Efficiently learning fermionic unitaries with few non-Gaussian gates

• URL: http://arxiv.org/abs/2504.15356v1
• Date: Mon, 21 Apr 2025 18:02:39 GMT
• Title: Efficiently learning fermionic unitaries with few non-Gaussian gates
• Authors: Sharoon Austin, Mauro E. S. Morales, Alexey Gorshkov,
• Abstract summary: We present a learning algorithm that learns an $n$-mode circuit containing parity-preserving non-Gaussian gates.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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