超导量子电路的量子效应与超导量子比特的退相干

The practical valuable quantum computation needs many qubits, and three kinds of qubits (charge qubits, phase qubits and flux qubits) can be realized by using superconducting Josephson junctions. In view of the significance of Josephson junctions in the solid-state quantum computation, it is necessary to construct the quantum theory of the complicated mesoscopic superconducting circuits consisting of a lot of Josephson junctions. In this work, based on the National Natural Science Foundation of China (Grant No.10574060) finished by us, we try to study the quantum fluctuation, quantum entanglement and other quantum effects existing in the mesoscopic circuits including many Josephson junctions, and construct the quantum theory of such kind of circuits in consideration of the discreteness of Cooper-pairs. We try to study the nonlinear effect caused by the discreteness of Cooper-pairs, explore the interacting law between qubits based on Josephson junctions and the external environment, and among qubits, search for the source and the microscopic mechanism of noise that causes the superconducting qubits decoherence. We try to propose the theory schemes that reduce noise and improve superconducting qubits coherence so as to provide some theoretical reference for the experimenter to realize the large scale integration of the solid-state qubits.

真正有价值的量子计算需许多个量子比特,利用超导约瑟夫森结可实现三种类型的量子比特(电荷量子比特、位相量子比特和磁通量子比特);基于约瑟夫森结在固态量子计算中的重要性,有必要建立由多个约瑟夫森结组成的复杂介观超导电路的量子理论。本项目拟将在我们已结题国家自然科学基金项目(10574060)的基础上,研究在含有多个约瑟夫森结介观电路中的量子涨落、量子纠缠及其它量子效应;建立在考虑库珀对离散性情况下的含有多个约瑟夫森结复杂介观电路的量子理论,试图研究由库珀对离散性而导致的非线性效应;探索基于约瑟夫森结的量子比特之间以及与环境之间的相互作用规律,寻找引起超导量子比特退相干的噪声源的产生原因及其微观机制,并试图提出降低噪声、提高超导量子比特相干性的理论方案,以便为实验工作者实现固态量子比特的大规模集成提供一些理论参考。

含有约瑟夫森结的固态量子计算方案在实现现实的量子计算方面被人们寄予了厚望，研究这类系统的量子效应及其量子态的退相干机制具有较高的理论价值。鉴于此，本项目在我们已结题国家自然科学基金项目(10574060)的基础上，研究了受两种典型环境热库(玻色库和自旋库)影响的单个磁通量子比特的动力学演化和退相干；借助于正则量子化方法，给出了考虑超导环自感的基于超导量子干涉仪电荷量子比特的量子化，并借助于短时近似讨论了量子比特在欧姆情形下的退相干效应，进一步研究了穿过两超导环的外部经典磁通对体系中存在的量子纠缠的调控规律以及两超导环之间的互感对量子纠缠的影响。另外，针对量子纠缠态表象在量子计算领域的重要价值，应用纠缠态表象解析研究了双变量厄米多项式态的魏格纳函数以及退相干机制，并利用魏格纳算符和纠缠态投影算符所满足的拉登变换，得到了此态的层析图函数，讨论了此态的魏格纳函数在热通道中的演化特性；利用热纠缠态表象给出了扩散的非谐振子密度算符的确切时间演化公式和它的魏格纳函数。可以相信，本项研究成果的取得，对于人们最终实现固态量子计算机将会具有某些理论意义。. 目前，已发表论文9篇，其中被SCI收录论文7篇，培养研究生(毕业) 3人。