Verifying a stabilizer state with few observables but many shots

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.