Verifying a stabilizer state with few observables but many shots

TL;DR

This paper introduces a quantum-state-certification protocol for stabilizer states that requires few observables and is efficient for testing NISQ-era quantum computers, emphasizing minimal measurement basis switching.

Contribution

It presents a novel certification method based on Direct Fidelity Estimation with a minimum-over-estimates approach, improving efficiency and rigor in false rate analysis.

Findings

Protocol effectively certifies stabilizer states with limited observables

Mathematically rigorous false-positive and false-negative bounds established

Method suitable for in-situ testing of NISQ quantum devices

Abstract

We propose a quantum-state-certification protocol for stabilizer states, motivated by application in in-situ testing of NISQ-era quantum computer systems: The number of qubits is bounded, and in terms of cost of running the protocol, identical repetition of quantum circuits contribute negligibly compared to switching the measurement bases. The method builds on Direct Fidelity Estimation and work by Somma et al.~(2006), but replaces linear averages by a minimum over estimates of expectation values. We provide mathematically rigorous analysis of the false-negative and false-positive rates.