Efficiently estimating quantum thermal properties from exponentially fewer samples

Abstract:We present an efficient protocol for estimating $M$ observables to precision $\varepsilon$ from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state $\rho\propto\exp(-\beta H)$, given access to its Hamiltonian $H$. The protocol uses single-copy, nonadaptive measurements and a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(\beta M/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting. The key idea of our protocol is a new interpretation of quantum Gibbs samplers as detailed-balanced measurement channels: measurements that preserve the Gibbs state when outcomes are marginalized, and thus enable Gibbs samples to be reused for measuring subsequent observables. Consequently, shadow tomography of thermal states admits a general efficient algorithm when controlled Hamiltonian simulation is available, substantially boosting the data acquisition rate in quantum thermal simulation workflows.

arXiv:2603.16845 [quant-ph]

(or arXiv:2603.16845v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2603.16845 Focus to learn more arXiv-issued DOI via DataCite

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