving Hamiltonian, this interaction encodes the _Ising Hamiltonian_ and is the **most common choice in neutral-atom devices.** + +##### XY Hamiltonian + +If the information is stored in the Rydberg states $\left|0\right>$ and $\left|1\right>$ (the so-called `XY` basis), then + +$$ +\hat{U}_{ij}(R_{ij}) =\frac{C_3}{R_{ij}^3} (|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j) +$$ + +- The interaction strength is $\frac{C_3}{R_{ij}^3}$, with $C_3$ a coefficient that depends on the energy levels used to encode $\left|0\right>$ and $\left|1\right>$. +- The entangling operator between atom $i$ and $j$ is $\hat{\sigma}_i^{+}\hat{\sigma}_j^{-} + \hat{\sigma}_i^{-}\hat{\sigma}_j^{+} = |1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. + +This interaction hamiltonian is associated with the _XY Hamiltonian_ and is a less common mode of operation, usually accessible only in select neutral-atom devices. -For a system of atoms in the initial state $\left|\Psi_0\right>$, the final state of the system after a time $\Delta t$ is: -$$ \left|\Psi_f\right> = \exp\left(-\frac{i}{\hbar}\int_0^{\Delta t} H(t) dt\right)$$ +:::{important} +With Pulser, you program the interaction Hamiltonian by setting the distance between atoms, $R_{ij}$. Additionally, the choice of eigenstates used in the computation and the Rydberg level(s) targeted by the device fully determine the interaction strength. Most commonly, the ground and Rydberg states ($\left|g\right>$ and $\left|r\right>$) are used, such that +$H^\text{int}_{ij} = \frac{C_6}{R_{ij}^6} \hat{n}_i\hat{n}_j$ +When providing the distance between atoms, Pulser ensures that you respect the constraints of your chosen device. +::: ## Writing a Pulser program -As outlined above, Pulser lets you program an Hamiltonian so that you can manipulate the quantum state of a system of atoms, that encode the states. The series of necessary instructions is encapsulated in the so-called Pulser `Sequence`. Here is a step-by-step guide to create your own Pulser `Sequence`. +As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$](./programming.md#2-hamiltonian-evolves-the-state)) so that you can manipulate the quantum state of a system of atoms. The series of necessary instructions is encapsulated in the so-called Pulser `Sequence`. Here is a step-by-step guide to create your own Pulser `Sequence`. ### 1. Pick a Device @@ -84,40 +125,48 @@ As outlined above, Pulser lets you program an Hamiltonian so that you can manipu flowchart TB A[Picking a Device] --> B{Do I want to run on a QPU ?} - B -->|Yes| C["`Pick the Device from the [QPU backend](./tutorials/backends.nblink)`"] + B -->|Yes| C["`Pick the Device from the QPU backend`"] B -->|No| D["`Do I want to be constrained by all the QPU specs ?`"] D -->|Yes| E["`Use a Device (like _pulser.AnalogDevice_)`"] - D --> |No| F["`Use a [_VirtualDevice_](./tutorials/virtual_devices.nblink) (like _pulser.MockDevice_)`"] + D --> |No| F["`Use a _VirtualDevice_ (like _pulser.MockDevice_)`"] ``` -The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the interaction Hamiltonian are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](./programming.md/#22-interaction-hamiltonian) are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. Create the Register The `Register` defines the position of the atoms. This determines: - the number of atoms to use in the quantum computation, i.e, the size of the system (let's note it $N$). -- the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the interaction Hamiltonian. +- the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the [interaction Hamiltonian](./programming.md/#22-interaction-hamiltonian). ### 3. Pick the Channels A `Channel` targets the transition between two energy levels. Therefore, picking channels defines the energy levels that will be used in the computation. The channels must be picked from the `Device.channels`, so your device selection should take into account the channels it supports. -Picking the channel will initialize the state of the system, and fully determine the interaction Hamiltonian: -- If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_6}{R_{ij}^6}|r\rangle\langle r|_i |r\rangle\langle r|_j$. -- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is $H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$. +Picking the channel will initialize the state of the system, and fully determine the [interaction Hamiltonian](./programming.md#22-interaction-hamiltonian): +- If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is the [Ising Hamiltonian](./programming.md#ising-hamiltonian) -Note: It is possible to pick a `Rydberg` and a `Raman` channel, the information will then be encoded in 3 energy levels $\left|r\right>$, $\left|g\right>$ and $\left|h\right>$: the atoms are no-longer qubits but qutrits. However, it is not possible to pick the `Microwave` channel and another channel. +$$H^\text{int}_{ij} =\frac{C_6}{R_{ij}^6}|r\rangle\langle r|_i |r\rangle\langle r|_j$$ -At this stage, the interaction strength of the Hamiltonian is fully determined. +- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is the [XY Hamiltonian](./programming.md#xy-hamiltonian) +$$H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$$ + +:::{note} +It is possible to pick a `Rydberg` and a `Raman` channel, the information will then be encoded in 3 energy levels $\left|r\right>$, $\left|g\right>$ and $\left|h\right>$: the atoms are no-longer qubits but qutrits. However, it is not possible to pick the `Microwave` channel and another channel. +::: + +:::{important} +At this stage, the [interaction Hamiltonian](./programming.md#22-interaction-hamiltonian) is fully determined. +::: ### 4. Add the Pulses -By adding pulses to a channel, we incrementally construct the driving Hamiltonian: +By adding pulses to a channel, we incrementally construct the [driving Hamiltonian](./programming.md#21-driving-hamiltonian): - Each `Pulse` defines the Rabi frequency $\Omega(t)$, the detuning $\delta(t)$ and the phase $\phi$ of the driving Hamiltonian over a duration $\Delta t$. Similarly, a delay sets all these parameters to zero for a given amount of time. - The channel dictates the states $\left|a\right>$ and $\left|b\right>$ of the driving Hamiltonian. By applying a series of pulses and delays, one defines the entire driving Hamiltonian of each atom over time. -**Conclusion**: We have successfully defined the hamiltonian $H$ describing the evolution of the system over time. \ No newline at end of file +**Conclusion**: We have successfully defined the [Hamiltonian](./programming.md#2-hamiltonian-evolves-the-state) $H$ describing the evolution of the system over time. \ No newline at end of file From 429aaf8cd0a2d16776c0c08a968637a1dc5d1d1c Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 19 Dec 2024 12:09:02 +0100 Subject: [PATCH 10/19] Fix doc --- docs/source/conf.py | 2 +- docs/source/programming.md | 18 +++++++++--------- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/docs/source/conf.py b/docs/source/conf.py index 2161345a9..b2b920134 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -61,7 +61,7 @@ # "tasklist", ] -myst_heading_anchors = 3 +myst_heading_anchors = 5 # Add any paths that contain templates here, relative to this directory. templates_path = ["_templates"] diff --git a/docs/source/programming.md b/docs/source/programming.md index 838cfff93..f0f30beac 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -117,7 +117,7 @@ When providing the distance between atoms, Pulser ensures that you respect the c ## Writing a Pulser program -As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$](./programming.md#2-hamiltonian-evolves-the-state)) so that you can manipulate the quantum state of a system of atoms. The series of necessary instructions is encapsulated in the so-called Pulser `Sequence`. Here is a step-by-step guide to create your own Pulser `Sequence`. +As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$](programming.md#2-hamiltonian-evolves-the-state)) so that you can manipulate the quantum state of a system of atoms. The series of necessary instructions is encapsulated in the so-called Pulser `Sequence`. Here is a step-by-step guide to create your own Pulser `Sequence`. ### 1. Pick a Device @@ -132,25 +132,25 @@ flowchart TB ``` -The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](./programming.md/#22-interaction-hamiltonian) are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. Create the Register The `Register` defines the position of the atoms. This determines: - the number of atoms to use in the quantum computation, i.e, the size of the system (let's note it $N$). -- the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the [interaction Hamiltonian](./programming.md/#22-interaction-hamiltonian). +- the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian). ### 3. Pick the Channels A `Channel` targets the transition between two energy levels. Therefore, picking channels defines the energy levels that will be used in the computation. The channels must be picked from the `Device.channels`, so your device selection should take into account the channels it supports. -Picking the channel will initialize the state of the system, and fully determine the [interaction Hamiltonian](./programming.md#22-interaction-hamiltonian): -- If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is the [Ising Hamiltonian](./programming.md#ising-hamiltonian) +Picking the channel will initialize the state of the system, and fully determine the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian): +- If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is the [Ising Hamiltonian](programming.md#ising-hamiltonian) $$H^\text{int}_{ij} =\frac{C_6}{R_{ij}^6}|r\rangle\langle r|_i |r\rangle\langle r|_j$$ -- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is the [XY Hamiltonian](./programming.md#xy-hamiltonian) +- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is the [XY Hamiltonian](programming.md#xy-hamiltonian) $$H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$$ :::{note} @@ -158,15 +158,15 @@ It is possible to pick a `Rydberg` and a `Raman` channel, the information will t ::: :::{important} -At this stage, the [interaction Hamiltonian](./programming.md#22-interaction-hamiltonian) is fully determined. +At this stage, the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) is fully determined. ::: ### 4. Add the Pulses -By adding pulses to a channel, we incrementally construct the [driving Hamiltonian](./programming.md#21-driving-hamiltonian): +By adding pulses to a channel, we incrementally construct the [driving Hamiltonian](programming.md#21-driving-hamiltonian): - Each `Pulse` defines the Rabi frequency $\Omega(t)$, the detuning $\delta(t)$ and the phase $\phi$ of the driving Hamiltonian over a duration $\Delta t$. Similarly, a delay sets all these parameters to zero for a given amount of time. - The channel dictates the states $\left|a\right>$ and $\left|b\right>$ of the driving Hamiltonian. By applying a series of pulses and delays, one defines the entire driving Hamiltonian of each atom over time. -**Conclusion**: We have successfully defined the [Hamiltonian](./programming.md#2-hamiltonian-evolves-the-state) $H$ describing the evolution of the system over time. \ No newline at end of file +**Conclusion**: We have successfully defined the [Hamiltonian](programming.md#2-hamiltonian-evolves-the-state) $H$ describing the evolution of the system over time. \ No newline at end of file From 37655b64d4ca3c7aaf360ab7ac1b9c87589ca1ee Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 19 Dec 2024 19:57:39 +0100 Subject: [PATCH 11/19] Add picture --- docs/source/files/decision_diagram_device.png | Bin 0 -> 63164 bytes docs/source/programming.md | 30 ++++++++++++------ 2 files changed, 21 insertions(+), 9 deletions(-) create mode 100644 docs/source/files/decision_diagram_device.png diff --git a/docs/source/files/decision_diagram_device.png b/docs/source/files/decision_diagram_device.png new file mode 100644 index 0000000000000000000000000000000000000000..fbf0cbc118e47477dc350b7bbd0fd9df9536d907 GIT binary patch literal 63164 zcmdSBWmuKn+BT}9gwmjNPC%MTH>h;CNP~2DNhpGVFiDX{q#Fe3ly0Ou9;BqZYmeKt z)_z^@{;~gl-*X&3B6Hl=J+2&AoMV1eR+PecNc`~5ojVvZ(&DOj?%Znue+E&J!EX}L zpU8l}?mDYVy|`06K)Me8ao_y8!t*K^)A*B{(TEGus!=0%r^7qpwac2C_05;)CQ`?xq2l{lgQoS&v-y9o3lFlQ7= zonH%Pw}q#~6SY|&TQ0n*)Ua$<`4RrS?2FR)chbj=8jLbZ+ta(gw+1gzsRFQHNRz&R z$^ZH37cQ~UpWore4Wi;fKSfptNXBDBKef?vwSdK_R5Yw^VVe2 z^fDp&_zh~vpi(W114cLkNqG&Zme19XLjQ-4E)zl{!imNAdE9Gtb7Bt-%&Wh7i}@?rRWF)p)i{Noc}K-HS1MH$ zeZ-w+zpC!6wOtiy`DxDeHwAGLqaYaN>D=j8UB~v%PAi`^yI0~2SgYpTf@o;AVvAX$ zdSsL8uMUz9I!Jb9Tr0#B^fI@9{2rU|TE05`8TaAQMDPM!eerN#K)9i6@+5`BeTSoT z2Ic7(>B&*>)zOH}QgsR6>SWX9j(Mr}C9IfJb;`#7pr2Q?o26>jE?LTYboNfNJY=gJ z96*6YVsz7}GuwAtbLZ$z7jC~1SDc*a175ygEm7PujpW=GN6jgToXhq*XpE&w64JR< z8wRk|@3j~szVTztFtFH0qfmIOoAqmF(&1b_GFVXexTM~;KD%;A*(rm!Ecjl2()HeN zFLSrgV+}o-^;qhE12Zf=BKz*0xgB^bI$T!W{i@a_W7eTnK~-fx2Zv`ZDWrVo<7!0J zU&bXLh|_pHK7-+Z5uB(&s3-21>bWZ6`Rk+k(QR0muchra4?=G*m)+XxKu#}3=K&Jp zcw@7n6KJZrLo&5^VSYa6Z7IT%V`lnIW>%Km?Q4?BC$U%&$=b}5(rsOc6lL1@ z`!R*>Ph}GCj`Q_F=fI`*+gl;`yOwr4T;biW@+9n7GdA|Ohq}+I+0jHPmRSCBk59G% zMzw}cqSr?{Vfal4Jvs*yO*idlp~2tu!d@F0RY)or5#CB{WWN>gJRYl}rJ`zwkN@nsJ-ofT<)TK{y_jfP8J1%c zwhA)hXDdbk>s zp|a(W(uLX@3B(>WjTx^=&+nO<>~o^!v|YhV*!iXu*eA)GLJ}UD-kP;9Pd6u?ZtNTC ziPuKG-Umk8`&0Dika|=>NuxF+BlC3l)|RU0R%s458B(X$h(cA@c+q;T2;w-1!q;eP z?Tv6?L2<3N$oaB$e*^ja%|0#^GZE;2;#@aJ3zqOvZlb2T&$EZE4W}aXB@HLxq$0Dd zzyuTXONW@ePL@gNwzbcHg<5vh>RHk6pWS}{*~p7N6N#f=@6nK0#k=6G=Hf6OD+YGvOm$5@XBquEt*KXmcaBjiyu6^hjRQUu>~?c=8Hoe_XMmC6m0|QP#mZ#pi3@8hM{u>s z>1^-8sM=52AA82|-!d{@+!ys0Lsr~ntq~6-$v3mI9?M8dmfB30>tu8>y|fuRZjBSJ z!MPFZw|V*UW8wkt!qu~bgK&#WXQv+1i=zZ$3?+qr-oA6RgfR%S*Ww`ay5C8w~+tcI`oNyTbL;5!TqHBMt1x6v8}l^eclYLCjDsZPR@ z9)0)uFE_)p4T$P|1oNIUjqA;b5Mcnu6kmU_AsD#G6yIxIry zAi!u~UbB_xOWi}HkCp_w4t|o+_6^6FHA~@jS>L|BP&oLAfK#_|bH61v%9Norr4((F z6}dTM;+}*186K|E@B{4uPaGlgC7l$dE@x{zOPuvw6Mn<|iXhOnKXDtz(ehh7h<@+p z`tdN%%O#|C`Ilm|GqixH_b4i zA-YkcJnU*%&fek+lfYned_}oOL?Wknppi`!@&3=ZH)^o1U^D8uUsL7=qnL(puN?b; 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zR9GdGM317#U0M+ALm<@wYN9K`Km{}fFsT3cf+J~!jKRgg!JWeZV;xf}@v^=nzfcRE9MB zSj%q4I`QFtcYfjCwxqTdPP36tH<#K=H$%%^?))PSG+590J4kz_}(k$ZJy~%8N@pgt_G!P34ea>ZWG>Q@%^TQ0famXYXJt1y5={ynOv2Tt4Hm($Vz l)sUVX6%zWtzbVW8V>Kw}Ztg3l=CM=Yrmt(n2rDd literal 0 HcmV?d00001 diff --git a/docs/source/programming.md b/docs/source/programming.md index f0f30beac..0aa9d6031 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -15,12 +15,14 @@ $$ \end{align} $$ -where $\sum_{i_1, ..., i_N \in [1, ..., d]} |c_{i_1, ..., i_N}|^2 = 1$. If $d=2$ and $N=1$, you have the state of a qubit as above. If $d=2$, then for any number of atoms $N$ this becomes +where $\sum_{i_1, ..., i_N \in [1, ..., d]} |c_{i_1, ..., i_N}|^2 = 1$. If $d=2$, then this becomes $$ \left|\Psi\right> = c_{1, 1, ..., 1}\left|a_{1}a_{1}...a_{1}\right> + c_{1, 1, ..., 2}\left|a_{1}a_{1}...a_{2}\right> + ... + c_{2, 2, ..., 2}\left|a_{2}a_{2}...a_{2}\right> $$ +If $d=2$ and $N=1$, you have the state of a qubit as above $\left|\Psi\right> = c_{1}\left|a_{1}\right> + c_{2}\left|a_{2}\right>$. + ### 2. Hamiltonian evolves the state In quantum physics, the state of a quantum system evolves along time following the Schrödinger equation: @@ -58,7 +60,7 @@ In the Bloch sphere representation, this Hamiltonian describes a rotation around :::{figure} files/bloch_rotation_a_b.png :align: center :alt: Representation of the drive Hamiltonian's dynamics as a rotation in the Bloch sphere. -:width: 200 +:width: 300 Representation of the drive Hamiltonian's dynamics as a rotation in the Bloch sphere. The coherent excitation is driven between a lower energy level, $|a\rangle$, and a higher energy level, $|b\rangle$, with Rabi frequency $\Omega(t)$ and detuning $\delta(t)$. @@ -121,16 +123,26 @@ As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$] ### 1. Pick a Device + +:::{figure} files/decision_diagram_device.png +:align: center +:alt: Decision Diagram to select a Device for the computation +:width: 600 +::: + + + B{Do I want to run on a QPU ?} - B -->|Yes| C["`Pick the Device from the QPU backend`"] - B -->|No| D["`Do I want to be constrained by all the QPU specs ?`"] - D -->|Yes| E["`Use a Device (like _pulser.AnalogDevice_)`"] - D --> |No| F["`Use a _VirtualDevice_ (like _pulser.MockDevice_)`"] +flowchart TD + A[Picking a Device] --> B(Do I want to run on a QPU ?) + B --> |Yes| C(Pick the Device from the QPU backend) + B -->|No| D(Do I want to be constrained by all the QPU specs ?) + D -->|Yes| E("`Use a Device (like _pulser.AnalogDevice_)`") + D -->|No| F("`Use a _VirtualDevice_ (like _pulser.MockDevice_)`") -``` +``` +--> The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). From 3b84e6af858266b21d782be3d8570d0ed75fb924 Mon Sep 17 00:00:00 2001 From: a_corni Date: Fri, 20 Dec 2024 16:26:00 +0100 Subject: [PATCH 12/19] Addressing review comments --- docs/requirements.txt | 1 - docs/source/conf.py | 1 - docs/source/programming.md | 56 ++++++++++++++++++++++++-------------- 3 files changed, 36 insertions(+), 22 deletions(-) diff --git a/docs/requirements.txt b/docs/requirements.txt index 659ac9810..596a762ff 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -6,6 +6,5 @@ nbsphinx nbsphinx-link ipython >= 8.10 # Avoids bug with code highlighting myst-parser -sphinxcontrib-mermaid # Not on PyPI # pandoc diff --git a/docs/source/conf.py b/docs/source/conf.py index b2b920134..3faea6833 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -41,7 +41,6 @@ "sphinx.ext.mathjax", "sphinx.ext.napoleon", "sphinx_autodoc_typehints", - "sphinxcontrib.mermaid", ] myst_enable_extensions = [ diff --git a/docs/source/programming.md b/docs/source/programming.md index 0aa9d6031..62c9151e2 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -52,7 +52,7 @@ and $j$. The driving Hamiltonian describes the effect of a pulse on two of energies levels of an individual atom, $|a\rangle$ and $|b\rangle$. A pulse is determined by its Rabi frequency $\Omega(t)$, its detuning $\delta(t)$ and its phase $\phi(t)$. $$ -H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-i\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{i\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| +H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-j\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{j\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| $$ In the Bloch sphere representation, this Hamiltonian describes a rotation around the axis **$\Omega$**$(t) = (\Omega(t)\cos(\phi), -\Omega(t)\sin(\phi), -\delta(t))^T$, with angular velocity $\Omega_{eff}(t) = |$**$\Omega$**$(t)| = \sqrt{\Omega^2(t) + \delta^2(t)}$. @@ -130,20 +130,6 @@ As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$] :width: 600 ::: - - B(Do I want to run on a QPU ?) - B --> |Yes| C(Pick the Device from the QPU backend) - B -->|No| D(Do I want to be constrained by all the QPU specs ?) - D -->|Yes| E("`Use a Device (like _pulser.AnalogDevice_)`") - D -->|No| F("`Use a _VirtualDevice_ (like _pulser.MockDevice_)`") - -``` ---> - The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. Create the Register @@ -158,19 +144,35 @@ The `Register` defines the position of the atoms. This determines: A `Channel` targets the transition between two energy levels. Therefore, picking channels defines the energy levels that will be used in the computation. The channels must be picked from the `Device.channels`, so your device selection should take into account the channels it supports. Picking the channel will initialize the state of the system, and fully determine the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian): + - If the selected Channel is the `Rydberg` or the `Raman` channel, the system is initialized in $\left|gg...g\right>$ and the interaction Hamiltonian is the [Ising Hamiltonian](programming.md#ising-hamiltonian) $$H^\text{int}_{ij} =\frac{C_6}{R_{ij}^6}|r\rangle\langle r|_i |r\rangle\langle r|_j$$ -- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is the [XY Hamiltonian](programming.md#xy-hamiltonian) +- If the selected Channel is the `Microwave` channel, the system is initialized in $\left|00...0\right>$ and the interaction Hamiltonian is the [XY Hamiltonian](programming.md#xy-hamiltonian) + $$H^\text{int}_{ij} =\frac{C_3}{R_{ij}^3}|1\rangle\langle 0|_i |0\rangle\langle 1|_j + |0\rangle\langle 1|_i |1\rangle\langle 0|_j$$ -:::{note} -It is possible to pick a `Rydberg` and a `Raman` channel, the information will then be encoded in 3 energy levels $\left|r\right>$, $\left|g\right>$ and $\left|h\right>$: the atoms are no-longer qubits but qutrits. However, it is not possible to pick the `Microwave` channel and another channel. +:::{important} +At this stage, the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) is fully determined. ::: +A `Channel` is also determined by its addressing. This defines the number of atoms that are going to be targeted by a pulse. If the addressing of a `Channel` is `Global`, all the atoms will experience the same pulse targetting the same transition. In the [Hamiltonian $H$](programming.md#2-hamiltonian-evolves-the-state), all the driving Hamiltonians $H^D_i$ are expressed as + +$$ +H^D_i(t) / \hbar = \frac{\Omega(t)}{2} e^{-j\phi(t)} |a\rangle_i \langle b|_i + \frac{\Omega(t)}{2} e^{j\phi(t)} |b\rangle_i\langle a|_i - \delta(t) |b\rangle_i\langle b|_i +$$ + +If the addressing of a `Channel` is `Local`, then only certain atoms (the atoms "target") will experience the pulse and have their evolution follow $H^D_i$. The driving hamiltonian of the other atoms is $H^D_i = \hat{0}_i$. The hamiltonian $H$ can also be rewritten: + +$$ +H(t) = \sum_{i \in targeted\_ atoms} H^D_i(t) + \sum_i \sum_{j$ under a Hamiltonian $H(t)=\frac{\Omega(t)}{2} |g\rangle_i \langle r|_i+\frac{\Omega(t)}{2} |r\rangle\langle g|$, with $\Omega$ chosen such that the final state of the atom is the excited state $\left|r\right>$. + +Many concepts have been introduced here and you might want further explanations. +- The `Device` object contains all the constraints and physical quantities that are defined in a QPU. [This section in the fundamentals](apidoc/core.rst) details these and provides examples of `Devices`. The `VirtualDevices` were also mentioned in this document ([here](programming.md#1-pick-a-device)), this is a most advanced feature described [here](tutorials/virtual_devices.nblink). +- There are multiple ways of defining a `Register`, this is further detailed [in this section](tutorials/reg_layouts.nblink). +- The energy levels associated with each `Channel` and the interaction Hamiltonian they implement are summed up in [the conventions page](conventions.md). The channels contain lots of constraints and physical informations, they are detailed in [the same section as the `Device`](apidoc/core.rst). +- The quantities in a `Pulse` are defined using `Waveform`s, read more about this [on this page](tutorials/composite_wfs.nblink). \ No newline at end of file From c7d99be9041941fdf2ec2053c035de1e228bd1e4 Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 2 Jan 2025 14:05:26 +0100 Subject: [PATCH 13/19] Add figure, vector on the bloch sphere, complement to the Device --- docs/source/files/bloch_rotation.png | Bin 98261 -> 103350 bytes docs/source/files/programming_qutrit.png | Bin 0 -> 125631 bytes docs/source/programming.md | 14 +++++++++++--- 3 files changed, 11 insertions(+), 3 deletions(-) create mode 100644 docs/source/files/programming_qutrit.png diff --git a/docs/source/files/bloch_rotation.png b/docs/source/files/bloch_rotation.png index bb3d22165fe4115b1f817665aaa34de7bd03b8c5..9a374eaa7272a3dd792a93e2b0cee928ed2a7523 100644 GIT binary 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its levels +:width: 300 + +Example of a neutral atom: The Rubidium atom has one valence electron (e- in left picture), who has multiple energy levels (represented by lines in right picture). Among these energy levels, some of the most used one are the ground-rydberg level $\left|g\right>$, the rydberg level $\left|r\right>$ and the hyperfine level $\left|h\right>$. +::: + ### 2. Hamiltonian evolves the state In quantum physics, the state of a quantum system evolves along time following the Schrödinger equation: @@ -55,7 +63,7 @@ $$ H^D(t) / \hbar = \frac{\Omega(t)}{2} e^{-j\phi(t)} |a\rangle\langle b| + \frac{\Omega(t)}{2} e^{j\phi(t)} |b\rangle\langle a| - \delta(t) |b\rangle\langle b| $$ -In the Bloch sphere representation, this Hamiltonian describes a rotation around the axis **$\Omega$**$(t) = (\Omega(t)\cos(\phi), -\Omega(t)\sin(\phi), -\delta(t))^T$, with angular velocity $\Omega_{eff}(t) = |$**$\Omega$**$(t)| = \sqrt{\Omega^2(t) + \delta^2(t)}$. +In the Bloch sphere representation, this Hamiltonian describes a rotation around the axis $\overrightarrow{\Omega}(t) = (\Omega(t)\cos(\phi), -\Omega(t)\sin(\phi), -\delta(t))^T$, with angular velocity $\Omega_{eff}(t) = |\overrightarrow{\Omega}(t)| = \sqrt{\Omega^2(t) + \delta^2(t)}$. :::{figure} files/bloch_rotation_a_b.png :align: center @@ -63,7 +71,7 @@ In the Bloch sphere representation, this Hamiltonian describes a rotation around :width: 300 Representation of the drive Hamiltonian's dynamics as a rotation in the Bloch sphere. The coherent excitation is driven between a lower energy level, $|a\rangle$, and a higher energy level, -$|b\rangle$, with Rabi frequency $\Omega(t)$ and detuning $\delta(t)$. +$|b\rangle$, with Rabi frequency $\Omega(t)$, detuning $\delta(t)$ and phase $\phi$. ::: @@ -130,7 +138,7 @@ As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$] :width: 600 ::: -The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. Notably, the `Device` defines the list of `Channels` that can be used in the computation, that have a direct impact on the Hamiltonian that can be implemented (see [the section below](#3-pick-the-channels)). For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. Create the Register From db0586d2ad00b9f4042d8ad4bdd795a9461f47eb Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 2 Jan 2025 14:16:49 +0100 Subject: [PATCH 14/19] Make introduction --- docs/source/programming.md | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/docs/source/programming.md b/docs/source/programming.md index b7035369b..9211a320e 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -1,5 +1,10 @@ # Programming a neutral-atom QPU +Pulser enables to program Quantum Processing Units (QPUs) based on neutral atoms (also named _cold-atom Quantum Processing Units_). In this page, you will learn: + +- What are the objects that you are programming with neutral-atom QPUs. +- How to program these objects using Pulser. + ## Introduction ### 1. Atoms encode the state From 639eb56117e61e744a9c7790239697a5b4ede8d2 Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 2 Jan 2025 14:37:01 +0100 Subject: [PATCH 15/19] Add programming.md in ref --- docs/source/programming.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/programming.md b/docs/source/programming.md index 9211a320e..63d739e13 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -143,7 +143,7 @@ As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$] :width: 600 ::: -The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. Notably, the `Device` defines the list of `Channels` that can be used in the computation, that have a direct impact on the Hamiltonian that can be implemented (see [the section below](#3-pick-the-channels)). For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. Notably, the `Device` defines the list of `Channels` that can be used in the computation, that have a direct impact on the Hamiltonian that can be implemented (see [the section below](programming.md#3-pick-the-channels)). For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. Create the Register From 06c0eadae8fef9e3526ac08f792b025989dcf644 Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 2 Jan 2025 15:00:18 +0100 Subject: [PATCH 16/19] Add label --- docs/source/conventions.md | 2 +- docs/source/programming.md | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/source/conventions.md b/docs/source/conventions.md index 73c7e3b34..a3d59d6a6 100644 --- a/docs/source/conventions.md +++ b/docs/source/conventions.md @@ -166,7 +166,7 @@ of $|a\rangle$ and $|b\rangle$. ##### Pulser's state-vector definition -In Pulser, we consistently define the state vectors according to their relative energy. +In Pulser, we consistently define the state vectors according to their relative energy (i.e. from the lowest to the highest energy level). In this way we have, for any given basis, that $$ diff --git a/docs/source/programming.md b/docs/source/programming.md index 63d739e13..4843c0ca0 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -152,7 +152,7 @@ The `Register` defines the position of the atoms. This determines: - the number of atoms to use in the quantum computation, i.e, the size of the system (let's note it $N$). - the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian). -### 3. Pick the Channels +### 3. Pick the Channels {#3-pick-the-channels} A `Channel` targets the transition between two energy levels. Therefore, picking channels defines the energy levels that will be used in the computation. The channels must be picked from the `Device.channels`, so your device selection should take into account the channels it supports. From 828abc7386128e8c50eb3e7766a9e4c80ef4ec16 Mon Sep 17 00:00:00 2001 From: a_corni Date: Thu, 2 Jan 2025 15:10:40 +0100 Subject: [PATCH 17/19] delete ref --- docs/source/programming.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/programming.md b/docs/source/programming.md index 4843c0ca0..0b0b1fa25 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -143,7 +143,7 @@ As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$] :width: 600 ::: -The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. Notably, the `Device` defines the list of `Channels` that can be used in the computation, that have a direct impact on the Hamiltonian that can be implemented (see [the section below](programming.md#3-pick-the-channels)). For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). +The `Device` you select will dictate some parameters and constrain others. For instance, the value of the $C_6$ and $C_3$ coefficients of the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian) are defined by the device. Notably, the `Device` defines the list of `Channels` that can be used in the computation, that have a direct impact on the Hamiltonian that can be implemented. For a complete view of the constraints introduced by the device, [check its description](./apidoc/core.rst). ### 2. 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z=eY&ARl{d&)`HF~yUQ|`45~YvNI`E_mn$Ya+^=~Ohwsk0kGX`B-ZCaJ*9Y60^V^M@ z_w1=A-EgTF&Ai})tw zhNG?`R)k!*D{7$d_kSmWH0dCc`L87YD~bQVcgHVXU)Gk-6&|_Ioft$c) diff --git a/docs/source/programming.md b/docs/source/programming.md index 0b0b1fa25..88af9149e 100644 --- a/docs/source/programming.md +++ b/docs/source/programming.md @@ -2,13 +2,17 @@ Pulser enables to program Quantum Processing Units (QPUs) based on neutral atoms (also named _cold-atom Quantum Processing Units_). In this page, you will learn: -- What are the objects that you are programming with neutral-atom QPUs. -- How to program these objects using Pulser. +- **What are the mathematical objects your are programming with Pulser ?** In quantum computing, the evolution of a quantum state is defined by an Hamiltonian. What is a quantum state in Pulser ? What are the Hamiltonians that can be defined in Pulser ? +- **How do you program these mathematical objects ?** How do you define the quantum state in Pulser ? How do you define the Hamiltonian ? We will propose you a receipe to design your quantum program using Pulser. ## Introduction ### 1. Atoms encode the state +

+ + Click to expand + Neutral atoms store the quantum information in their energy levels (also known as [_eigenstates_](./conventions.md)). When only two eigenstates are used to encode information, each atom is a qubit. If these eigenstates are $\left|a\right>$ and $\left|b\right>$, then the state of an atom is described by $\left|\psi\right> = \alpha \left|a\right> + \beta \left|b\right>$, with $|\alpha|^2 + |\beta|^2 = 1$. When multiple atoms are used, the state of the system is described by a linear combination of the _eigenstates_ of the multi-atom system, whose set is obtained by making the cross product of the set of eigenstate of each atom. If each atom is described by $d$ eigenstates labelled ${\left|a_1\right>, \left|a_2\right>...\left|a_d\right>}$ (each atom is a _qudit_), and if there are $N$ atoms in the system, then the state of the whole system is provided by @@ -28,13 +32,7 @@ $$ If $d=2$ and $N=1$, you have the state of a qubit as above $\left|\Psi\right> = c_{1}\left|a_{1}\right> + c_{2}\left|a_{2}\right>$. -:::{figure} files/programming_qutrit.png -:align: center -:alt: Rubidium atom and 3 of its levels -:width: 300 - -Example of a neutral atom: The Rubidium atom has one valence electron (e- in left picture), who has multiple energy levels (represented by lines in right picture). Among these energy levels, some of the most used one are the ground-rydberg level $\left|g\right>$, the rydberg level $\left|r\right>$ and the hyperfine level $\left|h\right>$. -::: +
### 2. Hamiltonian evolves the state @@ -62,6 +60,10 @@ and $j$. #### 2.1. Driving Hamiltonian +
+ + Click to expand + The driving Hamiltonian describes the effect of a pulse on two of energies levels of an individual atom, $|a\rangle$ and $|b\rangle$. A pulse is determined by its Rabi frequency $\Omega(t)$, its detuning $\delta(t)$ and its phase $\phi(t)$. $$ @@ -84,8 +86,14 @@ $|b\rangle$, with Rabi frequency $\Omega(t)$, detuning $\delta(t)$ and phase $\p With Pulser, you program the driving Hamiltonian by setting $\Omega(t)$, $\delta(t)$ and $\phi(t)$, all the while Pulser ensures that you respect the constraints of your chosen device. ::: +
+ #### 2.2. Interaction Hamiltonian +
+ + Click to expand + The interaction Hamiltonian depends on the distance between the atoms $i$ and $j$, $R_{ij}$, and the energy levels in which the information is encoded in these atoms, that define the interaction between the atoms $\hat{U}_{ij}$ $$ @@ -130,6 +138,8 @@ $H^\text{int}_{ij} = \frac{C_6}{R_{ij}^6} \hat{n}_i\hat{n}_j$ When providing the distance between atoms, Pulser ensures that you respect the constraints of your chosen device. ::: +
+ ## Writing a Pulser program As outlined above, Pulser lets you program an Hamiltonian ([the Hamiltonian $H$](programming.md#2-hamiltonian-evolves-the-state)) so that you can manipulate the quantum state of a system of atoms. The series of necessary instructions is encapsulated in the so-called Pulser `Sequence`. Here is a step-by-step guide to create your own Pulser `Sequence`. @@ -152,7 +162,7 @@ The `Register` defines the position of the atoms. This determines: - the number of atoms to use in the quantum computation, i.e, the size of the system (let's note it $N$). - the distance between the atoms, the $R_{ij} (1\le i, j\le N)$ parameters in the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian). -### 3. Pick the Channels {#3-pick-the-channels} +### 3. Pick the Channels A `Channel` targets the transition between two energy levels. Therefore, picking channels defines the energy levels that will be used in the computation. The channels must be picked from the `Device.channels`, so your device selection should take into account the channels it supports. @@ -204,7 +214,7 @@ We have successfully defined the [Hamiltonian](programming.md#2-hamiltonian-evol - Selecting the `Channels` of the `Device` to use, that defined the energy levels of the atoms to use: that step completely defined the [interaction Hamiltonian](programming.md#22-interaction-hamiltonian). The addressing property of each `Channel` also dictates the atoms that will be targeted by the `Pulse`. - Adding `Pulse` and delays to the `Channel`s defines the [driving Hamiltonian](programming.md#21-driving-hamiltonian) of each atom along time. -You can now simulate your first Hamiltonian by programming your first `Sequence` ! [In this tutorial](tutorials/creating.nblink), you will simulate the evolution of the state of an atom initialized in $\left|g\right>$ under a Hamiltonian $H(t)=\frac{\Omega(t)}{2} |g\rangle_i \langle r|_i+\frac{\Omega(t)}{2} |r\rangle\langle g|$, with $\Omega$ chosen such that the final state of the atom is the excited state $\left|r\right>$. +You can now simulate your first Hamiltonian by programming your first `Sequence` ! [In this tutorial](tutorials/creating.nblink), you will simulate the evolution of the state of an atom initialized in $\left|g\right>$ under a Hamiltonian $H(t)=\frac{\Omega(t)}{2} |g\rangle \langle r|+\frac{\Omega(t)}{2} |r\rangle\langle g|$, with $\Omega$ chosen such that the final state of the atom is the excited state $\left|r\right>$. Many concepts have been introduced here and you might want further explanations. - The `Device` object contains all the constraints and physical quantities that are defined in a QPU. [This section in the fundamentals](apidoc/core.rst) details these and provides examples of `Devices`. The `VirtualDevices` were also mentioned in this document ([here](programming.md#1-pick-a-device)), this is a most advanced feature described [here](tutorials/virtual_devices.nblink). From f1c2fed22058844776aa75db3be32bf3539a7107 Mon Sep 17 00:00:00 2001 From: a_corni Date: Fri, 3 Jan 2025 17:37:56 +0100 Subject: [PATCH 19/19] Create tutorial Excitation to rydberg state --- docs/source/index.rst | 1 - docs/source/intro_rydberg_blockade.ipynb | 243 --------------- tutorials/creating_sequences.ipynb | 361 +++++++++-------------- 3 files changed, 144 insertions(+), 461 deletions(-) delete mode 100644 docs/source/intro_rydberg_blockade.ipynb diff --git a/docs/source/index.rst b/docs/source/index.rst index 06fa2a7a4..48e74c0b3 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -52,7 +52,6 @@ computers and simulators, check the pages in :doc:`review`. installation programming - intro_rydberg_blockade tutorials/creating tutorials/simulating diff --git a/docs/source/intro_rydberg_blockade.ipynb b/docs/source/intro_rydberg_blockade.ipynb deleted file mode 100644 index 35cef0446..000000000 --- a/docs/source/intro_rydberg_blockade.ipynb +++ /dev/null @@ -1,243 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Quickstart: The Rydberg Blockade" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The following walkthrough highlights some of Pulser's core features and uses them to display a crucial physical effect for neutral atom devices: the **Rydberg blockade**. Bear in mind that it is not meant to be a comprehensive step-by-step guide on how to use Pulser, but rather a showcase of Pulser in action. \n", - "\n", - "For a more detailed introduction to Pulser, check the tutorials on [Pulse Sequence Creation](tutorials/creating.nblink) and [Simulation of Sequences](tutorials/simulating.nblink). To better understand neutral atom devices and how they serve as quantum computers and simulators, check the pages in [Quantum Computing with Neutral Atoms](review.rst)." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Pulser's main features" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import pulser\n", - "from pulser_simulation import QutipEmulator" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "With ``pulser``, it is easy to define a ``Register`` consisting of any arrangement of atoms in a quantum processor. For example, we can generate a register with hexagonal shape:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "layers = 3\n", - "reg = pulser.Register.hexagon(layers, prefix=\"q\")\n", - "reg.draw(with_labels=False)" - ] - }, - { - "attachments": { - "download%20%282%29.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "In fact, we can place the atoms in arbitrary positions by specifying the positions of each one. As an exotic example, here is a picture of the Gioconda as a register of neutral atoms made using Pulser:\n", - "\n", - "![download%20%282%29.png](attachment:download%20%282%29.png)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "It is also simple to create and design a ``Pulse`` that will act on the atom array:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "duration = 1000 # Typical: ~1 µsec\n", - "pulse = pulser.Pulse(\n", - " amplitude=pulser.BlackmanWaveform(duration, np.pi),\n", - " detuning=pulser.RampWaveform(duration, -5.0, 10.0),\n", - " phase=0,\n", - ")\n", - "pulse.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Each pulse acts on a set of atoms at a certain moment of time. The entire ``Sequence`` is stored by Pulser and can then be either simulated or sent to a real device. Below is the example of a sequence sending the same $\\pi$-pulse to two atoms, sequentially, using the same channel." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "reg = pulser.Register.rectangle(1, 2, spacing=8, prefix=\"atom\")\n", - "reg.draw()\n", - "\n", - "pi_pulse = pulser.Pulse.ConstantDetuning(\n", - " pulser.BlackmanWaveform(duration, np.pi), 0.0, 0.0\n", - ")\n", - "\n", - "seq = pulser.Sequence(reg, pulser.DigitalAnalogDevice)\n", - "\n", - "seq.declare_channel(\"ryd\", \"rydberg_local\", \"atom0\")\n", - "\n", - "seq.add(pi_pulse, \"ryd\")\n", - "seq.target(\"atom1\", \"ryd\")\n", - "seq.add(pi_pulse, \"ryd\")\n", - "\n", - "seq.draw()" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Probing the Rydberg Blockade Mechanism" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Rydberg atoms are a prominent architecture for exploring condensed matter physics and quantum information processing. For example, one can use Pulser to write a sequence of succesive $\\pi$-pulses on a two atom system, each one coupling the atom to its excited Rydberg state. This will allow us to study the *Rydberg Blockade* effect, using the dedicated ``pulser_simulation`` library:\n", - "\n", - "The presence of the van der Waals interaction when both atoms are in the Rydberg state, prevents the collective ground state $|gg\\rangle$ to couple to $|rr\\rangle$, which is shifted out of resonance. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Hamiltonian for the two-atom system can be written as:\n", - "\n", - "$$H = \\frac{\\hbar \\Omega_1(t)}{2} \\sigma_1^x + \\frac{\\hbar \\Omega_2(t)}{2} \\sigma_2^x + U n_1n_2 $$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We shall explore this blockade by changing the interatomic distance $R$:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "data = []\n", - "distances = np.linspace(6.5, 14, 7)\n", - "\n", - "r = [1, 0] # |r>\n", - "rr = np.kron(r, r) # |rr>\n", - "occup = [np.outer(rr, np.conj(rr))] # |rr>$ is measured in the rydberg state $\\left|r\\right>$ after a time $\\Delta t$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can see that we only have the `Rydberg.Global` channel available. To be used in the `Sequence`, we have to declare the channel and provide it a name. Note how a declared channel is no longer reported as available." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "seq.declare_channel(\"ch0\", \"rydberg_global\")\n", - "print(\"Available channels after declaring 'ch0':\")\n", - "pprint(seq.available_channels)" + "### 1. Picking a `Device`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "At any time, we can also consult which channels were declared, their specifications and the name they were given by calling:" + "We need a `Device` that will enable us to target the transition between the ground and the rydberg state. The `Device` `pulser.AnalogDevice` contains the `Rydberg.Global` channel, that targets the transition between these two states. Let's select this `Device` !" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "seq.declared_channels" + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "Register parameters:\n", + " - Dimensions: 2D\n", + " - Rydberg level: 60\n", + " - Maximum number of atoms: 25\n", + " - Maximum distance from origin: 35 µm\n", + " - Minimum distance between neighbouring atoms: 5 μm\n", + " - SLM Mask: No\n", + "\n", + "Layout parameters:\n", + " - Requires layout: Yes\n", + " - Accepts new layout: No\n", + " - Minimal number of traps: 1\n", + " - Maximum layout filling fraction: 0.5\n", + "\n", + "Device parameters:\n", + " - Maximum number of runs: 2000\n", + " - Maximum sequence duration: 4000 ns\n", + " - Channels can be reused: No\n", + " - Supported bases: ground-rydberg\n", + " - Supported states: r, g\n", + " - Ising interaction coefficient: 865723.02\n", + "\n", + "Channels:\n", + " - 'rydberg_global': Rydberg(addressing='Global', max_abs_detuning=125.66370614359172, max_amp=12.566370614359172, min_retarget_interval=None, fixed_retarget_t=None, max_targets=None, clock_period=4, min_duration=16, max_duration=100000000, min_avg_amp=0, mod_bandwidth=8, custom_phase_jump_time=None, eom_config=RydbergEOM(limiting_beam=, max_limiting_amp=188.49555921538757, intermediate_detuning=2827.4333882308138, controlled_beams=(,), mod_bandwidth=40, custom_buffer_time=240, multiple_beam_control=True, blue_shift_coeff=1.0, red_shift_coeff=1.0), propagation_dir=None)\n" + ] + } + ], + "source": [ + "device = pulser.AnalogDevice\n", + "print(device.specs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## 4. Adding a Pulse" + "### 2. Creating the `Register`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Now that we have declared a `Channel`, we can add `Pulses` to this channel. `Pulses` are defined by three quantities: the amplitude $\\Omega$ (in rad/µs), the detuning $\\delta$ (in rad/µs) and the phase $\\phi$ (in rad).\n", + "We want to excite one atom. There will therefore be only one atom in the `Register`, whose position does not matter because it will not interact with another atom (in this specific case, the [interaction Hamiltonian](docs/programming.md#22-interaction-hamiltonian) is the operator 0 and $H(t)=H^D(t)$).\n", "\n", - "With Pulser, we can define the value of the amplitude and detuning at each nanosecond using `Waveforms`, while the phase is constant within each pulse.\n", - "\n", - "The are many ways to define a `Pulse` and its `Waveforms`. Read the [Pulse section in the Fundamentals](https://pulser.readthedocs.io/en/stable/apidoc/core.html#module-pulser.pulse) to learn more about these." - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Let's program a `Pulse` that excites the atom in the Rydberg state. As described in [the white paper of Pulser](https://quantum-journal.org/papers/q-2020-09-21-327/pdf/) (see figure 7 on the `NOT` gate), a `Pulse` with $\\int_0^{\\Delta t} \\Omega(u) du = \\pi$, $\\delta(t)=0$ and $\\phi=0$ will perform just that.\n", - "\n", - "Among the waveforms available in Pulser, the [`BlackmanWaveform`](https://pulser.readthedocs.io/en/stable/apidoc/core.html#pulser.waveforms.BlackmanWaveform) can be defined by its area under the curve. Let's define a Pulse having as amplitude a `BlackmanWaveform` of area under the curve `pi`, and having detuning and phase constant equal to 0." + "Let's then create a `Register` containing one atom at the coordinate (0, 0)." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "pi_wvf = pulser.BlackmanWaveform(600, np.pi)\n", - "print(\"Integral of the waveform is:\", pi_wvf.integral)\n", - "pi_wvf.draw(ylabel=\"BlackmanWaveform of area $\\\\pi$\")\n", - "pi_pulse = pulser.Pulse.ConstantDetuning(pi_wvf, 0, 0)" + "register = pulser.Register.from_coordinates([(0, 0)], prefix=\"q\")\n", + "register.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "Let's add this pulse to `'ch0'`:" + "At this stage, we can initialize the `Sequence`, our quantum program. This will check that the created `Register` matches the parameters set by the `Device` we picked. " ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ - "seq.add(pi_pulse, \"ch0\")" + "sequence = pulser.Sequence(register, device)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The `Sequence` can be printed, and we can see that the Pulse has been added to it:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "scrolled": true - }, - "outputs": [], - "source": [ - "print(seq)" + "### 3. Picking the Channels" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We can also draw the sequence, for a more visual representation:" + "The only channel we need to pick is a `Rydberg` channel to target the transition between $\\left|g\\right>$ and $\\left|r\\right>$. Since we only have one atom, the addressing does not matter, the `Rydberg.Global` channel will address the atom in the register. " ] }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seq.draw()" - ] - }, - { - "cell_type": "markdown", + "execution_count": 5, "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The available channels were {'rydberg_global': Rydberg(addressing='Global', max_abs_detuning=125.66370614359172, max_amp=12.566370614359172, min_retarget_interval=None, fixed_retarget_t=None, max_targets=None, clock_period=4, min_duration=16, max_duration=100000000, min_avg_amp=0, mod_bandwidth=8, custom_phase_jump_time=None, eom_config=RydbergEOM(limiting_beam=, max_limiting_amp=188.49555921538757, intermediate_detuning=2827.4333882308138, controlled_beams=(,), mod_bandwidth=40, custom_buffer_time=240, multiple_beam_control=True, blue_shift_coeff=1.0, red_shift_coeff=1.0), propagation_dir=None)}\n", + "The states used in the computation are ['r', 'g']\n" + ] + } + ], "source": [ - "After this, you could add multiple `Pulses` to this channel, or define other channels to target other transitions. But let's move on to the final step: the measurement." + "print(\"The available channels were\", sequence.available_channels)\n", + "sequence.declare_channel(\"ch_0\", \"rydberg_global\")\n", + "print(\n", + " \"The states used in the computation are\", sequence.get_addressed_states()\n", + ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## 5. Measurement" + "At this stage, the atom is initialized in the ground state $\\left|g\\right>$ and only two energy levels are used in the computation: the state of the system is described by a qubit." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "To finish a sequence, we measure it. A measurement signals the end of a sequence, so after it no more changes are possible. We can measure a sequence by calling:" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seq.measure(basis=\"ground-rydberg\")" + "### 4. Adding the pulses" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "When measuring, one has to select the desired measurement basis. The availabe options depend on the device and can be consulted by calling:" + "Let's now add a pulse to the `Rydberg.Global` channel to modify the state of the atom and make it reach the state $\\left|r\\right>$.\n", + "\n", + "Since $H=H^D$, the final state after a pulse of duration $\\Delta t$, constant amplitude $\\Omega$, detuning $\\delta=0$ and phase $\\phi=0$ is:\n", + "\n", + "$$\n", + "\\begin{align}\n", + "\\left|\\Psi_f\\right> &= \\exp\\left(-i \\frac{\\Omega}{2} \\Delta t (|g\\rangle\\langle r| + |r\\rangle\\langle g|)\\right) \\left|g\\right> \\\\\n", + "&= \\left(I \\cos\\left(\\frac{\\Omega}{2} \\Delta t\\right) - i \\sin\\left(\\frac{\\Omega}{2} \\Delta t\\right)(|g\\rangle\\langle r| + |r\\rangle\\langle g|)\\right)\\left|g\\right>\n", + "\\end{align}\n", + "$$\n", + "\n", + "From which we get that for $\\frac{\\Omega}{2} \\Delta t = \\frac{\\pi}{2}$, the final state should be equal to $\\left|r\\right>$ (up to a phase, that is irrelevant when measuring with cold atoms since we measure $\\left|\\left<\\Psi_f\\right|\\left|r\\right>\\right|^2$, see below).\n", + "\n", + "We then only have to select $\\Omega$ and $\\Delta t$ to fulfill this condition. We choose $\\Delta t = 1000\\ ns$ and $\\Omega=\\pi\\ rad/\\mu s$:" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "image/png": 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KFSvkcDjU0tKi0tJS1dbWqqOjQ3v27NGLL76o733ve/rkk090zjnn6Morr1RhYWGwv4yASE2UKhp63maxSBNHSAnWnrfbHVIKw/tBqcpZpcKaQrV1tDFwokGDBg0aNGjQoEGDBg0aNGjQoHHcDYvFouS45LAcOElSa0erHK0Ord67WpXOSp/7gcEqoodOP/vZz3T++edr27Zt2rJli+6++26de+65Sk5O7rHOMAyNHTtW119/vf7617+qsrJSTz31lLZu3aq//vWvQdp9YE3OlT7ZfmxrP9netd5fhp883H8nx3HrcHeowF4gu8Ou5LjkiLi4oUGDBg0aNGjQoEGDBg0aNGjQoBGcRlx0nAwZMmV67w+XgVN3I8uWpaioKG0u3iyPx+OzDhiMInrotHPnTr300kuaNGlSn46Lj4/XjTfeqL179+r6668f0D0tXrxYp512mpKTk5WVlaXLL79cBQUFRzzmhRdekGEYPT7i4ny/qffHVadJq3dLf9905HVLN3at+98zBzTfg6PS4b+T47gdqjukXRW7lJmUGTEXNzRo0KBBgwYNGjRo0KBBgwYNGjSC0zCM8B44dTdGDhmpgsoCHaw56LMWGIwieug0duzYfh0fFRWl0aNHD9BuuqxevVoLFy7UF198oeXLl6ujo0MXXHCBmpubj3iczWZTRUWF96O4uHhA9/XjOdK4odL3/iTd85ZUXN3z/uJq6TdvStc8Lk0YLv1o9oDme2iqbfLfyXFcml3N2npoqxJiEpQ7JDdiLm5o0KBBgwYNGjRo0KBBgwYNGjRoBKfx7aFTuA6coixRSohNULQlWpuLN8vV4fI5BhhsooO9gVBgmqb279+vuLg45eb68XXjJH388cc9Pn/hhReUlZWlTZs26ZxzzjnscYZhKCcnp19ti8WiTrfR633WGGnZndLFD0u/Wyo9uFSyxXd9OFu7PkxJ44dKy/5v1/pj0enpGt71RVR039bD/w5WH1R1Y7UmD58cURc3NGjQoEGDBg0aNGjQoEGDBg0aNILTMGTINE25PW7tr94flgOnbsNSh2l/5X4VVBZoyogpPscCg4nl6EsixzvvvKP58+ervr7ee1tRUZGmTJmi8ePHa9SoUbrmmmvkdrsDtieHo+ul5IYM8f2G/G1NTU3Ky8tTbm6uLrvsMu3cufOwa10ul5xOZ48PSUpNTVWl8/D/yE/Ikr5+UPrD9dJZ46Qoi1TR0PXXs8dLf5wvbX5QGpV5bF+bxyNVOUylpaUd2wH/MvrUgX12GfqnvqVeuyt264TME3wGiOF+cUODBg0aNGjQoEGDBg0aNGjQoEEjOA3DMOTxeFRgD89nOH2bxbCoprlGn+35TE1tvIoTBrdBNXRasmSJtmzZ0mMIcvvtt2vnzp0699xzNWXKFL355pt67rnnArIfj8ej2267TWeeeeYR33dq3Lhxeu655/Tee+/p5Zdflsfj0axZs1RaWtrr+sWLFyslJcX70f3srbPOOku7Szt0oPLwe4qLlX52obT6N1LNU1L7S11/XfWf0i0XdN1/rNbvk+oaO3Xuuece+0GSDnx5oE/r4T+maepA1QFFW6Jli7f1uC8SLm5o0KBBgwYNGjRo0KBBgwYNGjRoBKdhmqYcbY6wHzh1N+Jj4tXY2qid5Yd/sgAwGAyqodOuXbs0c+ZM7+eNjY364IMP9P3vf1+ffvqpvvrqK02YMCFgQ6eFCxdqx44deu211464Lj8/X/Pnz9e0adM0e/ZsvfPOO8rMzNRTTz3V6/pFixbJ4XB4Pw4dOiRJuuCCCxQfb9UD73Y9C8mfOjqlxe8bGjY0S7NmzerTsaZpHn0RAqKmqUblDeXKSM7ocXukXNzQoEGDBg0aNGjQoEGDBg0aNGjQCE6jvbNdnZ5Ojc0ZG/YDp9b2Vo0fOl65Q3K1rXSb6prrfM4FDBaDauhUV1fX432R1q5dq87OTl177bWSpJiYGJ1//vk6cMD/z7S55ZZbtGzZMq1cuVIjRozo07ExMTGaPn269u/f3+v9VqtVNputx4ckJSYm6oknluiltYaueVxas1tyD/DwqaNT+mSbdOkjhj7ZEaUlTz7j80PlaGxZtqMvgt95TI8KqwtlyuxxcRFJFzc0aNCgQYMGDRo0aNCgQYMGDRo0gtPwmB7ZYm1KtCb6nCPcBk7djSGJQ9TQ0qAdZTt8zgcMFtHB3kAg2Ww21dbWej9fuXKlLBaLzj77bO9tMTExam5u9tseTNPUz372M7377rtatWqVRo/u+/sXud1ubd++Xd/97nf7fOwNN9yg6Oho3b3ol3rzd3bFWy1KTYySxejzqXz35ZHqm9xydXh04gkj9c47j+uSSy7p83kS0xLVZrb1f0Pol6rGKtmddqUnpntvi7SLGxo0aNCgQYMGDRo0aNCgQYMGDRrBacTHxne9f/i/vehRuA6cpK73qcpOydau8l2aMHSCMpMzfc4NRLpBNXQaP3683n//ff3ud79TVFSUXn31Vc2YMaPHezwVFxcrOzvbb3tYuHChXn31Vb333ntKTk6W3W6XJKWkpCg+Pl6SNH/+fA0fPlyLFy+WJN1///0644wzNGbMGDU0NOjhhx9WcXGxbrzxxuPaw/XXX6/rrrtOX375pb788ks5HI4BeUk7i8Wi1NRUnX322Zo2bZoM4/gmWRUFFYod24c3j8KAc3vcKqwplCFDsdFd/ywi8eKGBg0aNGjQoEGDBg0aNGjQoEGDRnAam0s2+/xOMpwHTt3SEtK0u3y3tpRs0fkTz/c5PxDpBtXQ6ec//7muvvpqjRgxwvuMpt/97nc91nzxxRc65ZRT/LaHJUuWSJLmzJnT4/bnn39eP/zhDyVJJSUlPb4p19fX66abbpLdbldaWppmzJihdevW6eSTTz7ufVgsFuXn5ys/P/+4z4HIVdVYpSpHlfe9nCL14oYGDRo0aNCgQYMGDRo0aNCgQYNGcBoWwyLzX/+TImPg1N1wdbq05dAWTcmdomyb/57gAISiQTV0uuqqq/TEE0/o2WeflSRdc8013kGPJK1evVpOp1MXXXSR3/ZwLM8oWrVqVY/PH330UT366KN+2lHoGTZ+mGo8NcHexqDl9rhVVFMki8WimKiYiL64oUGDBg0aNGjQoEGDBg0aNGjQoBG8RiQOnErrSzUuZ5yaXE3aUbaDoRMGnUE1dJKkn/70p/rpT3/a632zZ89WfX19gHeEf9dU2ySlHX0d/KO6sVpVzq5nOQX7woMGDRo0aNCgQYMGDRo0aNCgQYNGZDYMw5DMrkFNVWNVxAycuhvOVqf22vdq0vBJDJ4wqFiOvmRw+fWvf61rrrkm2NsY1JzVzmBvYdBye9wqrC2UxWJRlBEV8Rc3NGjQoEGDBg0aNGjQoEGDBg0aNILTMGSopb1FZQ1lETdwkiRbvE3N7c3aVbbLZz0QyQbVM53uv//+I97f2dmp1157TXa7PUA7Qm8MixHsLQxa1U3VqnZWKy0hLegXHjRo0KBBgwYNGjRo0KBBgwYNGjQit9Hh7lCHu0PDU4dH3MCpW05KjraXbdekEZOUmZzpcywQiQbV0Onee+894v2G0TXsuPbaawOwGxzOiTNPVEldSbC3Meh4TI9KaktkekxVNVYF/cKDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2XJ0upcSlKCclx+f+SBg4SVKUJUo7yndoZ9lOzRk/x+d+IBINqqHTypUre729ra1Ne/fu1RNPPKHOzk498sgjAd4Zvu3gxoOKPmFQ/dEMCbVNtapwVKi1s1Ue0xP0Cw8aNGjQoEGDBg0aNGjQoEGDBg0akduIi46TNcbqc3+kDJy6G1m2LO2x79GU3Cm9/n8KRJpB9Zv92bNnH/a+Cy+8UAsWLNDkyZP1s5/9TG+88UYAd4Zv83R6gr2FQcc0TR2qO6RKR6WS4pJC4sKDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2rDFWmabZ4/5IGzjFx8ZrbNZY7a/ar732vTrjxDN81gKRpt9DJ5fLpd27d6u8vFyNjY2SpOTkZA0bNkwTJkyQ1eo7rQ5VNptNF198sV5++eVgb2VQS05PlkuuYG9jUKlvqVeBvUCx0bEhc+FBgwYNGjRo0KBBgwYNGjRo0KBBI3IbhgyZMr2Dp0gcOHU3MpIztLN8p04edrJs8TafY4BIclxDJ9M09cILL+ill17S2rVr5fH0/swUi8Wis846SwsWLNCCBQu875kUymJiYhQTExPsbQxqtiybqt3Vwd7GoFJSW6K65jpNHjE5ZC48aNCgQYMGDRo0aNCgQYMGDRo0aERuwzC6hk5SZA+cJGlI4hDtte/V/qr9OiXvFJ/jgEhiOfqSng4dOqTp06frxhtv1OrVq+V2u2WaZq8fbrdbq1ev1o9//GOdcsopKi0t9cfXMGBcLpc+/PBDXX755cHeyqBWtrss2FsYVJytThVUFuiEzBNC6sKDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2DMOQTKnZ1RzRAydJshgWJccla/2B9Wptb/U5FogkfXqmU1NTk8455xwVFxdLkubMmaN58+Zp0qRJGj58uBISEiRJLS0tKisr044dO/Txxx9r5cqV2rp1q2bPnq2tW7cqKcn3QRsIL730Uq+3m6ap8vJyvfLKK3I4HJoxY4bP2vnz5wdii0DAlTWUyTRNpSel+9wX6Rc3NGjQoEGDBg0aNGjQoEGDBg0aNILTMGSo092pgsoCpSWmRezAqbtR11KnioYKHaw+qInDJ/qcA4gUhvnv79Z2BPfee6/uv/9+DRs2TG+99ZbOOOOMYzruyy+/1FVXXaWKigr99re/1T333HPcG+4Pi8XS60v8/fv/Bd9eY5qmDMOQ2+32+/78xel0KiUlRQ6HQzZb6L9m6GufvaY6o065Q3KDvZWI19reqtV7VyvKEqWU+JQe9wX7woMGDRo0aNCgQYMGDRo0aNCgQYNG5Db+vvXvamxr1A/zf6gpuVMieuDU3UiKS9LItJG6YvoVionmLV4QXP6aG/TpmU7vvPOODMPQiy++eMwDJ0k6/fTT9eKLL+r888/X22+/HbSh03PPPRcW7ys12LU2tkqhPxuLCHanXS3tLRqeOrzH7aFw4UGDBg0aNGjQoEGDBg0aNGjQoEEjchstrhZZDIvGZI0J+jAoUI3YqFiV1JXoUP0hnZB5gs/5gEjQp6FTYWGhEhISdN555/U5dN555ykhIUGFhYV9PrY//vznP+uyyy7T8OHD9cMf/jCgbRwfh92hWFtssLcR8TrcHSquLVZCbEKPYWyoXHjQoEGDBg0aNGjQoEGDBg0aNGjQiNxGlCVKMdExPo1IHTh1NyyGRbvKd2lU+iifrx2IBH36Ux0VFXXcLzNnmqY8Hk/AH0i33HKLRo4cqdNOO00PPvigtm/fHtA+EKqqG6tV31Lf42X1QunCgwYNGjRo0KBBgwYNGjRo0KBBg0bkNpLiuoYwpr5565NIHzhJUk5Kjopqi2R32n3OC0SCPk2Axo4dK5fLpbfffrvPobffflttbW0aO3Zsn4/tjw0bNujuu+9We3u7fvOb32jatGk68cQT9Ytf/EKrV6+Wx+MJ6H5wdGPOGBPsLUQ8j+lRSV2Joi3R3h+KoXbhQYMGDRo0aNCgQYMGDRo0aNCgQSOCG4ZF35o3BX0YFKhGQmyCyuvLtbt8t8+5gUjQp6HTNddcI9M0deONN+rNN9885uPeeust3XTTTTIMQ9dee22fN9kfM2bM0AMPPKCtW7fq4MGD+n//7/9p5MiR+uMf/6jvfOc7ys7O1g033KClS5eqpaUloHtD74o2FwV7CxGvvrle1Y3VSk1IlRSiFx40aNCgQYMGDRo0aNCgQYMGDRo0IrZhGIZM05TM0BgGBbLR2tGq7eXb1dDS4HM/EO4M0zTNoy/r0tHRodNPP11btmyRYRg64YQTdNFFF2nSpEkaPny4EhISJEktLS0qKyvTjh079I9//EMHDhyQaZo65ZRT9MUXXyg6uk9vJeUXdXV1WrZsmZYuXarly5erublZcXFxOu+883TFFVfokksuUVZWVrC3OSCcTqdSUlLkcDhks9mCvZ2jeuypxxQ7Nla5Q3KDvZWIte3QNh2sOahhqcNC9sKDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2lu9arsa2Ri2at0hljrKQGAYFqjE8dbgaXY06b/x5OiXvFJ91QCD4a27Qp6GTJDU0NOg//uM/9PHHH3edwDCOuL779PPmzdMrr7yi1NTU49upH7lcLi1fvlzvvfeeli1bpsrKSlksFp1xxhlau3ZtsLfXb+E2dHrmzWfUkdHB0MlPmtqatHb/WsVGx6q9sz1kLzxo0KBBgwYNGjRo0KBBgwYNGjRoRG7j092fytHi0NWnXi3DMEJiGBTIht1hV3xMvK4+9WpZY6w+6wF/89fcwHL0JT2lpqbqww8/1Keffqrrr79e2dnZMk2z14/s7Gxdf/31+vTTT/XBBx+E5MBJkqxWqy655BI988wzKi8v1+eff65f/OIXqq2tDfbWBqW0YWnB3kJEszvtamlvkavDFdIXHjRo0KBBgwYNGjRo0KBBgwYNGjQityFTamlvUWtHaA2DAtXISMpQZWOlimuLfdYD4azPQ6du3/nOd/Tiiy+qvLxcNTU12rZtmz7//HN9/vnn2rZtm2pqalReXq4XX3xR3/nOdwZyz35lGIby8/P1+9//Xrt3D/ybuS1evFinnXaakpOTlZWVpcsvv1wFBQVHPe7NN9/U+PHjFRcXp8mTJ+vDDz8c8L2FitIdpcHeQsRq72zXobpD6nB3qLa5NqQvPGjQoEGDBg0aNGjQoEGDBg0aNGhEbqPJ1SS36daYzDEhNQwKVCM6KloxUTHaUb5DHo/H5zggXB330OnbhgwZokmTJik/P1/5+fmaNGmShgzx/WZzOG+++aZeeumlgdhKyFu9erUWLlyoL774QsuXL1dHR4cuuOACNTc3H/aYdevW6dprr9WPf/xjff3117r88st1+eWXa8eOHQHcOSJBdWO1yhvK5epwhfyFBw0aNGjQoEGDBg0aNGjQoEGDBo3Ibbg9bsXHxCvRmuhzjkgfOHVLsiZpY9FG2Z12n/uAcNXn93Tyh6FDh6q6ulqdnZ0Det4f/ehHx3WcYRh69tlnB3Qvh1NdXa2srCytXr1a55xzTq9rvv/976u5uVnLli3z3nbGGWdo2rRpevLJJ4/aCLf3dPrbp39TfVQ97+k0wDymR18c+EKbSzZrTNaYkL/woEGDBg0aNGjQoEGDBg0aNGjQoBG5jaKaItW11OmeS+6RLf6b31mGwjAokI26pjpdNeMqzR4322cN4E/+mhtED9iZ+skfs68XXnih19sNw+i11317IIdODodDko74zLD169frjjvu6HHbhRdeqKVLl/a63uVyyeVyeT93Op3932gAtbe2S77fp9FP9c312l+1XyOHjAyLCw8aNGjQoEGDBg0aNGjQoEGDBg0akdsoqy/z+R1tKA2DAtWYNnKa9lXu0/SR03sM34BwZTn6kvBVWFjY4+PAgQO65JJLlJ6ergceeECrVq3S7t27tWrVKt1///1KT0/XpZdeqn379gVkfx6PR7fddpvOPPNMTZo06bDr7Ha7srOze9yWnZ0tu733p10uXrxYKSkp3o/c3PB6xlB9eX2wtxCRyhrKZMpUTkqOz32heOFBgwYNGjRo0KBBgwYNGjRo0KBBI4IbRtd9proGT6E2DApUIz0pXfUt9SqqLfJZC4SjkHmmkz/k5eX1+Pyhhx7Sl19+qa1bt2ro0KHe28eNG6dzzjlHN9xwg6ZPn6633npLv/zlL/2+v4ULF2rHjh1au3btgJ530aJFPZ4Z5XQ6w27whIHV0t6i4tpiDU8b7nNfyF540KBBgwYNGjRo0KBBgwYNGjRo0IjYhqFvXo0qFIdBgWwkxyVrZ9lOTciZoJjoGJ/jgHBiOfqSyPHss8/qe9/7Xo+B07cNHz5c3/ve9/TMM8/4fS+33HKLli1bppUrV2rEiBFHXJuTk6PKysoet1VWVionx/cZK5JktVpls9l6fISTE047IdhbiDjVjdXqdHcq2Zrc4/ZQvvCgQYMGDRo0aNCgQYMGDRo0aNCgEbkNi2GRKVMVDRUhOwwKVCMzOVMVjq7/H4BwN6iGTqWlpYqL8/3m+W1xcXEqLfXfg9s0Td1yyy1699139dlnn2n06NFHPSY/P18rVqzocdvy5cuVn5/vr20G1aHth4K9hYji9rhVUlcia4xVhmF4bw/1Cw8aNGjQoEGDBg0aNGjQoEGDBg0akdswDEPt7nZVOCpCdhgUqEaUJUrFtcXaVb7L51gg3AyqodOIESP07rvvqq2trdf7W1pa9O677x71mUf9sXDhQr388st69dVXlZycLLvdLrvdrtbWVu+a+fPna9GiRd7Pb731Vn388cd65JFHtGfPHt17773auHGjbrnlFr/tM5g62jqCvYWIUtdcp7rmOqXEp3hvC4cLDxo0aNCgQYMGDRo0aNCgQYMGDRqR22hpb1F7Z7uGpgwN2WFQIBux0bEqrClUXXOdzzmAcDKohk433nijDh48qDPPPFPvvfeeamtrJUm1tbVaunSpzjrrLBUVFemmm27y2x6WLFkih8OhOXPmaOjQod6P119/3bumpKREFRUV3s9nzZqlV199VU8//bSmTp2qt956S0uXLtWkSZP8ts9gSkhJCPYWIkpZQ5lM01RMVNfrwYbLhQcNGjRo0KBBgwYNGjRo0KBBgwaNyG20tLcoxhKjnJQcn/tDaRgUqMb0kdPV2tGqwupCn/MA4SQ62BsIpDvvvFN79+7V888/ryuvvFKSZLFY5PF4JHW99N0NN9ygO++802976H5zvCNZtWqVz21XX321rr76aj/sKPRk5GXI3mYP9jYiQpOrSXaHXbb4rvf1CqcLDxo0aNCgQYMGDRo0aNCgQYMGDRqR20iyJqmxrdHn96WhNgwKZCMlIUW77bs1ecRkxUbH+pwTCAeDauhksVj07LPPav78+XrxxRe1bds2ORwOpaSkaOrUqbr++us1Z86cYG9z0CvZVqLYsXxTHQjVjdVqaW9RWkJa2F140KBBgwYNGjRo0KBBgwYNGjRo0IjcRm1zrUwxcPp2IyMpQ0W1RTpUd0gnZp3oc14gHAyqoVO32bNna/bs2cHeBuBXne5OHao7pPiYeLk6XWF34UGDBg0aNGjQoEGDBg0aNGjQoEEjchsWWSRT3sFTKA+DAtWIiYqRRRbtrtitEzJPkGEYPucHQp3l6EuAwMocnRnsLUSE2uZa1bfUyxptDcsLDxo0aNCgQYMGDRo0aNCgQYMGDRqR2zAMg4FTLw2P6dHGoo2qbar1uQ8IByHxTKfvfe97cjqdAW263W7V1NTI5XL1ev/IkSMDuh98w93hlmKCvYvwV+GokKvTpWZXc1heeNCgQYMGDRo0aNCgQYMGDRo0aNCI3IZhGDJNU82uZhXWFIb8MChQjfqWenV6OlVUW6SM5AyfNUCoC4mh0x/+8IeAtTZt2qS7775ba9asUXt7e69rDMNQZ2dnwPaEnupK63hPp35qcjWprL5MTW1NSolPCcsLDxo0aNCgQYMGDRo0aNCgQYMGDRqR2zBkyG26tb96v7Jt2SE/DApkw2JYtKdijyYPnyxrjNVnLRDKBmzotH79em3btk11dXXq6Og44tp77rlnoLJ9smXLFp199tmKjo7WBRdcoPfff19Tp05VTk6ONm/erOrqas2ZM0d5eXlB2R8wUKobq1VcV6yspKywvfCgQYMGDRo0aNCgQYMGDRo0aNCgEbmNTk+nXB0uxUeHzzAoUI0Od4eKaopUWl+qE7NO9FkPhLJ+D50+/fRT3XzzzSouLj7mY4I1dHrggQckSV9++aUmTJggi8WiK664Qvfcc49aW1v1i1/8Qm+99Zaee+65oOwPXUbPGK2yxrJgbyNsuT1u7bXvVVx0XNd/GRGmFx40aNCgQYMGDRo0aNCgQYMGDRo0IrfR0NIgi2HRCZknhM0wKFCNmKgYWQyL9lbuZeiEsNOvodNXX32lSy65xPsydaNHj9awYcMUHR0Sr9rnY+3atfpf/+t/acKECd7bTLPrzeri4+P1+OOPa926dbr77rv16quvBmubg1757nJpRLB3Eb5qm2pV6azU2KyxYX3hQYMGDRo0aNCgQYMGDRo0aNCgQSNyG9FR0d7hyreF8jAokI3M5Eztq9ynmaNnKj0p3edYIFT1azr0wAMPqL29XePHj9cbb7yhSZMmDdS+/MLhcOiEE07wfh4TE6Ompibv5xaLRXPmzNHf/va3YGwP/+JqcSlWvKfT8SqtL1VSXJJiY3r+fxhuFx40aNCgQYMGDRo0aNCgQYMGDRo0IrcxJGGIimt7vnpWOAyDAtWwWCzaWbFTRTVFDJ0QVixHX3J469evl2EY+utf/xryAydJysrKUn19vffznJwc7du3r8eatrY2tbS0BHpr+Ja4ZN8fWDg2za5mVTVWKTU+tcft4XjhQYMGDRo0aNCgQYMGDRo0aNCgQSNyG92DGlNdr0QVLsOgQDZS4lO0u2K3Ojo7fNYAoapfQ6eWlhYlJCRoxowZA7Ufvzr55JNVUFDg/fzMM8/UJ598ovXr10uSdu/erTfeeEPjx48P1hYhKfvE7GBvIWxVN1arpb1FidZE723heuFBgwYNGjRo0KBBgwYNGjRo0KBBI3IbhmF0vfWJGX7DoEA1Tht1mqqbqnWo/pDPOiBU9WvolJeXJ4/HM1B78buLL75Ya9asUUVFhSTpV7/6lUzT1FlnnaXMzExNnjxZDQ0Nuvvuu4O808GteEvx0RfBh9vj1qH6Q4qLiZNhGJLC+8KDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2DHX9/ioch0GBasTFxEmmtL9qv89aIFT1a+h01VVXqa2tTWvWrBmo/fjVT37yE5WVlSk9ves1MKdOnaoVK1booosuUkZGhubOnav3339fV1xxRZB3CvRdXXOd6pvrlRKfIin8Lzxo0KBBgwYNGjRo0KBBgwYNGjRoRG7DMAx5TI8O1hwMu2FQIBuZtkwV1hSqvrne5xggFEX35+C77rpLr7/+uhYuXKhVq1Z5hzmhKiYmRtnZPV+6bdasWfrggw+CtCP0JmNkhpxyBnsbYafSWSmP6VFMVExEXHjQoEGDBg0aNGjQoEGDBg0aNGjQiNyGaZrqcHeotaNVU3KnhN0wKFANW5xNZfVlKqkrUVpims+xQKg55qHT4Z7N9MADD2jhwoWaOHGibr75Zp1++ulKTk4+4rnOOeecvu1ygERFRemaa67RK6+8EpQ+4C+t7a0qbyhXclxyxFx40KBBgwYNGjRo0KBBgwYNGjRo0IjcRn1LvTymRydmnhiWw6BANTymR9VN1fqq8CtNHDZR0VH9eh4J4HfH/Cd0zpw53veJOZwHH3zwqOcxDEOdnZ3Hmh1QNptNubm5QWnj2NWU1Ch2bGywtxFWqpuq1eRq0lDb0Ii58KBBgwYNGjRo0KBBgwYNGjRo0KARuY1OT6eiLdGKj433OUc4DIMC2bBGW1XfUq/yhnKNTB/pcx4glFiOvuQbpmn2+8Pj8fjrazmqmTNnauvWrUHrA/7gMT0qrStVjCVG5Y7yiLnwoEGDBg0aNGjQoEGDBg0aNGjQoBG5jYykjK4nOZg9zxFOw6BANSYNn6RoS7QOVB3wOQ8Qao556OTxeAbsI1juvfdeffbZZ3rppZeCtgccXd60vGBvIazUN9erpqlGze3NEXXhQYMGDRo0aNCgQYMGDRo0aNCgQSNyG7HRvq90FG7DoEA2MpIytL96v5ytTp/zAaFkUL0A5PLlyzVnzhzdcMMN+tOf/qTTTjtN2dnZPi8baBiGfvOb3wRpl6g8UCkNDfYuwkels1IVjgolxyVH1IUHDRo0aNCgQYMGDRo0aNCgQYMGjchtGDK6Xh3rX091CtdhUKAaKQkp2le5TyV1JZo0fJLPeYFQ0a+hU3t7u/bs2aPY2FiNHz/+iGv37Nmj9vZ2TZgwQTExMf3JHrd7773X+/ebNm3Spk2bel3H0Cm42hrbFDuU93Q6Fq4Ol/ZX7ZfFsETchQcNGjRo0KBBgwYNGjRo0KBBgwaNyG0YhsHAqQ8Ni2FRQmyCth3apglDJ/gcC4SKfg2dXn/9df3whz/UTTfdpCeffPKIax988EG9+uqrevnll3Xttdf2J3vcVq5cGZTut61Zs0YPP/ywNm3apIqKCr377ru6/PLLD7t+1apVOvfcc31ur6ioUE5Ojh93GjzWBKv3Bw6OrLqpWhWOCo3LHhdxFx40aNCgQYMGDRo0aNCgQYMGDRo0IrdhqOv9nOwOu9rd7WE7DApko9PTqa2lWzV73GwNTxvucz8QCvo1dHr77bclSfPnzz/q2h//+Md65ZVX9NZbbwVt6DR79uygdL+tublZU6dO1Y9+9CNdeeWVx3xcQUGBbDab9/OsrCx/bC8kDJswTGWNZcHeRsgzTVNFNUVKT0pXgjXB5/5wv/CgQYMGDRo0aNCgQYMGDRo0aNCgEdmNTk+n7E67poyYEtbDoEA1qhurFWVE6WDNQYZOCFn9Gjrt2LFD0dHRmjlz5lHXnnnmmYqOjtb27dv7kwx78+bN07x58/p8XFZWllJTUwd+QyGocFOhYsfy8npH42h1qLa5VlnJvgPISLnwoEGDBg0aNGjQoEGDBg0aNGjQoBGZjSZXk9ymW9m27LAfBgWyERsdq332fTpl5ClKtCb6rAWCzXL0JYdXXl6ulJQURUcffXYVExOjlJQUVVRU9CfZJxdddJE2bNhwXMc2NzfroYce0hNPPDHAuzo+06ZN09ChQ3X++efr888/P+Jal8slp9PZ4wORp9JZKY/H4/NDO1IuPGjQoEGDBg0aNGjQoEGDBg0aNGhEbqOxrVEWw6JsW7bP/eE4DApUIy0hTfUt9SqpK/FZC4SCfg2dYmNj1djYeExrTdNUU1OTDMPoT7JPqqurdcYZZ+jcc8/V888/L4fDcdRjvvjiC91yyy3Ky8vTAw88oOxs3296gTR06FA9+eSTevvtt/X2228rNzdXc+bM0ebNmw97zOLFi5WSkuL9yM3NDeCO+2/ICN8fZuipw92hsoYyn5fVi6QLDxo0aNCgQYMGDRo0aNCgQYMGDRqR27DF22QxfH89Ha7DoEA1oixRssZYVWAvkMfj8TkGCLZ+vbze6NGjtW3bNq1fv175+flHXLtu3Tq5XC6NGTOmP8k+2bRpk1588UXdd999+vGPf6ybbrpJ48aN04wZM5Sdna3U1FS1tbWprq5OBQUF2rhxoxobGxUVFaVrrrlGv/vd7zRy5MiA7bc348aN07hx47yfz5o1SwcOHNCjjz6qv/71r70es2jRIt1xxx3ez51OZ1gNnqJioo6+aJCrbqyWs9XZ478EibQLDxo0aNCgQYMGDRo0aNCgQYMGDRqR22hobZBpmj3uD+dhUCAbmcmZKqwuVFVjlXJScnyOBYKpX0On888/X1u3btVdd92lFStWHPZl9jo7O7Vo0SIZhqELLrigP8k+W7BggebPn68PP/xQzz//vFatWqWXX37ZZ53FYtGUKVN0xRVX6MYbb9TQoUMDus++mDlzptauXXvY+61Wq6xWawB3NLCqC6t5T6ejKHeUy2JYvD+wIvHCgwYNGjRo0KBBgwYNGjRo0KBBg0bkNhytDpkyvYOnSBgGBarhMT3abd+tg9UHGToh5PRr6PTzn/9cjz/+uNauXau5c+fq0Ucf1fTp03us2bx5s26//XatXbtWcXFxuvXWW/u14eNhGIYuvvhiXXzxxZKk3bt3q7S0VLW1tYqPj1dmZqYmTpyolJSUgO/teGzZsiWkh2LwL2erU1XOKtnibZIi98KDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2vv02LJEyDApkY0jiEO2t3KvpI6crPjbeZx0QLP0aOo0YMUJPPfWUfvjDH+qf//ynTj31VOXk5CgvL0+SVFxcLLvdLtM0ZRiGnn766aC/XJ0kTZgwQRMmTAhKu6mpSfv37/d+XlhYqC1btmjIkCEaOXKkFi1apLKyMr300kuSpMcee0yjR4/WxIkT1dbWpr/85S/67LPP9MknnwRl/4EwcspI2dvswd5GyKpqrFJre6sykjIi+sKDBg0aNGjQoEGDBg0aNGjQoEGDRuQ2DBkyTVPN7c2yO+0RMwwKVGPy8MkqrCnUobpDGpsz1mctECz9GjpJ0vXXX68hQ4boZz/7mYqKilRRUaGKiooea0444QQ9/vjjuuiii/qbC3sbN27Uueee6/28+72XFixYoBdeeEEVFRUqKSnx3t/e3q5f/OIXKisrU0JCgqZMmaJPP/20xzkiTU1xjZR99HWDUae7U6X1pUq0Jkb8hQcNGjRo0KBBgwYNGjRo0KBBgwaNyG0YRtfQqbC6ULnpuREzDApkIzY6Vnsr9+qk7JN6PHMMCCbD/Pd3aztObrdbK1eu1Lp162S322UYhnJycjRr1iyde+65Pt+UEDhOp1MpKSlyOByy2WzB3s5RPfbUY4odG6vcIbnB3krIsTvs+rLwS0VbolXfUh/RFx40aNCgQYMGDRo0aNCgQYMGDRo0IrdxoOqA3t3yrhbOWaizTjorooZBgWo0tTWpvqVe/3vG/1aWLcvnOOBI/DU36PcznbpFRUVp7ty5mjt37kCdEoNUTFxMsLcQssobyuVsccqwGBF/4UGDBg0aNGjQoEGDBg0aNGjQoEEjchvVjdWSpFHpoyJuGBSoRlJckg7VHVJhTSFDJ4QMy9GXAIGVO5lnOPWmsa1RJXUlcrldQb8ooEGDBg0aNGjQoEGDBg0aNGjQoEGjP43Y6FhZDItPIxKGQYFs1LbU6quDX8nV4fI5HggGhk4IOQc3HAz2FkJSdWO1SutLNTx1eNAvCmjQoEGDBg0aNGjQoEGDBg0aNGjQ6E8jKzlL//7OL5E0DApUIzYqVo2urv9YHQgFDJ2AMNDp7lSBvUAZSRlKT0r3uT8SLzxo0KBBgwYNGjRo0KBBgwYNGjRoRH7DVNfgKdKGQYFqnDzsZCVYE7S3cq/PEA8IBoZO/8bpdKqkhKlwMKUNSwv2FkJOTXONGloaNHLISJ/7Iv3CgwYNGjRo0KBBgwYNGjRo0KBBg0bkNQzD8A5JInEYFMhGVnKWSmpLVNNU43M+INAG1dDp73//u6644goNHz5c8fHxGjZsmObOnatnn31WbrdbkvToo49q9OjRQd7p4BYbHxvsLYSc8vpyJcQmKDoqusftkXzhQYMGDRo0aNCgQYMGDRo0aNCgQSNyG4YMmTLldkfuMChQjeS4ZDW5mlRYXehzTiDQoo++JPw1NTXpuuuu07Jly3o8xdBut8tut2vlypV6/PHH9dprrwVxl+hWeaBSsWMZPHVramtSVWOVbPG2HrdH+oUHDRo0aNCgQYMGDRo0aNCgQYMGjchtGIYhSSqqLZIt3haRw6BANlITU7Xl0BZNzZ0qa4zV5/xAoFiOviT8XXvttXr//fc1Y8YMvfnmm7Lb7XK5XDp48KDeeustzZkzR1u3btW5556rPXv2BHu7QA+Vzkq1tLcoITbBe1uwLwpo0KBBgwYNGjRo0KBBgwYNGjRo0OhPw/SYcnvcau2I7GFQoBodnR3aWb5TJXUlPvcBgRTxQ6elS5fqgw8+0H/8x39o/fr1uuqqq5SVlaWYmBiNGjVKV155pVasWKGXXnpJDQ0NeuONN4K95UFvxKQRwd5CyOh0d+pQ/SElxCZ4/+uPULgooEGDBg0aNGjQoEGDBg0aNGjQoEGjP42qpipJ0uiM0RE9DApUo8JRoeS4ZBXYC3q82hcQaBE/dHr++eeVmZmpp59+WlFRUYdd94Mf/ECvv/46D8gQUF9eH+wthIyapho5Wh2yxXW9tF6oXBTQoEGDBg0aNGjQoEGDBg0aNGjQoNGfRoe7Q5IUHxPvc45IGgYFsjFx2ESV1JWourHaZx0QKBH/nk4bNmzQxRdfrISEhKOuvfTSS/Xwww9rx44dAdgZDqe5rlmxGbynkySVNZTJkKHoqOiQuiigQYMGDRo0aNCgQYMGDRo0aNCgQaM/jZyUHJ/jpcgcBgWyUVpfqoPVB5Vly/JZDwRCxA+damtrNWyY74P6cH7xi1/4cTc4FtGxEf/H8pg4W52qdFbKFm8LuYsCGjRo0KBBgwYNGjRo0KBBgwYNGjT602h2Ncv81/+6RfIwKFCNIYlDVGAv0NTcqYqP9X0WGeBvlqMvCW8pKSmqrj72pxO+9dZbuv/++/24IxzNqFNGBXsLIcHutKuto00WwxJyFwU0aNCgQYMGDRo0aNCgQYMGDRo0aPSnYRiGZErdM6dIHwYFqpGelK7ShlIV1xb7HAcEQsQPnaZNm6aPPvpIHR0dR127fv16XXvttbrvvvsCsDMczv4v9gd7C0HX3tmu0vpSRVuiQ/KigAYNGjRo0KBBgwYNGjRo0KBBgwaN/ja6n+UU7EFNJDVaO1pVVl+mLYe2yOPx+NwP+FvED52uvfZalZaW6q677jriujVr1ujyyy+X2+0O0M6Aw6turFZtU62crc6QvSigQYMGDRo0aNCgQYMGDRo0aNCgQeN4G4ZhyJSpqsaqoA9qIq2Rk5KjSmelKhwVPmsAf4v4odP8+fN12mmn6bHHHtOVV16pzZs3e+/zeDzasmWLbr75Zp1//vlqaWnRBRdcEMTdQpJSclKCvYWg8pgeldSWqLqxWvGx8SF5UUCDBg0aNGjQoEGDBg0aNGjQoEGDRn8ahgyZpqlKZ2VIDGoiqTFlxBR1ejq1v4pXlELgRfzQKSoqSu+9956mTZumpUuX6rTTTlNycrJGjBihuLg4zZgxQ3/5y1+UmZmpf/zjH8rPzw/2lge9+OTB/QZ39c312le1T2kJaSF7UUCDBg0aNGjQoEGDBg0aNGjQoEGDRn8ajlaHJCnLlhUSg5pIa2QkZWhf5T45W50+6wF/ivihkyTl5ORo/fr1euyxxzR58mS1tLSovLxcnZ2dysvL0913362dO3dq1qxZkiTTNIO848HNvs8e7C0EVVlDmdo62zQ6Y3TIXhTQoEGDBg0aNGjQoEGDBg0aNGjQoNGfRn1LvSQpIynD5/5IHgYFqpGakKr6lnoV1hT6HAP4U3SwNxAosbGx+vnPf66f//zncrlcqqurU2pqquLjez6r5oc//KHmzJkTnE1i0Gtpb9GBqgManc7AiQYNGjRo0KBBgwYNGjRo0KBBg0bkNrrP/+9PAIj0YVCgGhbDogRrgjYUbdDJQ09WTHSMz/GAPwyaodO3Wa1WDR06tNf78vLylJeXF+Ad4duGTxiuand1sLcRFJXOSrlNt2zxth63h9pFAQ0aNGjQoEGDBg0aNGjQoEGDBg0a/WnERP1rCPKtmVOwBzWR1mhoaVBtU61K6kp0YtaJPucA/MFy9CUYSGvWrNGll16qYcOGyTAMLV269KjHrFq1SqeccoqsVqvGjBmjF154we/7DCZnlTPYWwiKTnenSmpLlGRNkmEY3ttD8aKABg0aNGjQoEGDBg0aNGjQoEGDBo3+NLp//2X+a+oUKoOaSGp0uDuUmZypPfY9vKUMAoahU4A1Nzdr6tSpeuKJJ45pfWFhoS6++GKde+652rJli2677TbdeOON+sc//uHnnQZPY21jsLcQFFWNVapvrZct7ptnOYXqRQENGjRo0KBBgwYNGjRo0KBBgwYNGv1pGOoaOnlMT0gNaiKtMSpjlIpqilTprPQ5F+APg/Ll9YJp3rx5mjdv3jGvf/LJJzV69Gg98sgjkqQJEyZo7dq1evTRR3XhhRf2eozL5ZLL5fJ+7nQ6+7fpALNED75ZqGmaKq0vlUUWRUd1PSxD+aKABg0aNGjQoEGDBg0aNGjQoEGDBo3+NLqf6dTsag65QU2kNcrqy7Svap9yUnJ8zgkMtMH32/0ws379es2dO7fHbRdeeKHWr19/2GMWL16slJQU70dubq6/tzmgTjj1hGBvIeDqmutU1ViltIQ0SaF/UUCDBg0aNGjQoEGDBg0aNGjQoEGDRn8a3c90Kq4tDslBTSQ1MpIyVFBRIGer0+e8wEBj6BTi7Ha7srOze9yWnZ0tp9Op1tbWXo9ZtGiRHA6H9+PQoUOB2OqAOfDVgWBvIeDKG8rV6e6UNcYaFhcFNGjQoEGDBg0aNGjQoEGDBg0aNGj0p+Hq7Hqlptjo2JAc1ERSY0jiEB2sPqiD1Qd9zg0MNF5eLwJZrVZZrdZgb+O4mZ7B9aZ2TW1NKmsoky3OFjYXBTRo0KBBgwYNGjRo0KBBgwYNGjRo9KdR3lAuSRqRNiIkBzWR1KhwVMjR5tCmok2aMHSCrDHh+7tjhD7L0ZcgmHJyclRZ2fNN3iorK2Wz2RQfHx+kXfmXLdMW7C0EVIWjQi3tLYqPiQ+biwIaNGjQoEGDBg0aNGjQoEGDBg0aNPrT6D7WsBg97g+VQU2kNSYOm6j61noV1hT6rAEGEkOnEJefn68VK1b0uG358uXKz88P0o78Lynd95tjpHJ1uFRSV6KEmASVO8rD5qKABg0aNGjQoEGDBg0aNGjQoEGDBo3+NIalDPOet1uoDWoiqZE7JFdxMXHaVb5Lbo/bZy0wUBg6BVhTU5O2bNmiLVu2SJIKCwu1ZcsWlZSUSOp6P6b58+d71//kJz/RwYMH9ctf/lJ79uzRn//8Z73xxhu6/fbbg7H9gCjfUx7sLQSM3WlXQ0uDGl2NYXVRQIMGDRo0aNCgQYMGDRo0aNCgQYNGfxpRUVHec0uhOaiJtEaOLUcl9SU6VHfIZz0wUBg6BdjGjRs1ffp0TZ8+XZJ0xx13aPr06brnnnskSRUVFd4BlCSNHj1aH3zwgZYvX66pU6fqkUce0V/+8hddeOGFQdk/Bk6nu1NFNUVytDrU4e4Iq4sCGjRo0KBBgwYNGjRo0KBBgwYNGjT60zDU9bJ6psyQHtREUsMaY5VMaWfZTpmm6XMcMBCig72BwWbOnDlHfEC/8MILvR7z9ddf+3FXoWXouKGqNWuDvQ2/q2qs0sGag4qJigm7iwIaNGjQoEGDBg0aNGjQoEGDBg0aNPrTMIyuoVOnpzOkBzWR1kiKS9L6g+s1PW96r/cD/WU5+hIgsJrrm4O9Bb9ze9zaV7VPre2tykvPC7uLAho0aNCgQYMGDRo0aNCgQYMGDRo0+tuQpNL60pAf1ERSo7S+VM42p3ZX7Pa5HxgIDJ0QcpxVzmBvwe9qmmp0sOqgxuWMC9uLAho0aNCgQYMGDRo0aNCgQYMGDRo0jrfR/WpQrg5XyA9qIq0xI2+G9lbuVXVjtc86oL8YOiHkdD+1NlJ5TI/2V+5XclyykuOSfe4Ph4sCGjRo0KBBgwYNGjRo0KBBgwYNGjT60yhvKJckDU0ZGhaDmkhqDEkcoiZXk/bY9/isBfqLoRNCzomnnxjsLfhVbVOtqhqrlJ2S7XNfuFwU0KBBgwYNGjRo0KBBgwYNGjRo0KDRn0a7u12SFBsd63OOUBzURFojKzlLu8t3q7653ucYoD8YOiHkFG4sDPYW/MY0TRXXFstiscgabe1xXzhdFNCgQYMGDRo0aNCgQYMGDRo0aNCg0d+GJJkye6wJ5UFNJDXSEtLU0NqgXeW7fI4D+oOhE0KOu9Md7C34TV1znexOu9IS0nxuD7eLAho0aNCgQYMGDRo0aNCgQYMGDRo0+tMwZOjbM6dQH9REUsNjetTQ2qC1+9bK0eLwOR44XgydEHKS0n2/iUaC7mc5dbo7e/zgDteLAho0aNCgQYMGDRo0aNCgQYMGDRo0+tMwDEMeeSSFx6Am0hoxlhi53C7e2wkDiqETQk5Kdkqwt+AXdc11qnBUKC0xrcdt4XpRQIMGDRo0aNCgQYMGDRo0aNCgQYNGfxsejyesBjWR1Bg/dLxyh+Rqe9l2nu2EAcPQCSGnbFdZsLcw4Lqf5dTh7lB8TLykyLgooEGDBg0aNGjQoEGDBg0aNGjQoEHjeBuGYaiuuS6sBjWR1khPTFddc512V+z2OR9wPBg6AQFQ21yrsoYy7w/nSLgooEGDBg0aNGjQoEGDBg0aNGjQoEGjP43uTrgNaiKpYRiGspKztKNsh+qb633OC/QVQyeEnJyTcoK9hQHlMT0qqi6Sx/QoLiYuYi4KaNCgQYMGDRo0aNCgQYMGDRo0aNDoT0OmlJqQGnaDmkhrDEkcov3V+7W9bLvPuYG+YuiEkNPW2BbsLQyo6sZqlTvKNSRxSERdFNCgQYMGDRo0aNCgQYMGDRo0aNCg0Z+GYRhKifN9f/dwGNREUqPCUSFXh0sbizaqprHG536gLxg6IeQ02BuCvYUB4/a4dbDmoCSp2dUcURcFNGjQoEGDBg0aNGjQoEGDBg0aNGj0p2ExLPLI0+P+cBnURFpj/NDx8pgebS/dLtM0fdYBx4qhE+BHdoddlc5KGYYRcRcFNGjQoEGDBg0aNGjQoEGDBg0aNGj0p2EYRo8BR7gNaiKtMTRlqHbZd6nCUeGzFjhWDJ0Qck48/cRgb2FAdLg7dLDmoFpcLXK0OiLuooAGDRo0aNCgQYMGDRo0aNCgQYMGjf42PGbXM53CdVATSQ1bvE2uDpe2lGyRx+PxOQY4FgydEHKKtxQHewsDorS+VEU1Rep0d0bsRQENGjRo0KBBgwYNGjRo0KBBgwYNGsfb6H6mUzgPaiKtMTxtuHaU71BRbZHPccCxYOiEkNPp6gz2Fvqtpb1Fuyt2q7m9WVm2rIi8KKBBgwYNGjRo0KBBgwYNGjRo0KBBoz8NQ4baOtrCflATSQ2P6VFhTaHW7lur9s52n/uBo2HohJCTmJYY7C3028HqgzpQdUB5Q/Ii9qKABg0aNGjQoEGDBg0aNGjQoEGDBo3+NEyZsjvtYT+oibTGiLQRsjvt2mPf47MGOBqGTgg5Q0b4/gAKJ3XNddpaulXD04YrPSnd5/5IuSigQYMGDRo0aNCgQYMGDRo0aNCgQaM/DdM0FWOJiYhBTSQ1Jg6bqLSENG0q2iRnq9NnLXAkDJ2C5IknntCoUaMUFxen008/XV999dVh177wwgsyDKPHR1yc7zfySHFo+6Fgb+G4uT1u7SrfJbfHrRFpI3zuj6SLAho0aNCgQYMGDRo0aNCgQYMGDRo0+tMwDEOZSZkRMaiJtEaWLUs1TTX6uuRrmabpcwxwOAydguD111/XHXfcod/+9rfavHmzpk6dqgsvvFBVVVWHPcZms6miosL7UVxcHMAd41iVN5SruLZYJ2ae6HNfpF0U0KBBgwYNGjRo0KBBgwYNGjRo0KDRn0aUJUoyet4fzoOaSGpYDIuGpQ7T1kNbdagufJ8kgMBj6BQE//M//6ObbrpJN9xwg04++WQ9+eSTSkhI0HPPPXfYYwzDUE5OjvcjOzs7gDsOrKwTs4K9hePS0t6inWU7lZ6UrpiomB73ReJFAQ0aNGjQoEGDBg0aNGjQoEGDBg0a/WkYMuSRx3t/uA9qIq2RaE3UwZqDWrN3jdo7232OB3rD0CnA2tvbtWnTJs2dO9d7m8Vi0dy5c7V+/frDHtfU1KS8vDzl5ubqsssu086dOw+71uVyyel09vgIJx1tHcHeQp+Zpql9lfvU0tGitIS0HvdF6kUBDRo0aNCgQYMGDRo0aNCgQYMGDRr9aRiGIY/ZNXSKlEFNpDWSrEkqqi3S9tLtPucAesPQKcBqamrkdrt9nqmUnZ0tu93e6zHjxo3Tc889p/fee08vv/yyPB6PZs2apdLS0l7XL168WCkpKd6P3NzcAf86/Km+rD7YW+izSmelSupKlJ6YLsP45jnBkXxRQIMGDRo0aNCgQYMGDRo0aNCgQYNGfxqGDJmmGXGDmkhqTBw+UcNSh2lT8SZVOit9zgX8O4ZOYSA/P1/z58/XtGnTNHv2bL3zzjvKzMzUU0891ev6RYsWyeFweD8OHeI1N/2praNNBZUFMgxD8bHxPW6P5IsCGjRo0KBBgwYNGjRo0KBBgwYNGjT63XB7Im5QE2mNzORMNboa9dXBr9TRGX6vUoXAYugUYBkZGYqKilJlZc+pcGVlpXJyco7pHDExMZo+fbr279/f6/1Wq1U2m63HRzg54dQTgr2FY2aapvZX7ff+YO0WEj+wadCgQYMGDRo0aNCgQYMGDRo0aNAI4YZhGKpuro7IQU2kNfLS81RQWaAd5Tt8zgt8G0OnAIuNjdWMGTO0YsUK720ej0crVqxQfn7+MZ3D7XZr+/btGjp0qL+2GVSlO3t/2cBQVOGoUGFNoTISM2Qxuh5OofADmwYNGjRo0KBBgwYNGjRo0KBBgwaNUG+4PW61u9sjdlATSQ1rtFUd7g69v/V9VTRU+Jwf6MbQKQjuuOMOPfPMM3rxxRe1e/du/fSnP1Vzc7NuuOEGSdL8+fO1aNEi7/r7779fn3zyiQ4ePKjNmzfrBz/4gYqLi3XjjTcG60vwq/bW9mBv4Zg0uZq0x75HUUaU92X1QuUHNg0aNGjQoEGDBg0aNGjQoEGDBg0aod6QpPSE9Igd1ERao6W9Ra5Ol9YdWKe2jjafNYAkRQd7A4PR97//fVVXV+uee+6R3W7XtGnT9PHHHys7O1uSVFJS0uMbcX19vW666SbZ7XalpaVpxowZWrdunU4++eRgfQl+FW+Ll1vuYG/jiDrdndpj36OGlgYNTx0uKbR+YNOgQYMGDRo0aNCgQYMGDRo0aNCgEeqNaEu0oi2+v6KOpEFNpDWykrO0r2qfvir8SmefdLYMw/BZj8HNME3TDPYm4F9Op1MpKSlyOBxh8f5O73zxjuytduUOyQ32Vg5rb+Ve7SzbqczkTMVGx4bcD2waNGjQoEGDBg0aNGjQoEGDBg0aNEK98dznz+k7476j+bPme9dE4qAm0hqNbY2qaqzSRRMv0vih432OQXjw19zAcvQlQGCVbC0J9haOyO6wa1/lPqXEpzBwokGDBg0aNGjQoEGDBg0aNGjQoEHjOBuGDJn65jkRkTyoiaRGclyy4mPitbJgpSqdlT7HYXBj6AT0gbPVqZ3lO2XIUFJcUsj+wKZBgwYNGjRo0KBBgwYNGjRo0KBBIxwa3S/EFemDmkhrJMcla0vJFn204yM1tTX53I/Bi6ETQk7mqMxgb6FXbR1t2l62XY1tjUpPSg/5H9g0aNCgQYMGDRo0aNCgQYMGDRo0aIRywzC6nukUCkMUGn1r7K3cq7yMPFU6KvXPff9Ue2e7zzoMTr7v0gYEmcftCfYWfHS4O7SzfKcqnZUamjJUrk5XSP/ApkGDBg0aNGjQoEGDBg0aNGjQoEEj1BuGDDlbnSExRKFxfI1Od6d2lO1QojVRZ405y+fPAAYf/gQg5NQeqg32Fnpwe9zaU7FHxbXFyrZlq8PdEfI/sGnQoEGDBg0aNGjQoEGDBg0aNGjQCPWGx/Sosa0xpIYoNPrWsMZYNTxtuDYWbdTmks3el0vE4MUznYAj8JgeFdgLtL96vzKSMuT2uMPiBzYNGjRo0KBBgwYNGjRo0KBBgwYNGqHe6PR0KjE2MaSGKDT63kiOS5ar06WlXy9VbHSspoyY4nM8Bg/L0ZcAgTXqlFHB3oKkroHTvsp92lu5V2kJaZIUNj+wadCgQYMGDRo0aNCgQYMGDRo0aNAI9UZMVIwS4xJ97g/2EIVG3xtVjVVqbm/Wp7s+1c6ynT7nwODB0Akhp6KgIthb8A6cdtt3KyU+RRbDElY/sGnQoEGDBg0aNGjQoEGDBg0aNGjQCPVGtCXa5+XYQmWIQqPvjZmjZ8oWb9PKgpXaUbbD51wYHBg6IeS4ml1B7Xe/h9Ouil1KiUtRlCUq7H5g06BBgwYNGjRo0KBBgwYNGjRo0KAR6g3DMOQxPd77Q22IQqPvjWxbtuJj4vXZ7s+0pWQL7/E0CDF0QsiJS/L9gRQo7Z3t2lG2QwWVBUpLSGPgRIMGDRo0aNCgQYMGDRo0aNCgQYOGnxqGDO/9oTpEodH3RpYtS8nxyfr7lr9r/YH16nR3+pwfkYuhE0JOzkk5Qek2u5q15dAWHag+oIzEDF5SjwYNGjRo0KBBgwYNGjRo0KBBgwYNPzYMw5BpmiE/RKHR90Z7Z7saWhv00faPtKpglVrbW33WIDJFB3sDwL8r+rpIsWNjA9qsbqzWzvKdqmuuU44tR52ezrD+gU2DBg0aNGjQoEGDBg0aNGjQoEGDRjg0XJ2usBii0Oh7Y1zOOKUmpOrrQ1/L2erU2WPPVmZyps96RBaGThjU3B63imqKVFBZILfHreGpw+XqdEXED2waNGjQoEGDBg0aNGjQoEGDBg0aNEK5YZqmGloaFB8THkMUGsfXODHzRBXVFKlhS4Pyx+RrXPY4nz9PiBz8k0XISR+ZHpCOo9WhzcWbta1sm2KjYpVty2bgRIMGDRo0aNCgQYMGDRo0aNCgQYNGgBrt7nZFWaI0NntsWA1RaPStERMVozFZY+Roc+jZfz6r5buXy9nq9DkekYFnOiHkGIZx9EX90OHuUEltifZX7VdLe4uybFmKiYqJqB/YNGjQoEGDBg0aNGjQoEGDBg0aNGiEeiPKEiVbnE0Wo2cj1IcoNPreaG5vlqPVoeT4ZG0p2SK7w67TRp2msdljFR3FmCKS8E8TIaemuMYv7+nk9rhV6azUgeoDqm6sVnJcsoanDZcUeT+wadCgQYMGDRo0aNCgQYMGDRo0aNAI9YY12urzH6CHyxCFxvE3DMOQ3WHXxzs+1t7KvTpl5CnKHZLr9ycjIDAYOiHiuT1uVTdW60DVAdU01Sg6KlpDU4Z6v4FG4g9sGjRo0KBBgwYNGjRo0KBBgwYNGjRCvWEYhsx//U8K3yEKjb43hqUOk6vTpYPVB7WpeJNOzTtVp+Sd0uufPYQXhk4IOSOnjpS91d7v87g6XKpsrNS+yn2qclYpyZqkjOQMxUTFeNdE6g9sGjRo0KBBgwYNGjRo0KBBgwYNGjRCvWHIkGkycBqsjWhLtDo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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ - "AnalogDevice.supported_bases" + "pi_pulse = pulser.Pulse.ConstantPulse(1000, np.pi, 0, 0)\n", + "sequence.add(pi_pulse, \"ch_0\")\n", + "sequence.draw()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We've now obtained the final sequence!" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "seq.draw()" + "### Executing the Pulse Sequence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## 6. Submit the `Sequence` to a `Backend`\n", - "\n", - "We have tailored the `Pulse` such that the atoms all go from the ground state (measurement outcome: 0) to the excited state (measurement outcome: 1) (see the [Measurement section in the \"Conventions\" page](https://pulser.readthedocs.io/en/stable/conventions.html#state-preparation-and-measurement)). But is it really happening ? The `Sequence` can be simulated using a [`Backend`](https://pulser.readthedocs.io/en/stable/apidoc/backend.html), a common interface for execution of Sequences using the QPU or emulators. More details about the backends are provided in [its Fundamental section](https://pulser.readthedocs.io/en/stable/tutorials/backends.html).\n", - "\n", - "Prior to submitting the `Sequence` to the QPU, it is of good practice (if the number of atoms is not too big) to use an emulator to simulate the outcome of the Sequence. A list of all the available emulators is given [in the API](https://pulser.readthedocs.io/en/stable/apidoc/backend.html). Let's start with emulating the `Sequence` locally.\n", - "\n", - "Pulser comes with `pulser-simulation`, a package to simulate pulser `Sequence` using the python library [**QuTip**](https://qutip.org/). It implements the `QutipBackend` class. The `Backend` is initialized with a `Sequence`, and the simulation in itself is performed when calling the method `run`.\n", - "\n", - "The outcome of the `QutipBackend` for this kind of simulation is a `CoherentResult`. It stores the state of each atom in the Register at each simulation time. The state of the system at the end of the simulation can be obtained with the method `get_final_state`:\n" + "We are now done with our first Pulser program ! We can now submit it to a backend for execution. Pulser provides multiple backends, notably the QPUs, but also a backend to simulate small quantum systems on your laptop based on **Qutip**. Let's use this `QutipBackend` to simulate the final state of the system: " ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ - "sim = pulser_simulation.QutipBackend(seq)\n", - "res = sim.run()\n", - "res.get_final_state()" + "backend = pulser.backends.QutipBackend(sequence)\n", + "result = backend.run()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "The final state is the rydberg state, defined by $\\left|r\\right> = (1, 0)$ (see the [conventions page](https://pulser.readthedocs.io/en/stable/conventions.html) for details).\n", - "\n", - "On a QPU, this state cannot be accessed. We can only estimate the probability to measure the system in the ground state (measurement 0) and the excited state (measurement 1) by making multiple measurements. We can model the measurement by the QPU with the method `sample_final_state`:" + "The result object stores the state of the atom at each nanosecond. Let's measure the probability that the final state is in the excited state:" ] }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "res.sample_final_state(N_samples=1000)" - ] - }, - { - "cell_type": "markdown", + "execution_count": 24, "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability to measure the atom in the rydberg state: 0.9999997649778671\n" + ] + } + ], "source": [ - "In all the measurement outcomes, all the atoms are measured in the '1' state. This means they are all always measured in the excited state: the `Sequence` works as intended !" + "r_state = np.array([1, 0])\n", + "print(\n", + " \"Probability to measure the atom in the rydberg state:\",\n", + " np.abs(np.dot(result.get_final_state().full().T, r_state))[0] ** 2,\n", + ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "## Follow up" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "- Check a detailed description of all the components of the `Sequence` introduced here in the [Fundamentals section](https://pulser.readthedocs.io/en/stable/apidoc/pulser.html) !\n", - "\n", - "- In this `Sequence`, we only worked with 1 atom in the Register. Begin our tutorials with the same sequence of Pulses, applied on a Register of 2 atoms placed far appart !\n", - "\n", - "- To further study the influence of an amplitude Pulse on the state of the atoms, you can have a look at our tutorial where we excite the state of the atoms in a superposition state and perform a Rabi experiment." + "The probability to measure the atom in the rydberg state is very close to 1, which means we designed our quantum program correctly !" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3 (ipykernel)", + "display_name": "pulserenv", "language": "python", "name": "python3" }, @@ -392,7 +319,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.12" + "version": "3.12.3" } }, "nbformat": 4,