Abstract

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 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. In this chalk talk, I will define the problem of fidelity estimation, and provide a common approach for solving it — the Direct Fidelity Estimation algorithm.

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 scalable runtime.