Efficient Local Classical Shadow Tomography with Number Conservation

• URL: http://arxiv.org/abs/2311.09291v2
• Date: Mon, 12 Aug 2024 20:49:59 GMT
• Title: Efficient Local Classical Shadow Tomography with Number Conservation
• Authors: Sumner N. Hearth, Michael O. Flynn, Anushya Chandran, Chris R. Laumann,
• Abstract summary: Shadow tomography aims to build a classical description of a quantum state from a sequence of simple random measurements. We propose and analyze a new local shadow protocol adapted to systems with fundamental number conservation laws, such as ultracold atoms.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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