Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers

TL;DR

This paper introduces a digital quantum algorithm that efficiently simulates environmental interactions and thermal states in quantum systems using minimal ancilla qubits, enabling practical quantum Markov Chain Monte Carlo sampling.

Contribution

The authors develop a novel quantum algorithm combining spectral combing and resets to simulate large environments with few ancillas, advancing quantum simulation capabilities.

Findings

Successfully simulates thermal states of the transverse Ising model.

Demonstrates accurate Gibbs distribution sampling for probabilistic models.

Reduces resource requirements for environment simulation in quantum computing.

Abstract

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.