Mitiq Calibrator not working correctly due to incorrect qubit ordering

[sanketsharma]

When I provide the circuit to the Calibrator, it adds a classical register m0 into which the qubits are read but not in order. I think this has got something to do with how Cirq handles circuits internally. The following program should reproduce this

from functools import partial
from pprint import pprint

import numpy as np
from mitiq import Settings, Calibrator, MeasurementResult
from mitiq.calibration.calibrator import OutputForm
from mitiq.zne import LinearFactory
from mitiq.zne.scaling import fold_all
from qiskit import QuantumCircuit, transpile
from qiskit_ibm_runtime import SamplerV2
from qiskit_ibm_runtime.fake_provider import FakeFez

def executor(qc: QuantumCircuit, sampler: SamplerV2) -> MeasurementResult:
    measure_instructions = qc.get_instructions("measure")
    print(f"Measure instructions:")
    pprint(measure_instructions)

    backend = sampler.backend()
    transpiled_qc = transpile(qc, backend=backend, optimization_level=0) # So that the added gates are not optimized away
    result = sampler.run([transpiled_qc]).result()
    bit_array = result[0].data["m0"]
    return MeasurementResult.from_counts(bit_array.get_counts())


num_qubits = 3

parameters = [np.pi/4, np.pi/4]
circuit = QuantumCircuit(num_qubits)
circuit.x(0)
circuit.ry(2 * parameters[0], 1)
circuit.cx(1, 0)
circuit.cry(2 * parameters[1], 1, 2)
circuit.cx(2, 1)

ideal_state = {"001": np.cos(parameters[0]), "010": np.sin(parameters[0]) * np.cos(parameters[1]), "100": np.sin(parameters[0]) * np.sin(parameters[1])}
ideal_distribution = dict(zip(list(ideal_state.keys()), np.abs(np.square(list(ideal_state.values())))))

noisy_backend = FakeFez()
transpiled_circuit = transpile(circuit, backend=noisy_backend, optimization_level=2)

noisy_sampler = SamplerV2(mode=noisy_backend)
noisy_sampler.options.default_shots = 2 ** 10

settings = Settings(
    benchmarks = [{
        "circuit_type": "custom",
        "circuit": transpiled_circuit,
        "ideal_distribution":ideal_distribution
    }],
    strategies=[{
        "technique": "zne",
        "scale_noise": fold_all,
        "factory": LinearFactory([1.0, 3.0, 5.0])
    }]
)
noisy_executor = partial(executor, sampler=noisy_sampler)
cal = Calibrator(executor=noisy_executor, frontend="qiskit", settings=settings)
cal.run(log=OutputForm.flat)

Here is the output it produced

 $ python cal.py 
Measure instructions:
[CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 0),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 0),)),
 CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=**(Qubit(QuantumRegister(3, 'q'), 2),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 1),)),
 CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 1),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 2),))**]
Measure instructions:
[CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 0),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 0),)),
 **CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 2),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 1),)),
 CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 1),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 2),))**]
Measure instructions:
[CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 0),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 0),)),
 **CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 2),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 1),)),
 CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 1),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 2),))**]
Measure instructions:
[CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 0),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 0),)),
 **CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 2),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 1),)),
 CircuitInstruction(operation=Instruction(name='measure', num_qubits=1, num_clbits=1, params=[]), qubits=(Qubit(QuantumRegister(3, 'q'), 1),), clbits=(Clbit(ClassicalRegister(3, 'm0'), 2),))**]
┌─────────────────────────┬──────────────────────────────┬────────────────────────────┐
│ benchmark               │ strategy                     │ performance                │
├─────────────────────────┼──────────────────────────────┼────────────────────────────┤
│ Type: custom            │ Technique: ZNE               │ ✘                          │
│ Num qubits: 3           │ Factory: Linear              │ Noisy error: 0.2744        │
│ Circuit depth: 10       │ Scale factors: 1.0, 3.0, 5.0 │ Mitigated error: 0.2755    │
│ Two qubit gate count: 3 │ Scale method: fold_all       │ Improvement factor: 0.9962 │

I've highlighted the lines in the output where it shows that the qubits are not being read into the classical bits with the same indices, which is causing incorrect result being returned and the calibration not working properly.

Note: This doesn't happen every time. You might need to run the program multiple time to reproduce this.

[natestemen]

Thanks a lot for raising this. Looks like a bug to me. I've opened #2813 to try to address it. Feel free to leave any more details if you think I missed anything there, or give it a review! Only one line change needed, I think.