From 5abc5d65acfb9910226fe3084d1630585f7ffb93 Mon Sep 17 00:00:00 2001 From: Edoardo-Pedicillo Date: Fri, 13 Sep 2024 12:41:23 +0400 Subject: [PATCH 1/7] docs: write readout mitigation matrix docs --- doc/source/protocols/index.rst | 1 + .../protocols/readout_mitigation_matrix.png | Bin 0 -> 18604 bytes .../protocols/readout_mitigation_matrix.rst | 36 ++++++++++++++++++ 3 files changed, 37 insertions(+) create mode 100644 doc/source/protocols/readout_mitigation_matrix.png create mode 100644 doc/source/protocols/readout_mitigation_matrix.rst diff --git a/doc/source/protocols/index.rst b/doc/source/protocols/index.rst index 0a6ff4487..e271fec79 100644 --- a/doc/source/protocols/index.rst +++ b/doc/source/protocols/index.rst @@ -27,4 +27,5 @@ In this section we introduce the basics of all protocols supported by ``qibocal` dispersive_shift allxy flipping + readout_mitigation_matrix references diff --git a/doc/source/protocols/readout_mitigation_matrix.png 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qubit readout errors +by applying a corrective linear transformation to the readout results, in formula + +.. math:: + O_{noisy} = M O_{ideal}, + +where :math:`O_{noisy}` is the readout probabilities on the noisy device, +:math:`O_{ideal}` is the expected one and :math:`M` is the readout mitigation matrix. +The matrix :math:`M^{-1}` can be used to correct the noisy readouts. + +This protocol evaluates the readout matrix by preparing the qubit(s) in the +computational base and measuring their states. + +Pramateters +^^^^^^^^^^^ + +.. autoclass:: qibocal.protocols.readout_mitigation_matrix.ReadoutMitigationMatrixParameters + :noindex: + +Example +^^^^^^^ + +.. code-block:: yaml + + - id: readout_mitigation_matrix + operation: readout_mitigation_matrix + parameters: + nshots: 1000 + pulses: true + +After the protocol execution, the result is the following + +.. image:: readout_mitigation_matrix.png From c8465e92fa6e9a4dec0fd6c8534a35883543e19a Mon Sep 17 00:00:00 2001 From: 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.../protocols/readout_mitigation_matrix.rst | 6 ++-- 2 files changed, 18 insertions(+), 18 deletions(-) diff --git a/doc/source/protocols/avoided_crossing.rst b/doc/source/protocols/avoided_crossing.rst index 782fce1b4..5ee12050d 100644 --- a/doc/source/protocols/avoided_crossing.rst +++ b/doc/source/protocols/avoided_crossing.rst @@ -1,31 +1,31 @@ Avoided crossing ================ -In the avoided crossing experiment the goal is to study the qubit-flux dependency +In the avoided crossing experiment the goal is to study the qubit-flux dependency of a couple of qubits to precisely tune the interaction between them at specific -frequencies in order to calibrate the CZ and the iSWAP gates. +frequencies in order to calibrate the CZ and the iSWAP gates. -In the avoided crossing experiment for CZ qubit gates, the interaction between +In the avoided crossing experiment for CZ qubit gates, the interaction between two qubits is controlled by tuning their energy levels such that the :math:`\ket{11}` -(both qubits in the excited state) and :math:`\ket{02}` (one qubit in the ground state and -the other in the second excited state) states come into resonance. -At this resonance point, the energy levels of these states experience an avoided -crossing, a key phenomenon that enables the controlled-Z (CZ) gate operation. -By observing the avoided crossing, one can confirm that the coupling between the -qubits is strong enough to facilitate the necessary interaction for the CZ gate. -Hence, precise tuning of these states is essential for achieving the correct gate +(both qubits in the excited state) and :math:`\ket{02}` (one qubit in the ground state and +the other in the second excited state) states come into resonance. +At this resonance point, the energy levels of these states experience an avoided +crossing, a key phenomenon that enables the controlled-Z (CZ) gate operation. +By observing the avoided crossing, one can confirm that the coupling between the +qubits is strong enough to facilitate the necessary interaction for the CZ gate. +Hence, precise tuning of these states is essential for achieving the correct gate operation. -In the avoided crossing experiment for iSWAP qubit gates, the key focus is on +In the avoided crossing experiment for iSWAP qubit gates, the key focus is on the interaction between the :math:`\ket{10}` and :math:`\ket{01}` states. When tuning the qubits' energy levels, these two states come into resonance, -creating an avoided crossing, which is the fundamental operation of -the iSWAP gate. +creating an avoided crossing, which is the fundamental operation of +the iSWAP gate. In this protocol, for each qubit pair we execute a qubit flux dependency of the -01 and 02 transitions on the qubit with higher frequency and we fit the data to +01 and 02 transitions on the qubit with higher frequency and we fit the data to find the flux-frequency relationship that we use to estimate the bias needed to -reach the CZ and iSWAP interaction points. +reach the CZ and iSWAP interaction points. Parameters ^^^^^^^^^^ diff --git a/doc/source/protocols/readout_mitigation_matrix.rst b/doc/source/protocols/readout_mitigation_matrix.rst index d162e650d..b3e52b6e5 100644 --- a/doc/source/protocols/readout_mitigation_matrix.rst +++ b/doc/source/protocols/readout_mitigation_matrix.rst @@ -7,11 +7,11 @@ by applying a corrective linear transformation to the readout results, in formul .. math:: O_{noisy} = M O_{ideal}, -where :math:`O_{noisy}` is the readout probabilities on the noisy device, +where :math:`O_{noisy}` is the readout probabilities on the noisy device, :math:`O_{ideal}` is the expected one and :math:`M` is the readout mitigation matrix. The matrix :math:`M^{-1}` can be used to correct the noisy readouts. -This protocol evaluates the readout matrix by preparing the qubit(s) in the +This protocol evaluates the readout matrix by preparing the qubit(s) in the computational base and measuring their states. Pramateters @@ -24,7 +24,7 @@ Example ^^^^^^^ .. code-block:: yaml - + - id: readout_mitigation_matrix operation: readout_mitigation_matrix parameters: From b6bfeb7e39c24ccd616aa6705ad8944946e905c6 Mon Sep 17 00:00:00 2001 From: Edoardo-Pedicillo Date: Fri, 13 Sep 2024 18:18:00 +0400 Subject: [PATCH 4/7] docs: write readout optimization docs --- doc/source/protocols/index.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/doc/source/protocols/index.rst b/doc/source/protocols/index.rst index 7faa343cb..a2e142455 100644 --- a/doc/source/protocols/index.rst +++ b/doc/source/protocols/index.rst @@ -29,4 +29,5 @@ In this section we introduce the basics of all protocols supported by ``qibocal` flipping readout_mitigation_matrix avoided_crossing + readout_optimization references From 7985fb1c3dc14ebc7b7e2dea9f9eed6242a9bd68 Mon Sep 17 00:00:00 2001 From: Edoardo-Pedicillo Date: Thu, 26 Sep 2024 14:17:52 +0400 Subject: [PATCH 5/7] docs: improve the readout optimization docs --- 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zKr0U)c)AD62;)485c5e3G7WV}3Lb6wFu_>5Au zFjSm!&1`BZqvpE^+G@K8jf@Pu*T?Rmb82U zd%|wEhzVDDd?3-U7aA`OO+^e{c{r{7&>ym^J4MeGZ-^0a!Cf15UxV7kP{2EoIqGo$la5 wUk^+0%!Pj+|MZKzhv@6^|KtB@JIJ87OX5{=)Gqnclh$3ZvbQ9jx&H9q0MQheC;$Ke literal 0 HcmV?d00001 diff --git a/doc/source/protocols/readout_optimization.rst b/doc/source/protocols/readout_optimization.rst new file mode 100644 index 000000000..e9a1574d3 --- /dev/null +++ b/doc/source/protocols/readout_optimization.rst @@ -0,0 +1,32 @@ +Readout optimization +==================== + +Qibocal provides a protocol to improve the readout pulse amplitude by optimize +the assignment fidelity. + +Parameters +^^^^^^^^^^ + +.. autoclass:: qibocal.protocols.readout_optimization.resonator_amplitude.ResonatorAmplitudeParameters + :noindex: + + +Example +^^^^^^^ + +It follows an example runcard of the resonator amplitude routine with the plot +generated in the report. + +.. code-block:: yaml + + - id: resonator_amplitude + operation: resonator_amplitude + parameters: + amplitude_step: 0.0005 + amplitude_start: 0.001 + amplitude_stop: 0.005 + +As shown in the picture below, the protocol sweeps the readout amplitude and evaluates +the probability errors + +.. image:: readout_amplitude.png From b819c69b5a00108a2b03aa7cf1f90a375a0566df Mon Sep 17 00:00:00 2001 From: Edoardo-Pedicillo Date: Fri, 27 Sep 2024 19:41:58 +0400 Subject: [PATCH 6/7] docs: write standard rb docs --- doc/source/protocols/index.rst | 1 + doc/source/protocols/standard_rb.png | Bin 0 -> 40689 bytes doc/source/protocols/standard_rb.rst | 85 +++++++++++++++++++++++++++ doc/source/refs.bib | 40 +++++++++++++ 4 files changed, 126 insertions(+) create mode 100644 doc/source/protocols/standard_rb.png create mode 100644 doc/source/protocols/standard_rb.rst diff --git a/doc/source/protocols/index.rst b/doc/source/protocols/index.rst index a2e142455..95f421137 100644 --- a/doc/source/protocols/index.rst +++ b/doc/source/protocols/index.rst @@ -30,4 +30,5 @@ In this section we introduce the 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to the +maximally mixed state. +Such uniform space of unitaries is known as *Haar measure*. +It can be shown :cite:p:`Emerson_2005` that the average induced error is proportional +to the depolarization probability. +However, this approach is inefficient because we sample randomly from the Haar measure. +A simplification was proposed in :cite:p:`Knill2008` by restricting the unitaries +to the Clifford group, which consists of unitary rotations mapping the group +of Pauli operators in itself. +Among the advantages of such group are the fact of the number of Clifford +gates is finite given the Hilbert space and being a group we can easily found +the inverse within the group. +The generic procedure to perform a randomized benchmarking is the following: + +1. initialize the system in ground state +2. for each sequence length :math:`m` draw sequence of Clifford group elements +3. calculate inverse gate +4. measure sequence and inverse gate +5. repeat the process for multiple sequence of same length and varying the length + +The previous approach works because it has been shown :cite:p:`Nielsen_2002` that +randomization with Clifford gates provides again a depolarized noise channel + +.. math:: + :name: eq:1 + + \rho \rightarrow \frac{d}{2} I + ( 1 - d) \rho + +with depolarization probability :math:`d`. +If we follow the previous procedure and we measure the survival probability, i.e. +the probability of measuring the qubit in :math:`\ket{0}`, for +different sequence length :math:`m` we expect the following behavior + +.. math:: + :name: eq:2 + + F(m) = A p^m + B + +where :math:`1-p` is the rate of depolarization while :math:`A` and :math:`B` +capture state preparation and measurement errors. +Finally, we can extract the average error per Clifford as + +.. math:: + :name: eq:3 + + \epsilon_\text{Clifford} = \frac{1 - p}{1 - 2^{-n}} + +where :math:`n` is the number of qubits. The error per gate can be derived by dividing +the Clifford error by the physical gates per Clifford which usually is 1.875. +One of the main feature of RB is the possibility to estimate the gate fidelity +alone without taking into account both state preparation and measurement errors +which can be computed using the :math:`A` and :math:`B` terms in :ref:`Eq. 2 `. + +Parameters +^^^^^^^^^^ + + +.. autoclass:: + qibocal.protocols.randomized_benchmarking.standard_rb.StandardRBParameters + :noindex: + + +Example +^^^^^^^ + +It follows a runcard where we execute a standard RB. + +.. code-block:: yaml + + - id: standard rb + operation: standard_rb + parameters: + depths: [1,5,10,20,50,100] + niter: 20 + nshots: 100 + +The expected output is the following: + +.. image:: standard_rb.png diff --git a/doc/source/refs.bib b/doc/source/refs.bib index 7ef481d3d..b971ff08d 100644 --- a/doc/source/refs.bib +++ b/doc/source/refs.bib @@ -150,3 +150,43 @@ @misc{pedicillo2023 archivePrefix={arXiv}, primaryClass={id='quant-ph' full_name='Quantum Physics' is_active=True alt_name=None in_archive='quant-ph' is_general=False description=None} } + +@article{Knill2008, + title={Randomized benchmarking of quantum gates}, + volume={77}, + ISSN={1094-1622}, + url={http://dx.doi.org/10.1103/PhysRevA.77.012307}, + DOI={10.1103/physreva.77.012307}, + number={1}, + journal={Physical Review A}, + publisher={American Physical Society (APS)}, + author={Knill, E. and Leibfried, D. and Reichle, R. and Britton, J. and Blakestad, R. B. and Jost, J. D. and Langer, C. and Ozeri, R. and Seidelin, S. and Wineland, D. J.}, + year={2008}, + month={jan}, +} + +@article{Emerson_2005, + title={Scalable noise estimation with random unitary operators}, + volume={7}, + ISSN={1741-3575}, + url={http://dx.doi.org/10.1088/1464-4266/7/10/021}, + DOI={10.1088/1464-4266/7/10/021}, + number={10}, + journal={Journal of Optics B: Quantum and Semiclassical Optics}, + publisher={IOP Publishing}, + author={Emerson, Joseph and Alicki, Robert and Życzkowski, Karol}, + year={2005}, + month=sep, pages={S347–S352} } + +@article{Nielsen_2002, + title={A simple formula for the average gate fidelity of a quantum dynamical operation}, + volume={303}, + ISSN={0375-9601}, + url={http://dx.doi.org/10.1016/S0375-9601(02)01272-0}, + DOI={10.1016/s0375-9601(02)01272-0}, + number={4}, + journal={Physics Letters A}, + publisher={Elsevier BV}, + author={Nielsen, Michael A}, + year={2002}, + month=oct, pages={249–252} } From 22eddc589075226ab79b1f708e7dcabffd098479 Mon Sep 17 00:00:00 2001 From: "pre-commit-ci[bot]" <66853113+pre-commit-ci[bot]@users.noreply.github.com> Date: Fri, 27 Sep 2024 15:43:07 +0000 Subject: [PATCH 7/7] [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci --- doc/source/protocols/readout_optimization.rst | 4 ++-- doc/source/protocols/standard_rb.rst | 24 +++++++++---------- 2 files changed, 14 insertions(+), 14 deletions(-) diff --git a/doc/source/protocols/readout_optimization.rst b/doc/source/protocols/readout_optimization.rst index e9a1574d3..db388e3dc 100644 --- a/doc/source/protocols/readout_optimization.rst +++ b/doc/source/protocols/readout_optimization.rst @@ -1,8 +1,8 @@ Readout optimization ==================== -Qibocal provides a protocol to improve the readout pulse amplitude by optimize -the assignment fidelity. +Qibocal provides a protocol to improve the readout pulse amplitude by optimize +the assignment fidelity. Parameters ^^^^^^^^^^ diff --git a/doc/source/protocols/standard_rb.rst b/doc/source/protocols/standard_rb.rst index 534c7a6e0..c6bbf3343 100644 --- a/doc/source/protocols/standard_rb.rst +++ b/doc/source/protocols/standard_rb.rst @@ -1,20 +1,20 @@ Standard Randomize Benchmarking =============================== -An approach to obtain the average gate fidelity is to perform randomized +An approach to obtain the average gate fidelity is to perform randomized benchmarking :cite:p:`Emerson_2005`. -The key idea is that if we average the error process over the uniform space of -unitaries the result is a depolarizing channel that maps any pure state to the -maximally mixed state. +The key idea is that if we average the error process over the uniform space of +unitaries the result is a depolarizing channel that maps any pure state to the +maximally mixed state. Such uniform space of unitaries is known as *Haar measure*. It can be shown :cite:p:`Emerson_2005` that the average induced error is proportional to the depolarization probability. However, this approach is inefficient because we sample randomly from the Haar measure. -A simplification was proposed in :cite:p:`Knill2008` by restricting the unitaries -to the Clifford group, which consists of unitary rotations mapping the group +A simplification was proposed in :cite:p:`Knill2008` by restricting the unitaries +to the Clifford group, which consists of unitary rotations mapping the group of Pauli operators in itself. -Among the advantages of such group are the fact of the number of Clifford -gates is finite given the Hilbert space and being a group we can easily found +Among the advantages of such group are the fact of the number of Clifford +gates is finite given the Hilbert space and being a group we can easily found the inverse within the group. The generic procedure to perform a randomized benchmarking is the following: @@ -24,7 +24,7 @@ The generic procedure to perform a randomized benchmarking is the following: 4. measure sequence and inverse gate 5. repeat the process for multiple sequence of same length and varying the length -The previous approach works because it has been shown :cite:p:`Nielsen_2002` that +The previous approach works because it has been shown :cite:p:`Nielsen_2002` that randomization with Clifford gates provides again a depolarized noise channel .. math:: @@ -33,7 +33,7 @@ randomization with Clifford gates provides again a depolarized noise channel \rho \rightarrow \frac{d}{2} I + ( 1 - d) \rho with depolarization probability :math:`d`. -If we follow the previous procedure and we measure the survival probability, i.e. +If we follow the previous procedure and we measure the survival probability, i.e. the probability of measuring the qubit in :math:`\ket{0}`, for different sequence length :math:`m` we expect the following behavior @@ -42,7 +42,7 @@ different sequence length :math:`m` we expect the following behavior F(m) = A p^m + B -where :math:`1-p` is the rate of depolarization while :math:`A` and :math:`B` +where :math:`1-p` is the rate of depolarization while :math:`A` and :math:`B` capture state preparation and measurement errors. Finally, we can extract the average error per Clifford as @@ -53,7 +53,7 @@ Finally, we can extract the average error per Clifford as where :math:`n` is the number of qubits. The error per gate can be derived by dividing the Clifford error by the physical gates per Clifford which usually is 1.875. -One of the main feature of RB is the possibility to estimate the gate fidelity +One of the main feature of RB is the possibility to estimate the gate fidelity alone without taking into account both state preparation and measurement errors which can be computed using the :math:`A` and :math:`B` terms in :ref:`Eq. 2 `.