Measurement Error Mitigation
Correcting readout errors by characterizing and inverting the confusion between prepared and measured bitstrings.
Readout errors
Measuring a qubit is imperfect: a qubit prepared in |0> is sometimes read as 1, and vice versa. These readout or assignment errors distort measured probability distributions independently of gate errors. Because measurement is the final step, its errors directly bias every estimated observable. Measurement error mitigation corrects these using calibration data, without changing the circuit.
The confusion matrix
Characterize the readout by preparing each computational basis state and recording the distribution of measured outcomes. This fills a confusion (or response) matrix M, where entry M_{ij} is the probability of measuring outcome i given the true state was j. The observed distribution p_obs relates to the true distribution p_true by p_obs = M p_true. Inverting gives p_true = M^{-1} p_obs.
Practical concerns
- Full M has size 2^n by 2^n, infeasible to build for many qubits.
- Direct inversion can produce negative probabilities from statistical noise; constrained least-squares fixes this.
- Tensored calibration assumes independent qubit readout, reducing M to a product of two-by-two matrices per qubit.
Scalable approaches
For large registers, the full confusion matrix is intractable. Tensored mitigation calibrates each qubit separately and assumes independence, giving a compact correction. Correlated readout error models capture nearest-neighbor crosstalk without the full exponential cost. Iterative and matrix-free methods apply the inverse implicitly to only the observed outcomes, avoiding construction of the whole matrix.
Where it fits
Readout mitigation is cheap, targets a distinct and often dominant error source, and composes with other methods: apply it alongside zero-noise extrapolation or probabilistic error cancellation, which address gate noise. Because it only reweights measured statistics, it adds no qubits and modest classical cost, making it a routine first step in the error mitigation pipeline.