Markov Chain Monte Carlo methods are algorithms used to sample probability distributions, commonly used to sample the Boltzmann distribution of physical/chemical models (e.g., protein folding, Ising model, etc.). This allows us to study their properties by sampling the most probable states of those systems. However, the sampling capabilities of these methods are not sufficiently accurate when handling complex configuration spaces. This has resulted in the development of new techniques that improve sampling accuracy, usually at the expense of increasing the computational cost. One of such techniques is Parallel Tempering which improves accuracy by running several replicas which periodically exchange their states. Computationally, this imposes a significant slow-down, which can be counteracted by means of parallelization. These schemes enable MCMC/PT techniques to be run more effectively and allow larger models to be studied. In this work, we present a parallel implementation of Metropolis-Hastings with Parallel Tempering, using OpenMP and CUDA for the parallelization in modern CPUs and GPUs, respectively. The results show a maximum speed-up of 52x using OpenMP with 48 cores, and of 986x speed-up with the CUDA version. Furthermore, the results serve as a basic benchmark to compare a future quantum implementation of the same algorithm.

翻译：马尔可夫链蒙特卡洛方法是一类用于概率分布采样的算法，常用于对物理/化学模型的玻尔兹曼分布进行采样（例如蛋白质折叠、伊辛模型等）。通过采样这些系统的最可能状态，我们可以研究其性质。然而，在处理复杂构型空间时，这些方法的采样能力往往不够精确。这促使了新技术的发展，以提高采样精度，但通常以增加计算成本为代价。其中一种技术是并行回火，它通过运行多个副本并周期性地交换状态来提高精度。在计算上，这会带来显著的减速，但可以通过并行化来抵消。这些方案使MCMC/PT技术能够更有效地运行，并允许研究更大的模型。在本工作中，我们提出了一种结合并行回火的Metropolis-Hastings算法的并行实现，分别使用OpenMP和CUDA在现代CPU和GPU上进行并行化。结果显示，使用OpenMP在48个核心上实现了最高52倍的加速，而CUDA版本实现了986倍的加速。此外，这些结果为未来同一算法的量子实现提供了基础的性能基准。