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

• URL: http://arxiv.org/abs/2103.03207v1
• Date: Thu, 4 Mar 2021 18:21:00 GMT
• Title: Quantum Markov Chain Monte Carlo with Digital Dissipative Dynamics on Quantum Computers
• Authors: Mekena Metcalf, Emma Stone, Katherine Klymko, Alexander F. Kemper, Mohan Sarovar, and Wibe A. de Jong
• Abstract summary: We develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. We evaluate the algorithm by simulating thermal states of the transverse Ising model.
• Score: 52.77024349608834
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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