Counterdiabatic Hamiltonian Monte Carlo

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 citedoucet2001introduction. However, this approach can be inefficient, since it requires slow change between the initial and final distribution. Inspired by citesels2017minimizing, where a learned counterdiabatic term added to the Hamiltonian allows for efficient quantum state preparation, we propose 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.