用正交态方法实现非绝热几何量子计算  

Non-adiabatic Geometric QC Implemented with Orthogonal State Method

作　　者：高玉梅[1] 胡连[1] 

机构地区：[1]华南师范大学物理与电信工程学院,广东广州510631

出　　处：《光电子技术与信息》2005年第2期28-32,共5页Optoelectronic Technology & Information

基　　金：国家科学基金资助(10474022)

摘　　要：精确求解了自旋1/2粒子在旋转磁场下的Bloch方程,并用旋转坐标系方法得到此系统的精确波函数。对演化波函数取绝热极限可得到Berry几何相,并将这些结果与Bitter等的慢中子实验做了比较。对旋转磁场下的一般AA循环,本文得到了Aharonov-Anandan(AA)总相位和几何相的解析结果。当采取正交态的一般方法,即取入射初态为等权重的两个正交态的叠加,可以证明非对角动力学相与非对角几何相同对角动力学相一样在任意时刻抵消,剩下几何相的对角部分。对匀速旋转的圆锥磁场,此几何相类似Berry几何相为时间的线性函数。最后也讨论了正交态方法和最近用实验实现非绝热几何量子门工作的关系。This article obtained the exact wave function and accurate solution of Bloch equation for spin-1/2 particle under the rotating magnetic field. Berry's geometric phase was obtained by taking the adiabatic limit on the exact evolutional wave function and was compared with the slow helical neutron experiment done by Bitter and Dubbers. The analytic results of AA geometric phase and the total phase have been obtained for a general cyclic evolution in a conic magnetic field. This article also presented a general description for orthogonal state method. By taking the initial state as the two superposed orthogonal states with equal weight, we proved that the off-diagonals of geometric and dynamic phases cancel exactly at any time. The diagonal parts of dynamic phase also cancel automatically. For the uniform rotating magnetic field, the diagonal geometric phase will evolve as a linear function like the Berry's case. We also discussed the relationship between our studies and the experiment recently done by Du et al.

关 键 词：几何量子计算 正交态方法 

分 类 号：O411.1[理学—理论物理]