  Nature is governed by precise physical laws, which can inspire the discovery
of new computer-run simulation algorithms. Thermal states are the most
ubiquitous for they are the equilibrium states of matter. Simulating thermal
states of quantum matter has applications ranging from quantum machine learning
to better understanding of high-temperature superconductivity and quantum
chemistry. The computational complexity of this task is hopelessly hard for
classical computers. The existing quantum algorithms come with caveats: most
either require quantum phase estimation rendering them impractical for current
noisy hardware, or are variational which face obstacles such as initialization,
barren plateaus, and a general lack of provable guarantee. We provide two
quantum algorithms with provable guarantees to prepare thermal states on
(near-term) quantum computers that avoid these drawbacks. The first algorithm
is inspired by the natural thermalization process where the ancilla qubits act
as the infinite thermal bath. This algorithm can potentially run in polynomial
time to sample thermal distributions of ergodic systems -- the vast class of
physical systems that equilibrate in isolation with respect to local
observables. The second algorithm works for any system and in general runs in
exponential time. However, it requires significantly smaller quantum resources
than previous such algorithms. In addition, we provide an error mitigation
technique for both algorithms to fight back decoherence, which enables us to
run our algorithms on the near-term quantum devices. To illustration, we
simulate the thermal state of the hardcore Bose-Hubbard model on the latest
generation of available quantum computers.
