Non-Abelian Berry connections for quantum computation
Non-Abelian Berry connections for quantum computation
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DOI：
10.1103/physreva.61.010305
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发表时间：
1999-07
影响因子：
2.9
通讯作者：
J. Pachos;P. Zanardi;M. Rasetti
中科院分区：
文献类型：
--
作者：
J. Pachos;P. Zanardi;M. Rasetti
在量子计算的完整方法中，信息被编码在哈密顿参量族的简并本征空间中，并由相关的完整门操纵。这些是实现在非阿贝尔贝瑞连接，并通过驱动控制参数沿着绝热回路。我们展示了一个特定的模型如何明确地确定生成任何所需逻辑门的循环，从而产生一组通用的酉变换。在多体系统中，酉变换可以通过局部完整门序列有效地实现。此外，获得所需的哈密顿家族，频繁重复的脉冲的基础上，一个概念性的计划进行了讨论，连同一个可能的过程，从而可以准备的初始状态和最后一个可以测量。
In the holonomic approach to quantum computation, information is encoded in a degenerate eigenspace of a parametric family of Hamiltonians and manipulated by the associated holonomic gates. These are realized in terms of the non-Abelian Berry connection and are obtained by driving the control parameters along adiabatic loops. We show how it is possible for a specific model to explicitly determine the loops generating any desired logical gate, thus producing a universal set of unitary transformations. In a multipartite system unitary transformations can be implemented efficiently by sequences of local holonomic gates. Moreover, a conceptual scheme for obtaining the required Hamiltonian family, based on frequently repeated pulses, is discussed, together with a possible process whereby the initial state can be prepared and the final one can be measured.