直接估计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
摘要：
模拟开放量子系统的动力学和非平衡定态是传统计算机难以完成的计算任务。对于时间演化的模拟，最近已经开发了几种有效的量子算法。然而，计算非平衡稳态作为系统动力学的长时间限制往往不是一个可行的解决方案，因为非常长的瞬态特性或强量子关联的动力学。在这里，我们开发了一个有效的量子算法的直接估计的平均期望值的非平衡稳态的观测值，从而绕过时间积分的主方程。该算法将密度矩阵的矢量化表示编码在量子寄存器上，利用量子相位估计来逼近系统动力学生成元零本征值的本征向量。我们表明，该算法的输出状态允许估计的期望值的观测值的稳定状态。远离临界点，其中Liouvillian间隙按系统大小的幂律缩放，量子算法与精确对角化相比具有指数优势。
英文摘要：
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.
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