基于超导电路量子电动力学系统的非线性测量研究

Quantum measurements always disturb the system being measured and induce decoherence. According to the theory of open quantum system, both the evolution of the quantum state and its decoherence depend on the system-apparatus coupling strength and the basis in which the system is measured. Among measurement apparatus, superconducting Josephson junction circuits have great advantages because these are simultaneously nonlinear and non-dissipative. These types of circuits provide several simple high-fidelity qubit readout mechanisms, such as state-dependent dispersive-shift measurements and nonlinear measurements. This circuit is not only an excellent test-bed for studying the fundamental properties of quantum measurements, but it is also well suited for quantum control, especially quantum feedback control. First, superconducting qubits are localized and there is a high degree of electrical control over them. Second, the strong coupling between qubits and the resonator allows for a well-controlled atom-field interaction. Finally, the feedback control can be applied to either the qubits or the microwave resonator mode. This proposed project focuses on designing an effective nonlinear measurement setup with signal amplification and measurement-based feedback control, which are essential ingredients in future implementations of on-chip technologies. We expect the results of this work to be of considerable interest not only to the quantum control and quantum information community, but also to experimentalists who are involved in realizing control in mesoscopic systems. Further, this work is aimed at providing methods that allow the demonstration of measurement-based feedback control that can be readily implemented with present experimental technology, and thus should be especially relevant to experimentalists working with superconducting circuits.

有效地测量与反馈量子系统是量子技术走向实用化的本质问题之一。超导电路量子电动力学系统不仅具有非线性的测量放大等性质，更是实行量子反馈控制的良好载体。对于电路量子电动力学系统目前已有外置电场、控制耦合系数、以及利用辅助耦合系统进行控制等控制手段。本项目着重于考虑超导电路量子电动力学系统的kerr非线性测量以及反馈控制。我们将定量化刻画该系统有效的非线性区域，在该区域中进一步定量刻画测量的反作用以及分析系统稳定性的参数依赖关系。从而进一步分析量子信息读取与测量反作用的博弈，以及提升信息提取的信噪比SNR. 最后，利用超导电路量子电动力学系统的可延拓性进行混杂系统的信息存储和信息传输等方面的研究。

量子测量与估计是量子计算以及量子调控的基础. 其中量子态估计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。本项目研究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, 并精确地实时追踪量子态的演化. 同时，还研究了量子系统的参数估计.基于量子随机主方程给出的计算Fisher信息的一个有效算法，并考虑了Kerr非线性机制进行量子参数估计比线性机制带来的优点，并用多目标优化方法考虑了量子参数估计精度与测量带来的量子态变形之间的博弈，给出了多目标优化的最优解. 基于本项目资助，发表或接受发表7篇论文，另有3篇在投稿中，申请发明专利1项，论文被多个国际权威研究组引用。研究工作为量子反馈控制以及量子自适应控制打下良好的基础。