论文标题
用于直接估算开放量子系统稳态的量子算法
A quantum algorithm for the direct estimation of the steady state of open quantum systems
论文作者
论文摘要
模拟开放量子系统的动力学和非平衡稳态是常规计算机上的硬计算任务。为了模拟时间演化，最近已经开发了几种有效的量子算法。但是，将非平衡稳态计算为系统动力学的长时间限制通常不是可行的解决方案，因为动力学中的瞬态特征或强大的量子相关性。在这里，我们开发了一种有效的量子算法，用于直接估计在非平衡稳态上可观察到的平均期望值，从而绕过了主方程的时间整合。该算法编码量子寄存器上密度矩阵的向量表示，并利用量子相估计来近似系统动力学生成器的零特征值相关的特征向量。我们表明，该算法的输出状态允许估计稳态上可观察到的期望值。远离临界点，与精确的对角线化相比，量子算法缩放为系统大小的功率定律，量子算法具有指数优势。
Simulating the dynamics and the non-equilibrium steady state of an open quantum system are hard computational tasks on conventional computers. For the simulation of the time evolution, several efficient quantum algorithms have recently been developed. However, computing the non-equilibrium steady state as the long-time limit of the system dynamics is often not a viable solution, because of exceedingly long transient features or strong quantum correlations in the dynamics. Here, we develop an efficient quantum algorithm for the direct estimation of averaged expectation values of observables on the non-equilibrium steady state, thus bypassing the time integration of the master equation. The algorithm encodes the vectorized representation of the density matrix on a quantum register, and makes use of quantum phase estimation to approximate the eigenvector associated to the zero eigenvalue of the generator of the system dynamics. We show that the output state of the algorithm allows to estimate expectation values of observables on the steady state. Away from critical points, where the Liouvillian gap scales as a power law of the system size, the quantum algorithm performs with exponential advantage compared to exact diagonalization.
