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

• URL: http://arxiv.org/abs/2605.08251v1
• Date: Thu, 07 May 2026 17:01:52 GMT
• Title: The finite-shot help-harm boundary of zero-noise extrapolation
• Abstract summary: Zero-noise extrapolation (ZNE) reduces noise-induced bias but can increase sampling variance through Richardson coefficients and shot splitting.<n>We define a finite-shot help-harm boundary: the lower local mean-squared-error crossing where fixed ZNE changes from harmful to helpful.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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