Understand
Gibbs state preparation, or Gibbs sampling, is a key computational technique extensively used in physics, statistics, and other scientific fields.
- Recent efforts for designing fast mixing Gibbs samplers for quantum Hamiltonians have largely focused on commuting local Hamiltonians (CLHs), a non-trivial subclass of Hamiltonians which include highly entangled systems such as the Toric code and quantum double model.
- Most previous Gibbs samplers relied on simulating the Davies generator, which is a Lindbladian associated with the thermalization process in nature.
- Instead of using the Davies generator, we design a different Gibbs sampler for various CLHs by giving a reduction to classical Hamiltonians, in the sense that one can efficiently prepare the Gibbs state for some CLH $H$ on a quantum computer as long as one can efficiently do classical Gibbs sampling for the corresponding classical Hamiltonian $H^{(c)}$.