qartvm (pronounced 'kar-toom', like the capital of Sudan) is a quantum computing simulation package for Dart & Flutter.
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Quantum circuit definition
-
Built-in quantum gates:
- Hadamard
- Pauli X (NOT), Y, Z
- Phase S, T & custom
- Rotations
- Higher-level gates:
- swap
- Toffoli (CC-NOT)
- Fredkin (C-SWAP)
- Quantum Fourrier Transform (QFT) and inverse QFT
-
Gates acting on a single qubit can be parallelized
-
Gates can be controlled by one or several qubits
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Custom quantum gates
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Quantum register (n-qubits)
Some examples are provided in the /example folder.
final circuit = QCircuit(size: 2);
circuit.hadamard(0);
circuit.controlledNot(0, 1);
describe(circuit);
draw(circuit);
final qreg = QRegister.zero(2);
print('Initial states');
print(' * amplitudes: ${amplInfo(qreg.amplitudes, fractionDigits: 6)}');
print(' * probabilities: ${probInfo(qreg.probabilities, fractionDigits: 2)}');
circuit.execute(qreg);
print('Final states');
print(' * amplitudes: ${amplInfo(qreg.amplitudes, fractionDigits: 6)}');
print(' * probabilities: ${probInfo(qreg.probabilities, fractionDigits: 2)}');Output:
* hadamard on [0]
* pauliX on [1] controlled by [0]
---
0 ----| H |---- X ------
---
-----
1 -----------| NOT |----
-----
Initial states
* amplitudes: 00 (1.000000)
* probabilities: 00 (100.00 %)
Final states
* amplitudes: 00 (0.707107), 11 (0.707107)
* probabilities: 00 (50.00 %), 11 (50.00 %)
final circuit = QCircuit(size: 4);
circuit.toffoli(0, 1, 3);
circuit.controlledNot(0, 1);
circuit.toffoli(1, 2, 3);
circuit.controlledNot(1, 2);
circuit.controlledNot(0, 1);
describe(circuit);
draw(circuit);
for (var a = 0; a <= 1; a++) {
for (var b = 0; b <= 1; b++) {
final qreg = QRegister([
if (a == 1) Qbit.one else Qbit.zero,
if (b == 1) Qbit.one else Qbit.zero,
Qbit.zero,
Qbit.zero
]);
print('[$a/$b] Initial: ${stateInfo(qreg.probabilities)}');
circuit.execute(qreg);
print('[$a/$b] Outcome: ${stateInfo(qreg.probabilities)}');
final result = qreg.read(qubits: [3, 2]);
print('[$a/$b] $a + $b = $result');
}
}Output:
* toffoli on [3] controlled by [0, 1]
* pauliX on [1] controlled by [0]
* toffoli on [3] controlled by [1, 2]
* pauliX on [2] controlled by [1]
* pauliX on [1] controlled by [0]
0 ======= X ======== X =========================== X ======
----- -----
1 ======= X ======| NOT |===== X ======== X ====| NOT |====
----- -----
-----
2 ============================ X ======| NOT |=============
-----
-------- --------
3 ====| CC-NOT |===========| CC-NOT |======================
-------- --------
[0/0] Initial: 0000 (100 %)
[0/0] Outcome: 0000 (100 %)
[0/0] 0 + 0 = 0
[0/1] Initial: 0100 (100 %)
[0/1] Outcome: 0110 (100 %)
[0/1] 0 + 1 = 1
[1/0] Initial: 1000 (100 %)
[1/0] Outcome: 1010 (100 %)
[1/0] 1 + 0 = 1
[1/1] Initial: 1100 (100 %)
[1/1] Outcome: 1101 (100 %)
[1/1] 1 + 1 = 2
// qubit # = input bit / result bit
// 0 = a0 / (a+b)0
// 1 = a1 / (a+b)1
// 2 = a2 / (a+b)2 (carry)
// 3 = b0 / b0
// 4 = b1 / b1
// 5 = |0> (suppressed as this qubit is useless)
final circuit = QCircuit(size: 5);
circuit.qft([2, 1, 0]);
// circuit.controlledPhase(5, 2, math.pi); // suppressed because qubit 5 is always |0>
circuit.controlledPhase(4, 2, math.pi / 2);
circuit.controlledPhase(3, 2, math.pi / 4);
circuit.controlledPhase(4, 1, math.pi);
circuit.controlledPhase(3, 1, math.pi / 2);
circuit.controlledPhase(3, 0, math.pi);
circuit.invQft([2, 1, 0]);
describe(circuit);
draw(circuit);
final sw = Stopwatch();
sw.start();
verifyAddition(circuit);
sw.stop();
print('Completed in ${sw.elapsed} before compilation, total executions = $_nbExec (${sw.elapsedMicroseconds.toDouble() / _nbExec} µs/execution)');
circuit.compile();
describe(circuit);
draw(circuit);
sw.reset();
sw.start();
verifyAddition(circuit);
sw.stop();
print('Completed in ${sw.elapsed} after compilation, total executions = $_nbExec (${sw.elapsedMicroseconds.toDouble() / _nbExec} µs/execution)');Output:
* qft on [2, 1, 0]
* phase 0.5 pi on [2] controlled by [4]
* phase 0.25 pi on [2] controlled by [3]
* phase 1.0 pi on [1] controlled by [4]
* phase 0.5 pi on [1] controlled by [3]
* phase 1.0 pi on [0] controlled by [3]
* invqft on [2, 1, 0]
----- ----------- ---------
0 ----| QFT |---------------------------------------------------------------| P(1.0 pi) |--| INV-QFT |----
| | ----------- | |
| | ----------- ----------- | |
1 ----| QFT |---------------------------------| P(1.0 pi) |--| P(0.5 pi) |-----------------| INV-QFT |----
| | ----------- ----------- | |
| | ----------- ------------ | |
2 ----| QFT |--| P(0.5 pi) |--| P(0.25 pi) |-----------------------------------------------| INV-QFT |----
----- ----------- ------------ ---------
3 --------------------------------- X ---------------------------- X ------------ X ----------------------
4 ------------------ X ---------------------------- X ----------------------------------------------------
[0/0] Outcome: 0 + 0 = {0: 100}
[0/1] Outcome: 0 + 1 = {1: 100}
[0/2] Outcome: 0 + 2 = {2: 100}
[0/3] Outcome: 0 + 3 = {3: 100}
[1/0] Outcome: 1 + 0 = {1: 100}
[1/1] Outcome: 1 + 1 = {2: 100}
[1/2] Outcome: 1 + 2 = {3: 100}
[1/3] Outcome: 1 + 3 = {4: 100}
[2/0] Outcome: 2 + 0 = {2: 100}
[2/1] Outcome: 2 + 1 = {3: 100}
[2/2] Outcome: 2 + 2 = {4: 100}
[2/3] Outcome: 2 + 3 = {5: 100}
[3/0] Outcome: 3 + 0 = {3: 100}
[3/1] Outcome: 3 + 1 = {4: 100}
[3/2] Outcome: 3 + 2 = {5: 100}
[3/3] Outcome: 3 + 3 = {6: 100}
[4/0] Outcome: 4 + 0 = {4: 100}
[4/1] Outcome: 4 + 1 = {5: 100}
[4/2] Outcome: 4 + 2 = {6: 100}
[4/3] Outcome: 4 + 3 = {7: 100}
Completed in 0:00:01.382940 before compilation, total executions = 12000 (115.245 µs/execution)
* qft on [2, 1, 0] followed by phase 0.5 pi on [2] controlled by [4] followed by phase 0.25 pi on [2] controlled by [3] followed by phase 1.0 pi on [1] controlled by [4] followed by phase 0.5 pi on [1] controlled by [3] followed by phase 1.0 pi on [0] controlled by [3] followed by invqft on [2, 1, 0]
----------
0 ----| COMPILED |----
| |
| |
1 ----| COMPILED |----
| |
| |
2 ----| COMPILED |----
----------
3 -------- X ---------
4 -------- X ---------
[0/0] Outcome: 0 + 0 = {0: 100}
[0/1] Outcome: 0 + 1 = {1: 100}
[0/2] Outcome: 0 + 2 = {2: 100}
[0/3] Outcome: 0 + 3 = {3: 100}
[1/0] Outcome: 1 + 0 = {1: 100}
[1/1] Outcome: 1 + 1 = {2: 100}
[1/2] Outcome: 1 + 2 = {3: 100}
[1/3] Outcome: 1 + 3 = {4: 100}
[2/0] Outcome: 2 + 0 = {2: 100}
[2/1] Outcome: 2 + 1 = {3: 100}
[2/2] Outcome: 2 + 2 = {4: 100}
[2/3] Outcome: 2 + 3 = {5: 100}
[3/0] Outcome: 3 + 0 = {3: 100}
[3/1] Outcome: 3 + 1 = {4: 100}
[3/2] Outcome: 3 + 2 = {5: 100}
[3/3] Outcome: 3 + 3 = {6: 100}
[4/0] Outcome: 4 + 0 = {4: 100}
[4/1] Outcome: 4 + 1 = {5: 100}
[4/2] Outcome: 4 + 2 = {6: 100}
[4/3] Outcome: 4 + 3 = {7: 100}
Completed in 0:00:00.425942 after compilation, total executions = 12000 (35.49516666666667 µs/execution)
final circuit = QCircuit(size: 3);
circuit.hadamard(1);
circuit.controlledNot(1, 2);
circuit.controlledNot(0, 1);
circuit.hadamard(0);
circuit.measure(qubits: {0});
circuit.measure(qubits: {1});
circuit.controlledNot(1, 2);
circuit.controlledPauliZ(0, 2);
print('');
print('Verification before compilation');
describe(circuit);
draw(circuit);
checkTeleportation(circuit);
circuit.compile();
print('');
print('Verification after compilation');
describe(circuit);
draw(circuit);
checkTeleportation(circuit);Output:
Verification before compilation
* hadamard on [1]
* pauliX on [2] controlled by [1]
* pauliX on [1] controlled by [0]
* hadamard on [0]
* measure [0]
* measure [1]
* pauliX on [2] controlled by [1]
* pauliZ on [2] controlled by [0]
---
0 ---------------------- X ----| H |---[ / ]---------------------- X -----
---
--- -----
1 ----| H |---- X ----| NOT |-------------------[ / ]----- X -------------
--- -----
----- ----- ---
2 -----------| NOT |------------------------------------| NOT |--| Z |----
----- ----- ---
Initial states: 000 (0.467916 + 0.773411 i), 100 (-0.427065 + 0.022487 i)
Alice: 0 (81.71 %) / 1 (18.29 %)
Final states: 100 (0.467916 + 0.773411 i), 101 (-0.427065 + 0.022487 i)
Bob : 0 (81.71 %) / 1 (18.29 %)
Verification after compilation
* hadamard on [1] followed by pauliX on [2] controlled by [1] followed by pauliX on [1] controlled by [0] followed by hadamard on [0]
* measure [0, 1]
* pauliX on [2] controlled by [1] followed by pauliZ on [2] controlled by [0]
----------
0 ----| COMPILED |---[ / ]------- X ---------
| |
| |
1 ----| COMPILED |---[ / ]------- X ---------
| |
| | ----------
2 ----| COMPILED |-----------| COMPILED |----
---------- ----------
Initial states: 000 (-0.131496 + 0.329310 i), 100 (0.892845 + 0.277653 i)
Alice: 0 (12.57 %) / 1 (87.43 %)
Final states: 000 (-0.131496 + 0.329310 i), 001 (0.892845 + 0.277653 i)
Bob : 0 (12.57 %) / 1 (87.43 %)
print('');
print('USING STANDARD GATES');
final fredkinCircuitWithStandardGates = QCircuit(size: 3);
fredkinCircuitWithStandardGates.controlledNot(2, 1);
fredkinCircuitWithStandardGates.toffoli(0, 1, 2);
fredkinCircuitWithStandardGates.controlledNot(2, 1);
describe(fredkinCircuitWithStandardGates);
draw(fredkinCircuitWithStandardGates);
verifyFredkin(fredkinCircuitWithStandardGates);
print('');
print('USING CUSTOM GATE');
final cnot21 = QGates.controlled(3).not(2, 1);
final toffoli012 = QGates.highLevel(3).toffoli(0, 1, 2);
// Here, the custom Fredkin gate matrix is computed by multiplying
// the matrices of the standard gates that make it up.
// The Fredkin matrix (hard-coded) could have been provided as well.
final myFredkinGate = cnot21 * toffoli012 * cnot21;
final fredkinType = QGateType('My Fredkin gate', 'MY-C-SWAP');
final fredkinCircuitWithCustomGate = QCircuit(size: 3);
fredkinCircuitWithCustomGate.custom({1, 2}, myFredkinGate, controls: {0}, type: fredkinType);
print(myFredkinGate.toStringIndent(1));
describe(fredkinCircuitWithCustomGate);
draw(fredkinCircuitWithCustomGate);
verifyFredkin(fredkinCircuitWithCustomGate);
print('');
print('USING BUILT-IN GATE');
final fredkinCircuitWithBuiltInGate = QCircuit(size: 3);
fredkinCircuitWithBuiltInGate.fredkin(0, 1, 2);
describe(fredkinCircuitWithBuiltInGate);
draw(fredkinCircuitWithBuiltInGate);
verifyFredkin(fredkinCircuitWithBuiltInGate);Output:
USING STANDARD GATES
* pauliX on [1] controlled by [2]
* toffoli on [2] controlled by [0, 1]
* pauliX on [1] controlled by [2]
0 ================ X =================
----- -----
1 ====| NOT |===== X ======| NOT |====
----- -----
--------
2 ====== X ====| CC-NOT |==== X ======
--------
Initial: 000 (100 %) => Outcome: 000 (100 %): OK
Initial: 001 (100 %) => Outcome: 001 (100 %): OK
Initial: 010 (100 %) => Outcome: 010 (100 %): OK
Initial: 011 (100 %) => Outcome: 011 (100 %): OK
Initial: 100 (100 %) => Outcome: 100 (100 %): OK
Initial: 101 (100 %) => Outcome: 110 (100 %): OK
Initial: 110 (100 %) => Outcome: 101 (100 %): OK
Initial: 111 (100 %) => Outcome: 111 (100 %): OK
USING CUSTOM GATE
[
[1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1]
]
* My Fredkin gate on [1, 2] controlled by [0]
0 ========= X =========
-----------
1 ====| MY-C-SWAP |====
| |
| |
2 ====| MY-C-SWAP |====
-----------
Initial: 000 (100 %) => Outcome: 000 (100 %): OK
Initial: 001 (100 %) => Outcome: 001 (100 %): OK
Initial: 010 (100 %) => Outcome: 010 (100 %): OK
Initial: 011 (100 %) => Outcome: 011 (100 %): OK
Initial: 100 (100 %) => Outcome: 100 (100 %): OK
Initial: 101 (100 %) => Outcome: 110 (100 %): OK
Initial: 110 (100 %) => Outcome: 101 (100 %): OK
Initial: 111 (100 %) => Outcome: 111 (100 %): OK
USING BUILT-IN GATE
* fredkin on [1, 2] controlled by [0]
0 ======= X ========
--------
1 ====| C-SWAP |====
| |
| |
2 ====| C-SWAP |====
--------
Initial: 000 (100 %) => Outcome: 000 (100 %): OK
Initial: 001 (100 %) => Outcome: 001 (100 %): OK
Initial: 010 (100 %) => Outcome: 010 (100 %): OK
Initial: 011 (100 %) => Outcome: 011 (100 %): OK
Initial: 100 (100 %) => Outcome: 100 (100 %): OK
Initial: 101 (100 %) => Outcome: 110 (100 %): OK
Initial: 110 (100 %) => Outcome: 101 (100 %): OK
Initial: 111 (100 %) => Outcome: 111 (100 %): OK