量子动力学哈密顿蒙特卡洛
Quantum Dynamical Hamiltonian Monte Carlo
AI总结：
本文提出量子动力学哈密顿蒙特卡洛（QD-HMC）算法，通过用量子相干连续空间动力学模拟替代经典辛积分提议步骤，在保持细致平衡条件的同时实现采样过程的多项式加速，从而拓宽量子计算在概率推断中的应用范围。
摘要：
量子计算中的一个开放性挑战是找到有意义且实用的方法，利用量子计算加速经典机器学习工作流程。机器学习工作流程中一个普遍存在的问题是从概率分布中采样，而我们只能通过其对数概率来访问这些分布。为此，我们扩展了著名的哈密顿蒙特卡洛（HMC）方法，用于马尔可夫链蒙特卡洛（MCMC）采样，以混合方式利用量子计算作为提议函数。我们的新算法，量子动力学哈密顿蒙特卡洛（QD-HMC），将经典的辛积分提议步骤替换为在数字或模拟量子计算机上对量子相干连续空间动力学的模拟。我们证明QD-HMC保持了HMC的关键特性，例如通过动量反转维持细致平衡条件，同时在某些场景下相对于其经典对应方法具有多项式加速的潜力。由于采样是许多形式概率推断中的核心子程序，而连续参数化空间中的MCMC涵盖了大量潜在应用，这项工作拓宽了量子设备的适用领域。
英文摘要：
One of the open challenges in quantum computing is to find meaningful and practical methods to leverage quantum computation to accelerate classical machine learning workflows. A ubiquitous problem in machine learning workflows is sampling from probability distributions that we only have access to via their log probability. To this end, we extend the well-known Hamiltonian Monte Carlo (HMC) method for Markov Chain Monte Carlo (MCMC) sampling to leverage quantum computation in a hybrid manner as a proposal function. Our new algorithm, Quantum Dynamical Hamiltonian Monte Carlo (QD-HMC), replaces the classical symplectic integration proposal step with simulations of quantum-coherent continuous-space dynamics on digital or analogue quantum computers. We show that QD-HMC maintains key characteristics of HMC, such as maintaining the detailed balanced condition with momentum inversion, while also having the potential for polynomial speedups over its classical counterpart in certain scenarios. As sampling is a core subroutine in many forms of probabilistic inference, and MCMC in continuously-parameterized spaces covers a large-class of potential applications, this work widens the areas of applicability of quantum devices.
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