基于系统与热库联合态演化的开放系统几何相位研究

Investigation of geometric phases of open systems is important for implementation of geometric quantum computation that is robust against the effects of noises. In this project, we plan to study the geometric phases of open systems and investigate the effects of decoherence under the adiabatic and nonadiabatic conditions, respectively. In contrast with previous studies, we require neither to continuously monitor the state of the reservoir nor to trace out its degrees of freedom. Instead, we will consider the quantum system and reservoir as a whole. The geometric phase obtained in this way can completely reflect the geometric feature for the joint state evolution path of the quantum system and reservoir. First we will give an explicit definition on the condition for parallel transportation and the corresponding geometric phase for the joint system. Then we will investigate the geometric phase for a two-level system driven by a classical field and coupled to the environment under the adiabatic and nonadiabatic evolutions in this framework. On this basis, we will analyze the effect of decoherence on this phase and investigate the relation between the corresponding correction term and the system-reservoir entanglement. Next, we generalize the results, and study the geometric phase acquired by the state evolution of the composite system comprised of the Jaynes-Cummings model and reservoir. Finally, we study the features of the geometric phase for a harmonic oscillator that is driven by a classical field and coupled to the environment, and analyze the effects of dissipation on the fidelity of quantum logic gates based on this kind of phase.

开放系统几何相位的研究对可抵抗噪声影响的几何量子计算的实现具有重要意义。本项目拟研究开放系统中的几何相位，并探讨在绝热与非绝热条件下消相干效应的影响。与已有研究不同的是，我们既不要求对热库态的连续监测，也不需要将其自由度求迹消去，而是将量子系统与热库作为一个整体来考虑。这样所得到的几何相位可完整反映量子系统与热库联合态演化路径的几何属性。我们将首先对联合系统的平移条件及相关的几何相位做出明确的定义，然后在此框架中研究受经典场驱动并与环境耦合的双能级系统在绝热与非绝热演化情形下所产生的几何相位。在此基础上，进一步分析消相干对该相位的影响，并探讨相应修正项与系统－热库纠缠的关系。将结果进行推广，研究Jaynes-Cummings模型与热库所构成复合系统的态演化所产生的几何相位。最后研究受经典场驱动并与环境耦合的谐振子的几何相位特征，并分析耗散对基于这种相位的量子逻辑门保真度的影响。

几何相位是一种重要的量子力学效应，对可抵抗噪声影响的容错量子计算的实现具有重要意义。本项目着重研究开放系统的几何相位及其在量子计算中的应用。对所研究的量子系统与热库所构成联合系统的平移条件及相关的几何相位给出了明确的定义，在此基础上研究了受经典场驱动并与环境耦合的双能级系统经过一个循环演化所产生的几何相位。分析了系统与热库耦合所导致的退相干对该相位的影响，得到了相应修正项，并探讨了该相位与系统－热库纠缠的关系。进一步分析了与热库耦合的Jaynes-Cummings模型及受驱动谐振子的几何相位特征，并计算了相应的修正项。结果表明，基于系统-热库联合态演化所计算出的几何相位对耗散不敏感。在超导电路系统中提出并演示了连续变量系统几何相位的测量及多比特几何量子相位门的实现方案。在以往的多比特量子相位门实验中，需要将这些门分解为两比特及单比特的门，因此所需要的操作次数随着比特数量的增加而急剧增加，而我们的方案只要求一次几何操作，对于量子计算的实现具有重要意义。基于量子比特与谐振腔的相互作用，提出并演示了对量子比特波动性和粒子性同时观测的方案。基于谐振器所诱导的比特-比特耦合动力学，设计并演示了多对超导比特并行逻辑操作和多个比特最大纠缠态的实现方案。

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