Counterdiabatic Hamiltonian Monte Carlo

2026-02-24

AI Summary

This work addresses the slow convergence of Hamiltonian Monte Carlo (HMC) when sampling from complex, multimodal distributions by proposing a novel framework that integrates counterdiabatic control with sequential Monte Carlo (SMC). The method introduces a time-dependent Hamiltonian augmented with a learnable counterdiabatic term to construct an efficient sampling kernel that accelerates transitions between modes. An unbiased weighting mechanism is incorporated to ensure estimator consistency. Notably, this approach represents the first application of quantum-inspired counterdiabatic principles to HMC, offering a unified theoretical perspective on gradient-based sampling with learned drift terms. Empirical evaluations demonstrate that the proposed method significantly outperforms standard HMC and existing acceleration strategies across multiple multimodal benchmark distributions, achieving faster convergence and higher sampling efficiency.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities, but can converge slowly when applied to challenging multimodal problems. Running HMC with a time varying Hamiltonian, in order to interpolate from an initial tractable distribution to the target of interest, can address this problem. In conjunction with a weighting scheme to eliminate bias, this can be viewed as a special case of Sequential Monte Carlo (SMC) sampling \cite{doucet2001introduction}. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by \cite{sels2017minimizing}, where a learned \emph{counterdiabatic} term added to the Hamiltonian allows for efficient quantum state preparation, we propose \emph{Counterdiabatic Hamiltonian Monte Carlo} (CHMC), which can be viewed as an SMC sampler with a more efficient kernel. We establish its relationship to recent proposals for accelerating gradient-based sampling with learned drift terms, and demonstrate on simple benchmark problems.

Problem

• Hamiltonian Monte Carlo
• multimodal sampling
• slow convergence
• Sequential Monte Carlo
• sampling efficiency

Innovation

• Counterdiabatic
• Hamiltonian Monte Carlo
• Sequential Monte Carlo
• learned drift
• sampling acceleration