A Lightweight Protocol for Matchgate Fidelity Estimation

• URL: http://arxiv.org/abs/2404.07974v1
• Date: Thu, 11 Apr 2024 17:56:18 GMT
• Title: A Lightweight Protocol for Matchgate Fidelity Estimation
• Authors: Jędrzej Burkat, Sergii Strelchuk,
• Abstract summary: We use 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. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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