Sharpening Worst-Case Error Assessment for Fault-Tolerant Quantum Computing: Fidelity and Its Deviation

TL;DR

This paper introduces the fidelity deviation alongside gate fidelity to better estimate the worst-case error in quantum gates, especially for fault-tolerant quantum computing, providing a practical and accurate assessment method.

Contribution

The authors propose a new observable, fidelity deviation, to complement gate fidelity, enabling tight bounds on worst-case errors without full process tomography.

Findings

Fidelity deviation quantifies state-dependent fidelity fluctuations.

Fidelity and deviation together constrain spectral moments of error unitaries.

Method allows estimation from randomized experiments, avoiding full tomography.

Abstract

Gate fidelity -- an average fidelity over all possible input states -- is the workhorse metric for benchmarking quantum gates or circuits, yet fault-tolerant quantum computing ultimately depends on the worst-case behavior, typically quantifiable by so-called the diamond distance. In the low-error regime, the coherent errors can inflate the worst-case error even when the reported gate fidelity is high, making the gate fidelity alone an unreliable proxy for fault-tolerance readiness. To capture the missing information, we introduce a companion observable -- what we dub the fidelity deviation -- that quantifies how strongly the state-dependent fidelities fluctuate across input states. Adopting such fluctuations in assessing the fault-tolerance is physically natural because some input directions are nearly unaffected while others form narrow "valleys" that dominate adversarial circuit behavior. For coherent (unitary) gate errors on two or more qubits, we show that the gate fidelity together with the fidelity deviation constrains the relevant spectral moments of the error unitary, enabling an explicit and tight certificate of the worst-case error. Both quantities are estimated directly from the same randomized input-measurement experiment, without full process tomography. We show that the fidelity and its deviation can provide an economical, operationally meaningful, and accurate standard for assessing the fault tolerance of the engineered quantum gates and circuits.