Quantum algorithm for the simulation of open-system dynamics and thermalization
Quantum algorithm for the simulation of open-system dynamics and thermalization
复制标题
用于模拟开放系统动力学和热化的量子算法
DOI：
10.1103/physreva.101.012328
复制
发表时间：
2020
影响因子：
2.9
通讯作者：
Ying Li
中科院分区：
文献类型：
--
作者：
Hong-Yi Su;Ying Li
量子开放系统模拟是量子模拟的一个重要范畴。通过模拟零温度下的热化过程，我们可以解决量子系统的基态问题。为了在量子计算机上实现开放系统进化，我们需要使用量子比特对环境进行编码。然而，通常环境比系统大得多，即如果环境被直接编码，则需要许多量子比特。在本文中，我们提出了一种方法来模拟开放系统动态再现水库相关函数使用最小化希尔伯特空间。通过这种方式，我们只需要少量的量子位来表示环境。为了模拟无时间卷积主方程的$n $阶展开，通过再现多达$n$个时间相关函数，表示环境的量子比特数为$\sim \lfloor \frac{n}{2} \rfloor\log_2（N_\omega N_\beta）$。这里，$N_\omega$是离散环境频谱中的频率数，$N_\beta$是系统-环境相互作用中的项数。通过再生两次关联函数，即取n = 2，我们可以模拟马尔可夫量子主方程。在我们的算法中，量子计算机上的环境甚至可以比系统更小。
The quantum open-system simulation is an important category of quantum simulation. By simulating the thermalisation process at the zero temperature, we can solve the ground-state problem of quantum systems. To realise the open-system evolution on the quantum computer, we need to encode the environment using qubits. However, usually the environment is much larger than the system, i.e. numerous qubits are required if the environment is directly encoded. In this paper, we propose a way to simulate open-system dynamics by reproducing reservoir correlation functions using a minimised Hilbert space. In this way, we only need a small number of qubits to represent the environment. To simulate the $n$-th-order expansion of the time-convolutionless master equation by reproducing up to $n$-time correlation functions, the number of qubits representing the environment is $\sim \lfloor \frac{n}{2} \rfloor \log_2(N_\omega N_\beta)$. Here, $N_\omega$ is the number of frequencies in the discretised environment spectrum, and $N_\beta$ is the number of terms in the system-environment interaction. By reproducing two-time correlation functions, i.e. taking $n = 2$, we can simulate the Markovian quantum master equation. In our algorithm, the environment on the quantum computer could be even smaller than the system.