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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.05058 |
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| _version_ | 1866911433533423616 |
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| author | Christensen, Aria Zhao, Andrew |
| author_facet | Christensen, Aria Zhao, Andrew |
| contents | We revisit the problem of learning fermionic linear optics (FLO), also known as fermionic Gaussian unitaries. Given black-box query access to an unknown FLO, previous proposals required $\widetilde{\mathcal{O}}(n^5 / \varepsilon^2)$ queries, where $n$ is the system size and $\varepsilon$ is the error in diamond distance. These algorithms also use unphysical operations (i.e., violating fermionic superselection rules) and/or $n$ auxiliary modes to prepare Choi states of the FLO. In this work, we establish efficient and experimentally friendly protocols that obey superselection, use minimal ancilla (at most $1$ extra mode), and exhibit improved dependence on both parameters $n$ and $\varepsilon$. For arbitrary (active) FLOs this algorithm makes at most $\widetilde{\mathcal{O}}(n^4 / \varepsilon)$ queries, while for number-conserving (passive) FLOs we show that $\mathcal{O}(n^3 / \varepsilon)$ queries suffice. The complexity of the active case can be further reduced to $\widetilde{\mathcal{O}}(n^3 / \varepsilon)$ at the cost of using $n$ ancilla. This marks the first FLO learning algorithm that attains Heisenberg scaling in precision. As a side result, we also demonstrate an improved copy complexity of $\widetilde{\mathcal{O}}(n η^2 / \varepsilon^2)$ for time-efficient state tomography of $η$-particle Slater determinants in $\varepsilon$ trace distance, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05058 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Learning fermionic linear optics with Heisenberg scaling and physical operations Christensen, Aria Zhao, Andrew Quantum Physics Data Structures and Algorithms Machine Learning We revisit the problem of learning fermionic linear optics (FLO), also known as fermionic Gaussian unitaries. Given black-box query access to an unknown FLO, previous proposals required $\widetilde{\mathcal{O}}(n^5 / \varepsilon^2)$ queries, where $n$ is the system size and $\varepsilon$ is the error in diamond distance. These algorithms also use unphysical operations (i.e., violating fermionic superselection rules) and/or $n$ auxiliary modes to prepare Choi states of the FLO. In this work, we establish efficient and experimentally friendly protocols that obey superselection, use minimal ancilla (at most $1$ extra mode), and exhibit improved dependence on both parameters $n$ and $\varepsilon$. For arbitrary (active) FLOs this algorithm makes at most $\widetilde{\mathcal{O}}(n^4 / \varepsilon)$ queries, while for number-conserving (passive) FLOs we show that $\mathcal{O}(n^3 / \varepsilon)$ queries suffice. The complexity of the active case can be further reduced to $\widetilde{\mathcal{O}}(n^3 / \varepsilon)$ at the cost of using $n$ ancilla. This marks the first FLO learning algorithm that attains Heisenberg scaling in precision. As a side result, we also demonstrate an improved copy complexity of $\widetilde{\mathcal{O}}(n η^2 / \varepsilon^2)$ for time-efficient state tomography of $η$-particle Slater determinants in $\varepsilon$ trace distance, which may be of independent interest. |
| title | Learning fermionic linear optics with Heisenberg scaling and physical operations |
| topic | Quantum Physics Data Structures and Algorithms Machine Learning |
| url | https://arxiv.org/abs/2602.05058 |