Optimal strategies for estimating the average fidelity of quantum gates

TL;DR

This paper introduces a more efficient method for estimating the average fidelity of quantum gates, significantly reducing experimental effort and computational resources by using Monte Carlo sampling on two-designs.

Contribution

It presents an exponential reduction in resources needed for quantum gate characterization compared to existing protocols, using Monte Carlo sampling techniques.

Findings

Reduces experimental effort to 2^n for n qubits

Requires classical computational resources ~ n^2 2^{3n}

Optimal for Clifford gates with existing Monte Carlo methods

Abstract

We show that the minimum experimental effort to characterize the proper functioning of a quantum device scales as 2^n for n qubits and requires classical computational resources ~ n^2 2^{3n}. This represents an exponential reduction compared to the best currently available protocol, Monte Carlo characterization. The reduction comes at the price of either having to prepare entangled input states or obtaining bounds rather than the average fidelity itself. It is achieved by applying Monte Carlo sampling to so-called two-designs or two classical fidelities. For the specific case of Clifford gates, the original version of Monte Carlo characterization based on the channel-state isomorphism remains an optimal choice. We provide a classification of the available efficient strategies for device characterization in terms of the number of required experimental settings, average number of actual measurements and classical computational resources.