A Lightweight Protocol for Matchgate Fidelity Estimation

With the prospect of reaching hundreds of fault-tolerant qubits by the end of the decade, scaling up quantum computing infrastructure is as much of a theoretical as a practical challenge. Against the backdrop of progress in hardware, simple yet effective techniques are needed to address the question of how well our quantum computers can perform their intended task: implementing one, and two-qubit gates within a given computational model or architecture. In this talk, I will define the problem of fidelity estimation, and provide a common approach for solving it — the Direct Fidelity Estimation algorithm, originally devised for the Clifford + T model and recently extended for matchgate computations.

In the first part of the talk, I will outline the concept of Channel Fidelity and the closely-related Entanglement Fidelity of quantum processes. After introducing the necessary tools for estimating these quantities (via the Pauli-Liouville representation of quantum channels), I will present the Direct Fidelity Estimation (DFE) algorithm of Flammia & Liu [PRL 106, 230501], a commonly used technique for certifying quantum processes. In the second part I will also introduce Matchgates, a family of gates capable of universal quantum computation that is native to many quantum computing architectures. After modifying the DFE algorithm, we will arrive at Matchgate Fidelity Estimation [arXiv:2404.07974], a variant of DFE capable of benchmarking Matchgate circuits in a more favourable runtime.

This talk is based on arXiv:2404.07974, and will assume minimal knowledge of channel certification or benchmarking techniques.