Counterdiabatic Hamiltonian Monte Carlo

A team of researchers including Reuben Cohn-Gordon, Uroš Seljak, and Dries Sels has published a new paper on arXiv titled 'Counterdiabatic Hamiltonian Monte Carlo.' The work tackles a fundamental problem in computational statistics: the slow convergence of Hamiltonian Monte Carlo (HMC) when sampling from challenging, multimodal probability distributions. The authors' novel approach draws inspiration from quantum computing, specifically the concept of a 'counterdiabatic' term used to prepare quantum states efficiently without unwanted excitations. By learning and adding a similar term to the classical HMC Hamiltonian, their proposed CHMC algorithm can interpolate between an initial simple distribution and a complex target distribution far more rapidly than traditional methods.

Technically, CHMC can be framed as a more efficient kernel within a Sequential Monte Carlo (SMC) sampler framework. The key innovation is that it overcomes the inefficiency of requiring a very slow, adiabatic change between distributions, which is a limitation of prior SMC approaches using HMC. The paper establishes a theoretical connection to other recent methods for accelerating gradient-based sampling with learned components and provides demonstrations on benchmark problems. While still a research proposal, this quantum-inspired technique points toward a significant potential speedup for critical tasks in Bayesian inference, generative modeling, and other areas reliant on high-dimensional sampling.