Optimal Haar random fermionic linear optics circuits
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908385081819136 |
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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 |