Mapping the optimal route between two quantum states

摘要

本期封面所示为对在量子空间里将两个点连接起来的各个量子轨迹的一个表述。当进行测量时,经典系统不会被移动。但量子系统却不是这样的-在量子系统中,连续监测会沿一个随机路径引导量子态。Steve Weber等人对一个量子位中的量子轨迹进行了跟踪,后者由被沉积在硅上的一个可调约瑟夫森结连接起来的两个铝桨叶组成。作者试图确定一个初始量子态与一个最终量子态之间的可能路径中哪个是最可能的,发现这些"最佳路径"与理论预测的路径相一致,这相当于经典力学中关于最小作用（least action)决定连接两个点之间正确路径的原理在量子力学中的翻版。除了帮助认识测量动态与一个系统之演变之间的互动外,这项研究还为对复杂量子系统及信息处理中的控制序列进行"第一原理"综合提供了新的机会。%A central feature of quantum mechanics is that a measurement result is intrinsically probabilistic. Consequently, continuously monitoring a quantum system will randomly perturb its natural unitary evolution. The ability to control a quantum system in the presence of these fluctuations is of increasing importance in quantum information processing and finds application in fields ranging from nuclear magnetic resonance to chemical synthesis. A detailed understanding of this stochastic evolution is essential for the development of optimized control methods. Here we reconstruct the individual quantum trajectories of a superconducting circuit that evolves under the competing influences of continuous weak measurement and Rabi drive. By tracking individual trajectories that evolve between any chosen initial and final states, we can deduce the most probable path through quantum state space. These pre- and post-selected quantum trajectories also reveal the optimal detector signal in the form of a smooth, time-continuous function that connects the desired boundary conditions. Our investigation reveals the rich interplay between measurement dynamics, typically associated with wavefunction collapse, and unitary evolution of the quantum state as described by the Schroedinger equation. These results and the underlying theory, based on a principle of least action, reveal the optimal route from initial to final states, and may inform new quantum control methods for state steering and information processing.