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.

Questo articolo esplora i giri e le loro implicazioni.

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