Perturbative tomography of small errors in quantum gates

TL;DR

This paper introduces a perturbative protocol for efficiently reconstructing high-fidelity quantum gates, reducing measurement complexity by amplifying noise and non-unital components, with measurement scaling logarithmically with error rates.

Contribution

The authors develop a two-stage perturbative method for quantum gate tomography that improves efficiency and scalability over existing techniques.

Findings

Measurement number scales logarithmically with error rate.

Protocol effectively reconstructs both unital and non-unital parts.

Amplification techniques enable noise measurement similar to benchmarking.

Abstract

We propose an efficient protocol to fully reconstruct a set of high-fidelity quantum gates. Usually, the efficiency of reconstructing high-fidelity quantum gates is limited by the sampling noise. Our protocol is based on a perturbative approach and has two stages. In the first stage, the initial part of noisy quantum gates is reconstructed by measuring traces of maps, and the trace can be measured by amplifying the noise in a way similar to randomised benchmarking and quantum spectral tomography. In the second stage, by amplifying the non-unital part using the unital part, we can efficiently reconstruct the non-unital part. We show that the number of measurements needed in our protocol scales logarithmically with the error rate of gates.