Towards a benchmark for quantum computers based on an iterated post-selective protocol

TL;DR

This paper introduces a benchmarking protocol for quantum computers using an iterated post-selective quantum state matching scheme, tested on IBM superconducting devices, revealing device errors through phase dependence analysis.

Contribution

It proposes a novel benchmarking method based on post-selected quantum state matching and demonstrates its implementation on real quantum hardware.

Findings

Benchmark metric based on conditional probability of the final qubit

Standard deviation as a secondary metric for device fluctuations

Phase dependence analysis reveals coherent gate errors

Abstract

Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.