Efficient Tomography of Non-Interacting Fermion States
This provides an efficient tomography method for quantum systems with non-interacting fermions, which is incremental as it builds on existing state reconstruction techniques.
The paper tackles the problem of learning non-interacting fermion states efficiently, achieving a trace distance of at most ε with O(m^3 n^2 log(1/δ)/ε^4) copies and O(m^4 n^2 log(1/δ)/ε^4) time.
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 $O(m^3 n^2 \log(1/δ) / ε^4)$ copies of the input state and $O(m^4 n^2 \log(1/δ)/ ε^4)$ time are sufficient to learn the state to trace distance at most $ε$ with probability at least $1 - δ$. 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.