Efficient Local Classical Shadow Tomography with Number Conservation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866910564137041920 |
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| author | Hearth, Sumner N. Flynn, Michael O. Chandran, Anushya Laumann, Chris R. |
| author_facet | Hearth, Sumner N. Flynn, Michael O. Chandran, Anushya Laumann, Chris R. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_09291 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Efficient Local Classical Shadow Tomography with Number Conservation Hearth, Sumner N. Flynn, Michael O. Chandran, Anushya Laumann, Chris R. Quantum Physics Quantum Gases Strongly Correlated Electrons 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. |
| title | Efficient Local Classical Shadow Tomography with Number Conservation |
| topic | Quantum Physics Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2311.09291 |