Efficiently learning fermionic unitaries with few non-Gaussian gates

Fuente: arXiv
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Main Authors: Austin, Sharoon, Morales, Mauro E. S., Gorshkov, Alexey
Format: Preprint
Published: 2025
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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