Efficient Classical Shadow Tomography through Many-body Localization
Dynamics
- URL: http://arxiv.org/abs/2309.01258v2
- Date: Wed, 13 Sep 2023 03:36:03 GMT
- Title: Efficient Classical Shadow Tomography through Many-body Localization
Dynamics
- Authors: Tian-Gang Zhou and Pengfei Zhang
- Abstract summary: We introduce an alternative approach founded on the dynamics of many-body localization.
We demonstrate that our scheme achieves remarkable efficiency comparable to shallow circuits or measurement-induced criticality.
- Score: 5.816212175666671
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Classical shadow tomography serves as a potent tool for extracting numerous
properties from quantum many-body systems with minimal measurements.
Nevertheless, prevailing methods yielding optimal performance for few-body
operators necessitate the application of random two-qubit gates, a task that
can prove challenging on specific quantum simulators such as ultracold atomic
gases. In this work, we introduce an alternative approach founded on the
dynamics of many-body localization, a phenomenon extensively demonstrated in
optical lattices. Through an exploration of the shadow norm -- both
analytically, employing a phenomenological model, and numerically, utilizing
the TEBD algorithm -- we demonstrate that our scheme achieves remarkable
efficiency comparable to shallow circuits or measurement-induced criticality.
This efficiency provides an exponential advantage over the Pauli measurement
protocol for few-body measurements. Our findings are corroborated through
direct numerical simulations encompassing the entire sampling and
reconstruction processes. Consequently, our results present a compelling
methodology for analyzing the output states of quantum simulators.
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