  Modeling the dynamics of a quantum system connected to the environment is
critical for advancing our understanding of complex quantum processes, as most
quantum processes in nature are affected by an environment. Modeling a
macroscopic environment on a quantum simulator may be achieved by coupling
independent ancilla qubits that facilitate energy exchange in an appropriate
manner with the system and mimic an environment. This approach requires a
large, and possibly exponential number of ancillary degrees of freedom which is
impractical. In contrast, we develop a digital quantum algorithm that simulates
interaction with an environment using a small number of ancilla qubits. By
combining periodic modulation of the ancilla energies, or spectral combing,
with periodic reset operations, we are able to mimic interaction with a large
environment and generate thermal states of interacting many-body systems. We
evaluate the algorithm by simulating preparation of thermal states of the
transverse Ising model. Our algorithm can also be viewed as a quantum Markov
chain Monte Carlo (QMCMC) process that allows sampling of the Gibbs
distribution of a multivariate model. To demonstrate this we evaluate the
accuracy of sampling Gibbs distributions of simple probabilistic graphical
models using the algorithm.
