Practical and reliable error bars for quantum process tomography

TL;DR

This paper introduces a method to construct reliable error bars for quantum process tomography, enabling high-confidence estimation of process figures-of-merit, which enhances the operational interpretability of quantum process estimates.

Contribution

It presents a confidence region estimator for quantum processes, along with a software package, improving the reliability of quantum process characterization beyond point estimates.

Findings

Provides high-probability error regions for quantum processes

Enables reliable certification of quantum gate performance

Demonstrates effectiveness through simulated examples

Abstract

Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to the point estimate can also produce the observed data with near certainty. Unless appropriate error bars can be constructed, the point estimate does not carry any sound operational interpretation. Here, we provide a solution to this problem by constructing a confidence region estimator for quantum processes. Our method enables reliable estimation of essentially any figure-of-merit for quantum processes on few qubits, including the diamond distance to a specific noise model, the entanglement fidelity, and the worst-case entanglement fidelity, by identifying error regions which contain the true state with high probability. We also provide a software package---QPtomographer---implementing our estimator for the diamond norm and the worst-case entanglement fidelity. We illustrate its usage and performance with several simulated examples. Our tools can be used to reliably certify the performance of e.g. error correction codes, implementations of unitary gates or more generally any noise process affecting a quantum system.