Efficient Shadow Tomography of Thermal States

• URL: http://arxiv.org/abs/2603.16845v1
• Date: Tue, 17 Mar 2026 17:53:12 GMT
• Title: Efficient Shadow Tomography of Thermal States
• Abstract summary: We present a general protocol for estimating $M$ observables from only $mathcalO(log (M)/varepsilon2)$ copies of a Gibbs state whose Hamiltonian is accessible.<n>We show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited.
• Score: 0.5500249707065662
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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