Efficient Tomography of Non-Interacting Fermion States

TL;DR

This paper presents an efficient algorithm for learning non-interacting fermion states using a polynomial number of copies and measurements, enabling accurate reconstruction of the state with practical resource bounds.

Contribution

It introduces a novel, resource-efficient algorithm for tomography of non-interacting fermion states based on correlation measurements and state reconstruction.

Findings

Requires polynomial copies and time for accurate state learning.

Empirically estimates correlations in linear measurement bases.

Achieves trace distance error bounds with high probability.

Abstract

We give an efficient algorithm that learns a non-interacting fermion state, given copies of the state. For a system of $n$ non-interacting fermions and $m$ modes, we show that $O(m^3 n^2 \log(1/\delta) / \epsilon^4)$ copies of the input state and $O(m^4 n^2 \log(1/\delta)/ \epsilon^4)$ time are sufficient to learn the state to trace distance at most $\epsilon$ with probability at least $1 - \delta$. Our algorithm empirically estimates one-mode correlations in $O(m)$ different measurement bases and uses them to reconstruct a succinct description of the entire state efficiently.