Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-qubit Quantum Processor

TL;DR

This paper presents an efficient method using a unitary 2-design and twirling protocol to estimate the average fidelity of a Clifford gate on a 7-qubit quantum processor, significantly reducing experimental effort compared to full process tomography.

Contribution

It introduces a scalable, efficient protocol for estimating average fidelity of Clifford gates, applicable to multi-qubit systems, with practical experimental validation.

Findings

Estimated average fidelity of the Clifford gate is 55.1%.

Fidelity improves to 87.5% after removing decoherence effects.

Only 1656 experiments needed for 99% confidence, versus over 10^8 for full tomography.

Abstract

Quantum gates in experiment are inherently prone to errors that need to be characterized before they can be corrected. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than $10^8$ experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to 87.5% if the infidelity due to decoherence is removed. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications.