量子态估计简介及其在超导电路电动力学系统中的应用

A brief overview of quantum state estimation and its application in circuit quantum electrodynamics

量子态估计是量子计算以及量子调控的基础,一般分为量子态层析,即对未知量子态(或过程的初态)进行估计,以及量子滤波,即对量子态进行实时的估计.本文首先介绍了近年来量子态层析技术新的进展,内容包括极大似然方法,压缩感知方法和线性回归方法,并分析了它们的适用范围及各自的优缺点.进一步,基于量子计算的成熟载体超导电路电动力学系统,介绍了基于连续弱测量对量子态进行实时估计的贝叶斯方法,并分析了贝叶斯估计的适用情形.进一步,通过仿真实现了量子贝叶斯估计,可以很容易发现贝叶斯方法能够精确地实时追踪量子态的演化.

Quantum state estimation is of great importance in quantum computation and control. In general, quantum state estimation includes quantum state tomography that reconstructs the unknown quantum states(or the initial states of certain process) and quantum filter that real-time estimate the quantum states. Firstly, we introduce some recent progress of quantum state tomography including maximum-likelihood estimation, compressive sensing method and the linear regression estimation. We review their advantage and disadvantage and give their respective application range. Secondly, by focusing on the circuit quantum electrodynamics(circuit QED), we review the quantum Bayesian estimation method for real-time estimation of the quantum state, i.e., quantum filter, under the continuous weak quantum measurement. Moreover,we have implemented the quantum Bayesian estimation method by simulation, from which it is easy to find that the Bayesian estimation method can real-time precisely track the evolution of the quantum state.