Optimal Haar random fermionic linear optics circuits

Fuente: arXiv
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Main Authors: Braccia, Paolo, Diaz, N. L., Larocca, Martin, Cerezo, M., García-Martín, Diego
Format: Preprint
Published: 2025
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author Braccia, Paolo
Diaz, N. L.
Larocca, Martin
Cerezo, M.
García-Martín, Diego
author_facet Braccia, Paolo
Diaz, N. L.
Larocca, Martin
Cerezo, M.
García-Martín, Diego
contents Sampling unitary Fermionic Linear Optics (FLO), or matchgate circuits, has become a fundamental tool in quantum information. Such capability enables a large number of applications ranging from randomized benchmarking of continuous gate sets, to fermionic classical shadows. In this work, we introduce optimal algorithms to sample over the non-particle-preserving (active) and particle-preserving (passive) FLO Haar measures. In particular, we provide appropriate distributions for the gates of $n$-qubit parametrized circuits which produce random active and passive FLO. In contrast to previous approaches, which either incur classical $\mathcal{O}(n^3)$ compilation costs or have suboptimal depths, our methods directly output circuits which simultaneously achieve an optimal down-to-the-constant-factor $Θ(n)$ depth and $Θ(n^2)$ gate count; with only a $Θ(n^2)$ classical overhead. Finally, we also provide quantum circuits to sample Clifford FLO with an optimal $Θ(n^2)$ gate count.
format Preprint
id arxiv_https___arxiv_org_abs_2505_24212
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Optimal Haar random fermionic linear optics circuits
Braccia, Paolo
Diaz, N. L.
Larocca, Martin
Cerezo, M.
García-Martín, Diego
Quantum Physics
Sampling unitary Fermionic Linear Optics (FLO), or matchgate circuits, has become a fundamental tool in quantum information. Such capability enables a large number of applications ranging from randomized benchmarking of continuous gate sets, to fermionic classical shadows. In this work, we introduce optimal algorithms to sample over the non-particle-preserving (active) and particle-preserving (passive) FLO Haar measures. In particular, we provide appropriate distributions for the gates of $n$-qubit parametrized circuits which produce random active and passive FLO. In contrast to previous approaches, which either incur classical $\mathcal{O}(n^3)$ compilation costs or have suboptimal depths, our methods directly output circuits which simultaneously achieve an optimal down-to-the-constant-factor $Θ(n)$ depth and $Θ(n^2)$ gate count; with only a $Θ(n^2)$ classical overhead. Finally, we also provide quantum circuits to sample Clifford FLO with an optimal $Θ(n^2)$ gate count.
title Optimal Haar random fermionic linear optics circuits
topic Quantum Physics
url https://arxiv.org/abs/2505.24212