量子系统中的非正规哈密顿动力学及其在量子计算机上的实现
Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers
摘要：
非正规矩阵的本征谱是非厄米特物理学的一个中心问题，近年来得到了广泛的研究。然而，非正规矩阵的另一个特征经常被忽视：伪谱，或小扰动下的谱集。本文研究了开放量子系统中Lindblad主方程的非正规矩阵（哈密顿量）作为连续量子轨道所驱动的动力学，指出这种动力学可以揭示非正规哈密顿量的非常规赝谱的本质.特别地，我们研究了非正规化量子态的范数随非正规哈密顿量演化的瞬态动力学，这与观察到无量子跳跃的轨道的概率有关.我们制定的瞬态抑制的衰减率的规范由于伪谱行为，并得出一个非厄米特/非正常模拟的时间-能量的不确定性关系。我们还考虑了两种方法来实验实现非正常的动力学和观察我们的理论研究结果的量子计算机：一个使用的技术来实现量子线路上的非幺正操作，另一个利用量子经典的混合算法称为变分量子模拟。我们使用IBM Quantum提供的基于云的量子计算机进行的演示展示了瞬态时间中规范的冻结动力学，这可以被视为量子芝诺效应的非正常模拟。
英文摘要：
The eigenspectrum of a non-normal matrix, which does not commute with its Hermitian conjugate, is a central issue of non-Hermitian physics that has been extensively studied in the past few years. There is, however, another characteristic of a non-normal matrix that has often been overlooked: the pseudospectrum, or the set of spectra under small perturbations. In this paper, we study the dynamics driven by the non-normal matrix (Hamiltonian) realized as a continuous quantum trajectory of the Lindblad master equation in open quantum systems and point out that the dynamics can reveal the nature of unconventional pseudospectrum of the non-normal Hamiltonian. In particular, we focus on the transient dynamics of the norm of an unnormalized quantum state evolved with the non-normal Hamiltonian, which is related to the probability for observing the trajectory with no quantum jump. We formulate the transient suppression of the decay rate of the norm due to the pseudospectral behavior and derive a non-Hermitian/non-normal analog of the time-energy uncertainty relation. We also consider two methods to experimentally realize the non-normal dynamics and observe our theoretical findings on quantum computers: one uses a technique to realize non-unitary operations on quantum circuits and the other leverages a quantum-classical hybrid algorithm called variational quantum simulation. Our demonstrations using cloud-based quantum computers provided by IBM Quantum exhibit the frozen dynamics of the norm in transient time, which can be regarded as a non-normal analog of the quantum Zeno effect.
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