Quantum Dynamical Hamiltonian Monte Carlo
- URL: http://arxiv.org/abs/2403.01775v1
- Date: Mon, 4 Mar 2024 07:08:23 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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