Quantum trajectories of superconducting qubits
Quantum trajectories of superconducting qubits
复制标题
超导量子位的量子轨迹
DOI：
10.1016/j.crhy.2016.07.007
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发表时间：
2015
影响因子：
1.4
通讯作者：
I. Siddiqi
中科院分区：
文献类型：
--
作者：
Steven J. Weber;K. Murch;M. Kimchi;Nicolas Roch;I. Siddiqi
量子力学的标准描述考虑孤立量子系统的时间演化，其幺正动力学由薛定谔方程控制。测量被视为一个瞬时的非幺正过程，通过这个过程，量子系统以玻恩定则给出的概率被投影到被测可观测的本征态。实际上，没有系统是完全与其环境隔离的，测量从来都不是真正瞬时的，而是在被测系统与其环境之间相互作用的细节所确定的有限时间尺度上发生的。量子轨道理论[1，2]将测量视为时间上的连续过程，描述了量子系统的状态在测量过程中如何演变。由于环境的内在量子涨落，测量是一个固有的随机过程。如果一个量子系统从一个已知的量子态开始|如果它的量子轨道是π（0）π，那么通过精确地监测它的环境的波动，就有可能重建单个量子轨道。|量子轨道的概念最早是在20世纪90年代初发展起来的，作为一种理论工具来模拟连续监测的量子发射器[1，3，4]。在接下来的十年里，量子轨道主要用于量子光学领域，作为开放量子系统系综行为数值模拟的理论工具[3，5]。通常，开放量子系统的主方程不能解析求解，因此通常需要数值解。对于N维希尔伯特空间，密度矩阵ρ由N2个真实的数组成，通过主方程求解其时间演化所需的计算时间为N4 [6]。相反，纯量子态|单个量子轨迹的π（t）π可以用N个复数来描述。因此，模拟随机量子轨道的系综通常是有利的，可以将它们平均在一起以恢复密度矩阵ρ（t）的演化。虽然量子轨道的形式是从标准量子力学[7]构建的，但它可以提供对量子测量问题[8-10]等基础问题的洞察，并且与量子力学的一致历史解释非常相似[11]。尽管量子轨道在理论上得到了广泛的应用，但只在少数实验中进行了研究，部分原因是难以进行高效的连续量子测量。最早的连续监测单个量子系统的实验是在强测量的情况下，系统被迅速投射到测量的本征态，破坏了关于相干叠加相位的任何信息。在这样的实验中，有可能跟踪本征态之间的“量子跳跃”[12-15]。里德伯原子的腔量子电动力学（CQED）实验已经探索了弱测量机制，跟踪腔场从相干态坍缩到光子数本征态时的量子轨迹[16]。其他CQED实验使用腔探针来连续跟踪单个铯原子的位置[17]。量子轨迹首先被认为是固态系统中的量子点量子比特的背景下，在真实的时间监测的量子点接触电荷传感器[18，19]。在2007年，量子点的条件测量动力学进行了实验研究[20]。最近...
The standard description of quantum mechanics considers the time-evolution of isolated quantum systems whose unitary dynamics are governed by the Schrödinger equation. Measurement is treated as an instantaneous non-unitary process through which a quantum system is projected into an eigenstate of the measured observable with a probability given by Born’s rule. In reality, no system is completely isolated from its environment, and measurements are never truly instantaneous, but occur over some finite timescale determined by the details of the interaction between the measured system and its environment. The theory of quantum trajectories [1, 2] considers measurement as a continuous process in time, describing how the state of the quantum system evolves during measurement. Due to the intrinsic quantum fluctuations of the environment, measurement is an inherently stochastic process. If a quantum system starts in a known quantum state| ψ (0)〉, then by accurately monitoring the fluctuations of its environment it is possible to reconstruct single quantum trajectories| ψ (t)〉, which describe the evolution of the quantum state in an individual experimental iteration.The concept of quantum trajectories was first developed in the early 1990s as a theoretical tool to model continuously monitored quantum emitters [1, 3, 4]. For the next decade, quantum trajectories were used primarily in the quantum optics community, as a theoretical tool for numerical simulations of the ensemble behavior of open quantum systems [3, 5]. Typically, the master equation of an open quantum system cannot be solved analytically, and thus numerical solutions are often necessary. For a Hilbert space of dimension N, the density matrix ρ consists of N2 real numbers, and the computational time required to solve for its time evolution through the master equation scales as N4 [6]. In contrast, the pure quantum state| ψ (t)〉 of an individual quantum trajectory can be described by N complex numbers. Therefore, it is often advantageous to simulate an ensemble of stochastic quantum trajectories, which can be averaged together to recover the evolution of the density matrix, ρ (t). Although the formalism of quantum trajectories is constructed from standard quantum mechanics [7], it can provide insight into foundational questions such as the quantum measurement problem [8–10] and bears a close resemblance to the consistent histories interpretation of quantum mechanics [11]. Despite widespread theoretical use, quantum trajectories have only been investigated in a handful of experiments, due in part to the difficulty of performing highly efficient continuous quantum measurements. The earliest experiments to continuously monitor individual quantum systems were in the regime of strong measurement, where the system is quickly projected into an eigenstate of measurement, destroying any information about the phase of a coherent superposition. In such experiments, it is possible to track the ‘quantum jumps’ between eigenstates [12–15]. Cavity quantum electrodynamics (CQED) experiments with Rydberg atoms have explored the weak measurement regime, tracking the quantum trajectories of a cavity field as it collapses from a coherent state into a photon number eigenstate [16]. Other CQED experiments have used a cavity probe to continuously track the position of individual Cesium atoms [17]. Quantum trajectories were first considered for solid state systems in the context of a quantum dot qubit monitored in real time by a quantum point contact charge sensor [18, 19]. In 2007, the conditional measurement dynamics of a quantum dot were investigated experimentally [20]. More recently …