Error Mitigation on Noisy Devices

Error mitigation extracts better answers from noisy quantum runs at a steep sampling cost, extending NISQ usefulness but not solving the noise problem.

Mitigation, not correction

Error mitigation is distinct from error correction: it does not remove errors, it statistically cancels their effect on an expectation value by post-processing many noisy runs. It is the only tool that makes NISQ chemistry benchmarks meaningful at all, but it buys accuracy with exponentially growing sample counts.

Zero-noise extrapolation

Zero-noise extrapolation (ZNE) deliberately amplifies the noise (for example by stretching gate times or folding gates), measures the observable at several noise levels, and extrapolates back to the zero-noise limit.

# Zero-noise extrapolation
# run circuit at noise scale factors lambda = 1, 2, 3 (gate folding)
Es = [measure(scale_noise(circuit, lam)) for lam in (1,2,3)]
# fit E(lambda) ~ a + b*lambda (+ c*lambda^2) and evaluate at lambda=0
E_zero = extrapolate(lam=[1,2,3], vals=Es, model='richardson')
# E_zero approximates the noise-free expectation value

Probabilistic error cancellation and the sampling wall

Probabilistic error cancellation (PEC) inverts a characterized noise channel by sampling from a quasi-probability distribution. It is unbiased but its cost grows exponentially with circuit size, the fundamental wall all mitigation shares.

# PEC sampling overhead to hold variance fixed:
cost  ~  gamma^{2 * (number of noisy gates)}
#   gamma > 1 is the per-gate negativity of the quasi-probability
# -> exponential in gate count: mitigation delays, not defeats, noise

• ZNE is cheap and popular but assumes a smooth, extrapolatable noise model.
• PEC is rigorous but exponentially expensive, capping the circuits it can rescue.
• All mitigation multiplies the shot count, worsening the already heavy measurement cost of VQE.

For Kronos, mitigation is what lets us compare a NISQ VQE run against a classical reference on a tiny active space and see agreement. It does not enable a real first-wall calculation. That still requires error correction, and the honest framing is on the NISQ assessment page.