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Nature is governed by precise physical laws, which can inspire the discoveryof new computer-run simulation algorithms. Thermal states are the mostubiquitous for they are the equilibrium states of matter. Simulating thermalstates of quantum matter has applications ranging from quantum machine learningto better understanding of high-temperature superconductivity and quantumchemistry. The computational complexity of this task is hopelessly hard forclassical computers. The existing quantum algorithms come with caveats: mosteither require quantum phase estimation rendering them impractical for currentnoisy hardware, or are variational which face obstacles such as initialization,barren plateaus, and a general lack of provable guarantee. We provide twoquantum algorithms with provable guarantees to prepare thermal states on(near-term) quantum computers that avoid these drawbacks. The first algorithmis inspired by the natural thermalization process where the ancilla qubits actas the infinite thermal bath. This algorithm can potentially run in polynomialtime to sample thermal distributions of ergodic systems -- the vast class ofphysical systems that equilibrate in isolation with respect to localobservables. The second algorithm works for any system and in general runs inexponential time. However, it requires significantly smaller quantum resourcesthan previous such algorithms. In addition, we provide an error mitigationtechnique for both algorithms to fight back decoherence, which enables us torun our algorithms on the near-term quantum devices. To illustration, wesimulate the thermal state of the hardcore Bose-Hubbard model on the latestgeneration of available quantum computers.

Preparing thermal states on noiseless and noisy programmable quantum processors