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arXiv · 2311.09291

Efficient Local Classical Shadow Tomography with Number Conservation

Sumner N. Hearth·Michael O. Flynn·Anushya Chandran·Chris R. Laumann
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Abstract

Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. Physical observables are then reconstructed from the resulting classical shadow. Shadow protocols which use single-body random measurements are simple to implement and capture few-body observables efficiently, but do not apply to systems with fundamental number conservation laws, such as ultracold atoms. We address this shortcoming by proposing and analyzing a new local shadow protocol adapted to such systems. The "All-Pairs" protocol requires one layer of two-body gates and only $\textrm{poly}(V)$ samples to reconstruct arbitrary few body observables. Moreover, by exploiting the permutation symmetry of the protocol, we derive a linear time post-processing algorithm. We provide a proof-of-principle reference implementation and demonstrate the reconstruction of 2- and 4-point functions in a paired Luttinger liquid of hardcore bosons.

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Sumner N. Hearth, Michael O. Flynn, Anushya Chandran, Chris R. Laumann. 2023-11-15. Efficient Local Classical Shadow Tomography with Number Conservation. https://doi.org/10.1103/physrevlett.133.060802

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