Abstract Modeling the dynamics of a quantum system connected to the environment is critical for advancing our understanding of complex quantum processes, as most quantum processes in nature are affected by an environment. Modeling a macroscopic environment on a quantum simulator may be achieved by coupling independent ancilla qubits that facilitate energy exchange in an appropriate manner with the system and mimic an environment. This approach requires a large, and possibly exponential number of ancillary degrees of freedom which is impractical. In contrast, we develop a digital quantum algorithm that simulates interaction with an environment using a small number of ancilla qubits. By combining periodic modulation of the ancilla energies, or spectral combing, with periodic reset operations, we are able to mimic interaction with a large environment and generate thermal states of interacting many-body systems. We evaluate the algorithm by simulating preparation of thermal states of the transverse Ising model. Our algorithm can also be viewed as a quantum Markov chain Monte Carlo process that allows sampling of the Gibbs distribution of a multivariate model. To demonstrate this we evaluate the accuracy of sampling Gibbs distributions of simple probabilistic graphical models using the algorithm.

中文翻译：

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量子计算机上具有数字耗散动力学的量子马尔可夫链蒙特卡罗

摘要：建模与环境相关的量子系统的动力学对于促进我们对复杂量子过程的理解至关重要，因为自然界中的大多数量子过程都受到环境的影响。在量子模拟器上对宏观环境进行建模可以通过耦合独立的附属量子比特来实现，这些量子比特以适当的方式促进与系统的能量交换并模拟环境。这种方法需要大量且可能呈指数级的辅助自由度，这是不切实际的。相比之下，我们开发了一种数字量子算法，该算法使用少量辅助量子比特来模拟与环境的交互。通过将辅助能量的周期性调制或光谱组合与周期性复位操作相结合，我们能够模拟与大型环境的相互作用，并生成相互作用的多体系统的热态。我们通过模拟横向伊辛模型的热态准备来评估算法。我们的算法也可以看作是一个量子马尔可夫链蒙特卡罗过程，它允许对多元模型的吉布斯分布进行采样。为了证明这一点，我们评估了使用该算法对简单概率图形模型的吉布斯分布进行采样的准确性。