Readout Mitigation

Readout errors make a measurement record the wrong bit. MENOS can undo them on average: it calibrates each measured bit's readout and inverts it. Mitigation is explicit opt-in. Nothing is mitigated unless you ask, and a mitigated result is never labelled exact.

How it works

Beside your circuit MENOS runs two calibration circuits: one measures every measured qubit from |0⟩, the other after an X on each. From their counts it estimates, for each measured clbit c, P(1|0) and P(0|1), and so the 2×2 readout matrix A_c. Your circuit's measured distribution p is then mapped to

q = (A_1⁻¹ ⊗ … ⊗ A_m⁻¹) p

computed exactly over all 2ᵐ outcomes. MENOS's readout errors are independent per measurement, so this per-bit (tensored) model is exact; only the matrices are estimated.

q is a quasi-distribution: it sums to 1, but entries can be slightly negative. It is reported as is, not projected onto a probability distribution, because projecting would bias it.

Each entry carries a standard error with two parts. The target's shot noise is computed exactly. The calibration's shot noise is computed by a first-order (delta-method) approximation. gamma = ∏ ‖A_c⁻¹‖₁ is the overhead: for an observable with eigenvalues in [−1, 1], an expectation computed from q has a shot-noise standard error of at most gamma / √shots.

The dense vectors take 40 · 2ᵐ bytes and are checked against the memory budget before anything runs.

With the SamplerV2

from qiskit import QuantumCircuit
from qiskit_aer.noise import NoiseModel, ReadoutError

from menos.qiskit import MENOSSampler

model = NoiseModel()
model.add_all_qubit_readout_error(ReadoutError([[0.95, 0.05], [0.1, 0.9]]))

qc = QuantumCircuit(2, 2)
qc.h(0)
qc.cx(0, 1)
qc.measure([0, 1], [0, 1])

sampler = MENOSSampler(noise_model=model, seed=1, readout_mitigation=True)
result = sampler.run([qc], shots=20000).result()[0]
mitigation = result.metadata["readout_mitigation"]
print(mitigation["quasi_dists"], mitigation["gamma"])

assert mitigation["exact"] is False
assert abs(mitigation["quasi_dists"]["01"]) < 5 * mitigation["stds"]["01"] + 1e-3

metadata["readout_mitigation"] holds quasi_dists and stds (binary keys over all clbits, clbit 0 rightmost), gamma, calibration_shots (the pub's shot count), calibration (P(1|0) and P(0|1) per clbit) and exact (False). The calibration circuits go through the same noise model as your circuit, so their X gates carry gate error, as they would on hardware.

With the native API

from menos import Circuit, Opcode, ReadoutMitigationOptions, RunOptions, run_readout_mitigated

circuit = Circuit(1, 1)
circuit.append(Opcode.X, [0])
circuit.append_measure(0, 0, [0.9, 0.1, 0.2, 0.8])

options = RunOptions()
options.shots = 10000
options.seed = 3
mitigation = ReadoutMitigationOptions()
mitigation.calibration_shots = 10000

result = run_readout_mitigated(circuit, None, options, mitigation)
print(result.explain())
assert abs(result.quasi_probabilities["0x1"] - 1.0) < 5 * result.standard_errors["0x1"]

Passing None as the calibration uses noiseless preparation. Pass your own (zero, one) pair of circuits to calibrate under gate noise. They must measure exactly the target's measured (qubit, clbit) pairs.

Refusals

• A circuit with no measurement, shots = 0 or calibration_shots = 0 raises InvalidCircuitError.
• An estimated readout no better than a coin flip (P(1|0) + P(0|1) ≥ 1) raises UnsupportedFeatureError, because it has no meaningful inverse.
• Mitigation vectors over the memory budget raise ResourceExceededError before any circuit runs.

Readout errors never change expectation values in MENOS, so MENOSEstimator needs no readout mitigation.