The finite-shot help-harm boundary of zero-noise extrapolation

TL;DR

This paper analyzes the conditions under which zero-noise extrapolation (ZNE) transitions from being beneficial to harmful in quantum computing, considering finite shot resources and noise reduction trade-offs.

Contribution

It introduces the finite-shot help-harm boundary concept and provides a theoretical framework supported by simulations and hardware diagnostics.

Findings

The help-harm boundary is governed by bias improvement and variance penalty.

Simulations support the separation between stabilizer and variational measurements.

Hardware diagnostics delineate measurement and hardware limits.

Abstract

Zero-noise extrapolation (ZNE) reduces noise-induced bias but can increase sampling variance through Richardson coefficients and shot splitting. We define a finite-shot help-harm boundary: the lower local mean-squared-error crossing where fixed Richardson ZNE changes from harmful to helpful. A local expansion shows that this boundary is governed by the first squared-bias improvement and first excess-variance penalty, producing either a shrinking power law, a budget threshold, or no shrinking lower boundary. Qiskit Aer simulations and variance-exponent fits support the predicted separation between deterministic stabilizer measurements and variational energy measurements, while readout-regime diagnostics and IBM Quantum checks delineate measurement-protocol and hardware-traceability limits.