Optimal Haar random fermionic linear optics circuits

• URL: http://arxiv.org/abs/2505.24212v1
• Date: Fri, 30 May 2025 04:52:40 GMT
• Title: Optimal Haar random fermionic linear optics circuits
• Authors: Paolo Braccia, N. L. Diaz, Martin Larocca, M. Cerezo, Diego García-Martín,
• Abstract summary: We introduce optimal algorithms to sample over the non-particle-preserving (active) and particle-preserving (passive) FLO Haar measures.<n>We also provide quantum circuits to sample Clifford FLO with an optimal $Theta(n2)$ gate count.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\Theta(n)$ depth and $\Theta(n^2)$ gate count; with only a $\Theta(n^2)$ classical overhead. Finally, we also provide quantum circuits to sample Clifford FLO with an optimal $\Theta(n^2)$ gate count.

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