A Lightweight Protocol for Matchgate Fidelity Estimation

TL;DR

This paper introduces a low-depth, efficient randomized protocol for estimating the fidelity of matchgate quantum circuits, significantly improving speed and enabling direct benchmarking of specific quantum gate subgroups.

Contribution

It presents a novel low-depth randomized algorithm using a modified Pauli-Liouville representation for matchgate fidelity estimation, with extensions for benchmarking various matchgate circuits.

Findings

Achieves a $1/\sqrt{n}$ speedup over previous protocols.

Enables direct benchmarking of matchgate subgroups.

Provides extensions for circuits with Clifford and nearest-neighbour gates.

Abstract

We present a low-depth randomised algorithm for the estimation of entanglement fidelity between an $n$-qubit matchgate circuit $\mathcal{U}$ and its noisy implementation $\mathcal{E}$. Our procedure makes use of a modified Pauli-Liouville representation of quantum channels, with Clifford algebra elements as a basis. We show that this choice of representation leads to a block-diagonal compound matrix structure of matchgate superoperators which enables construction of efficient protocols for estimating the fidelity, achieving a $1/\sqrt{n}$ speedup over protocols of Flammia & Liu [PRL 106, 230501]. Finally, we offer simple extensions of our protocol which (without additional overhead) benchmark matchgate circuits intertwined by Clifford circuits, and circuits composed of exclusively nearest-neighbour $XY(\theta)$ gates or Givens rotations - forming the first known method for direct benchmarking of matchgate subgroups.