Efficiently learning fermionic unitaries with few non-Gaussian gates
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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_ | 1866909588055392256 |
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| author | Austin, Sharoon Morales, Mauro E. S. Gorshkov, Alexey |
| author_facet | Austin, Sharoon Morales, Mauro E. S. Gorshkov, Alexey |
| contents | Fermionic Gaussian unitaries are known to be efficiently learnable and simulatable. In this paper, we present a learning algorithm that learns an $n$-mode circuit containing $t$ parity-preserving non-Gaussian gates. While circuits with $t = \textrm{poly}(n)$ are unlikely to be efficiently learnable, for constant $t$, we present a polynomial-time algorithm for learning the description of the unknown fermionic circuit within a small diamond-distance error. Building on work that studies the state-learning version of this problem, our approach relies on learning approximate Gaussian unitaries that transform the circuit into one that acts non-trivially only on a constant number of Majorana operators. Our result also holds for the case where we have a qubit implementation of the fermionic unitary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_15356 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficiently learning fermionic unitaries with few non-Gaussian gates Austin, Sharoon Morales, Mauro E. S. Gorshkov, Alexey Quantum Physics Fermionic Gaussian unitaries are known to be efficiently learnable and simulatable. In this paper, we present a learning algorithm that learns an $n$-mode circuit containing $t$ parity-preserving non-Gaussian gates. While circuits with $t = \textrm{poly}(n)$ are unlikely to be efficiently learnable, for constant $t$, we present a polynomial-time algorithm for learning the description of the unknown fermionic circuit within a small diamond-distance error. Building on work that studies the state-learning version of this problem, our approach relies on learning approximate Gaussian unitaries that transform the circuit into one that acts non-trivially only on a constant number of Majorana operators. Our result also holds for the case where we have a qubit implementation of the fermionic unitary. |
| title | Efficiently learning fermionic unitaries with few non-Gaussian gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2504.15356 |