Efficient Shadow Tomography of Thermal States
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918394110935040 |
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| author | Chen, Chi-Fang Gilyén, András |
| author_facet | Chen, Chi-Fang Gilyén, András |
| contents | We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(βM/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited. The key idea is a new interpretation of quantum Gibbs samplers as \textit{detailed-balance measurement channels}: measurements that preserve the Gibbs state when outcomes are marginalized. Consequently, shadow tomography of thermal states admits a general efficient algorithm when the Hamiltonian is known, substantially lowering the readout cost in quantum thermal simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Efficient Shadow Tomography of Thermal States Chen, Chi-Fang Gilyén, András Quantum Physics We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(βM/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited. The key idea is a new interpretation of quantum Gibbs samplers as \textit{detailed-balance measurement channels}: measurements that preserve the Gibbs state when outcomes are marginalized. Consequently, shadow tomography of thermal states admits a general efficient algorithm when the Hamiltonian is known, substantially lowering the readout cost in quantum thermal simulation. |
| title | Efficient Shadow Tomography of Thermal States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.16845 |