Hu Zixuan, Xia Rongxin, Kais Sabre
Department of Chemistry, Department of Physics, and Birck Nanotechnology Center, Purdue University, West Lafayette, IN, 47907, United States.
Qatar Environment and Energy Research Institute, College of Science and Engineering, HBKU, Doha, Qatar.
Sci Rep. 2020 Feb 24;10(1):3301. doi: 10.1038/s41598-020-60321-x.
Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment interaction found in most realistic physical models. In this work we propose and demonstrate a general quantum algorithm to evolve open quantum dynamics on quantum computing devices. The Kraus operators governing the time evolution can be converted into unitary matrices with minimal dilation guaranteed by the Sz.-Nagy theorem. This allows the evolution of the initial state through unitary quantum gates, while using significantly less resource than required by the conventional Stinespring dilation. We demonstrate the algorithm on an amplitude damping channel using the IBM Qiskit quantum simulator and the IBM Q 5 Tenerife quantum device. The proposed algorithm does not require particular models of dynamics or decomposition of the quantum channel, and thus can be easily generalized to other open quantum dynamical models.
设计用于模拟量子系统的量子算法已取得巨大进展，然而，尽管开放量子动力学在对大多数现实物理模型中发现的系统 - 环境相互作用进行建模方面具有重要意义，但针对开发开放量子动力学的量子算法的研究却很少。在这项工作中，我们提出并演示了一种用于在量子计算设备上演化开放量子动力学的通用量子算法。由Sz.-Nagy定理保证，支配时间演化的克劳斯算子可以被转换为具有最小扩张的酉矩阵。这使得初始状态能够通过酉量子门进行演化，同时使用的资源比传统的史汀斯普林扩张所需的资源少得多。我们使用IBM Qiskit量子模拟器和IBM Q 5特内里费量子设备在振幅阻尼通道上演示了该算法。所提出的算法不需要特定的动力学模型或量子通道的分解，因此可以很容易地推广到其他开放量子动力学模型。
