Counterdiabatic Hamiltonian Monte Carlo

• URL: http://arxiv.org/abs/2602.21272v1
• Date: Tue, 24 Feb 2026 15:56:58 GMT
• Title: Counterdiabatic Hamiltonian Monte Carlo
• Authors: Reuben Cohn-Gordon, Uroš Seljak, Dries Sels,
• Abstract summary: Hamiltonian Monte Carlo (HMC) is a state of the art method for sampling from distributions with differentiable densities.<n>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.<n>We propose emphCounterdiabatic Hamiltonian Monte Carlo (CHMC), which can be viewed as an SMC sampler with a more efficient kernel.
• Score: 0.0254890465057467
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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