Error mitigation reduces the effect of noise without correcting errors—it trades quantum resources (more circuits) for classical post-processing to improve result accuracy. Unlike error correction (which requires thousands of physical qubits per logical qubit), error mitigation works on current hardware.

Common techniques: zero-noise extrapolation, symmetry enforcement, readout error correction.

Run circuits at different noise levels by scaling gates, extrapolate to zero noise. Scale factors amplify noise, then fit the results to estimate the noiseless value:

$$\text{Cost}(\lambda) = A + B e^{-\lambda}$$

where $\lambda$ is the noise scaling factor. Solve for the noiseless limit.

from qiskit_aer import AerSimulator
from qiskit_aer.noise import NoiseModel, depolarizing_error
import numpy as np
 
# Evaluate at different noise scales
costs = []
scales = [1.0, 1.5, 2.0, 2.5, 3.0]
 
for scale in scales:
    # Scale noise by repeating 1-qubit gates
    scaled_qc = scale_noise_circuit(qc, scale)
    result = sim.run(scaled_qc, shots=1000).result()
    cost = compute_cost(result)
    costs.append(cost)
 
# Fit exponential and extrapolate
coeffs = np.polyfit(scales, costs, 1)
zero_noise_cost = np.polyval(coeffs, 0)
print(f"Mitigated cost: {zero_noise_cost}")

Measurement errors can be mitigated by calibrating the confusion matrix (which measurement outcomes are actually read) and inverting it:

from qiskit_experiments.library import LocalReadoutError
 
# Calibrate readout errors
exp = LocalReadoutError(qubits)
result = exp.run(backend).block_for_results()
readout_fitter = result.analysis_results(0).value
 
# Apply to measured data
mitigated_counts = readout_fitter.apply(raw_counts)

If your cost function has known symmetries, enforce them post-measurement. For example, if parity must be even, discard odd-parity results and renormalize.

Error mitigation is practical on current hardware but has limits: if noise is too high, no mitigation helps. It's a trade-off between circuit depth, classical resources, and accuracy improvement.