非绝热几何量子逻辑门的脉冲设计  

Designing the Non-adiabatic Geometric Quantum Gates

作　　者：杨小勇 延英 陆杰 YANG Xiao-yong;YAN Ying;LU Jie(Department of Physics,Shanghai University,Shanghai 200444,China;School of Optoelectronic Science and Engineering&Collaborative Innovation Center of Suzhou Nano Science and Technology,Soochow University,Suzhou 215006,China;Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province&Key Lab of Modern Optical Technologies of Education Ministry of China,Suzhou 215006,China;Engineering Research Center of Digital Imaging and Display,Ministry of Education,Soochow University,Suzhou 215006,China;Shanghai Key Lab for Astrophysics,SShanghai 200234,China)

机构地区：[1]上海大学理学院物理系,系上海200444 [2]苏州大学光电科学与工程学院苏州纳米科技协同创新中心,江苏苏州1215006 [3]江苏省先进光学制造技术重点实验室教育部现代光学技术重点实验室,江苏苏州215006 [4]苏州大学数码激光成像与显示教育部工程研究中心,江苏苏州215006 [5]上海市星系与宇宙学半解析研究重点实验室,上海200234

出　　处：《量子光学学报》2023年第2期41-50,共10页Journal of Quantum Optics

基　　金：江苏省先进光学制造技术重点实验室自主研究课题(ZZ2109)。

摘　　要：量子逻辑门是实现量子计算的基本组件之一,而高保真度和高鲁棒性是量子逻辑门必不可少的关键性质。在实现量子逻辑门的各种方法中,利用几何相位的全局特性来构造量子逻辑门是一个有效的方法,它可以对一些局域扰动有比较好的容错性。本文在非绝热几何量子计算的框架下,在三能级系统中构造出了任意的单比特量子逻辑门,并创建出在实验中方便实现的脉冲形式。本文进一步研究了量子系统中存在频率失谐和脉冲振幅偏差的情况,并考虑量子系统与环境之间的退相干效应,以设计出具有更好鲁棒性能的脉冲波形。Quantum gates are essential for realizing quantum computing.How to achieve high-fidelity quantum gate operations,in the meanwhile maintaining high robustness against multiple control errors has been an important issue.Among various methods to realize quantum gates,using the geometric phase to construct the gates is an effective way,as the geometric phase has built-in noise-resilient characteristics.A general theoretical scheme to realize non-adiabatic non-abelian geometric quantum gates is to force the system to evolve along one of the time-dependent basis,then obtain the constrained conditions for the pulses.However,there might be some singular points in the constructed Rabi frequency,which are not preferred in certain quantum systems such as superconducting quantum circuits.In this work,we proposed a general condition to eliminate such singular points and developed smooth pulses in the three-level system with a A configuration.For the purpose of optimizing the gate performance,we introduced a new parameter k,which serves as an additional degree of freedom and is then used to modulate the shape of the pulses.The influence of parameter k on the gate performance has been numerically investigated in various aspects utilizing the Lindblad master equation,where the decoherence effects are considered.We taking superconducting qubit gates as an example,studied the robustness of pulses produced by different k values by introducing the detuning error and the Rabi frequency error.We found that the pulses with larger k values are more robust against the detuning error,while the Rabi error rate is not sensitive to k.The reason is that a larger k generates a higher instantaneous amplitude in the Rabi frequency when the gate duration is fixed,so that the perturbative effect is relatively smaller.On the other hand,the Rabi error is proportional to the Rabi frequency by definition,so its robustness is irrelevant to the pulse envelope.These results show that the theoretical scheme in this work provides us with a simple and feasi

关 键 词：量子比特 量子逻辑门 几何相位 几何量子计算 脉冲设计 

分 类 号：O433.4[机械工程—光学工程]