Quantum Dynamical Hamiltonian Monte Carlo

• URL: http://arxiv.org/abs/2403.01775v2
• Date: Wed, 7 Aug 2024 07:14:45 GMT
• Title: Quantum Dynamical Hamiltonian Monte Carlo
• Authors: Owen Lockwood, Peter Weiss, Filip Aronshtein, Guillaume Verdon,
• Abstract summary: A ubiquitous problem in machine learning is sampling from probability distributions that we only have access to via their log probability. We extend the well-known Hamiltonian Monte Carlo (HMC) method for Chain Monte Carlo (MCMC) sampling to leverage quantum computation in a hybrid manner.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling from probability distributions that we only have access to via their log probability. To this end, we extend the well-known Hamiltonian Monte Carlo (HMC) method for Markov Chain Monte Carlo (MCMC) sampling to leverage quantum computation in a hybrid manner as a proposal function. Our new algorithm, Quantum Dynamical Hamiltonian Monte Carlo (QD-HMC), replaces the classical symplectic integration proposal step with simulations of quantum-coherent continuous-space dynamics on digital or analogue quantum computers. We show that QD-HMC maintains key characteristics of HMC, such as maintaining the detailed balanced condition with momentum inversion, while also having the potential for polynomial speedups over its classical counterpart in certain scenarios. As sampling is a core subroutine in many forms of probabilistic inference, and MCMC in continuously-parameterized spaces covers a large-class of potential applications, this work widens the areas of applicability of quantum devices.

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