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Error mitigation
Cheaper than correction: readout calibration, zero-noise extrapolation, and what mitigation cannot do.
- 01Describe readout error mitigation with a confusion matrix.
- 02Explain zero-noise extrapolation in one picture.
- 03State the cost: more shots, not more qubits.
Mitigation does not stop errors; it estimates what the noiseless answer would have been from several noisy runs. Readout mitigation measures how often each prepared basis state is misread, builds a confusion matrix M, and applies M⁻¹ to the measured histogram. Zero-noise extrapolation runs the circuit at amplified noise (for example by repeating each CZ three times, which cancels logically but triples the error) and extrapolates the expectation value back to zero noise.
Noise amplification by hand
This Bell circuit repeats its CNOT three times: ideally identical to one CNOT. Simulate on a fake backend and compare the fidelity with the single-CNOT version: the gap is the extra noise ZNE exploits.
OPENQASM 3.0;
include "stdgates.inc";
qubit[2] q;
bit[2] c;
h q[0];
cx q[0], q[1];
cx q[0], q[1];
cx q[0], q[1];
c = measure q;
- Mitigation improves expectation values, not individual shots: you cannot 'fix' a sampled bit string.
- Its price is variance: the mitigated estimate needs many more shots for the same error bar, growing exponentially with circuit size.
- It is the bridge until error correction, not a replacement for it.
2 questions · one try each counts
Readout mitigation with a confusion matrix corrects…
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Zero-noise extrapolation needs the ability to…
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