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量子计算中的量子完整性

Quantum Holonomies for Quantum Computing

Jiannis Pachos, Paolo Zanardi

备注：
16 pages, 2 figures, REVTEX
发表信息：
Int.J.Mod.Phys. B15 (2001) 1257-1286
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摘要：

完整量子计算是一种全几何的量子信息处理方法。在HQC策略中，信息被编码在哈密顿参数族的退化特征空间中。幺正量子门的计算网络是通过在控制流形中沿回路动态地驱动哈密顿参数来实现的。通过适当地设计这样的环，基础丛几何结构的非平凡曲率产生酉变换，即，实现所需酉变换的完整性。通用QC所需的条件是由控制流形上的非阿贝尔规范势（连接）的曲率来表示的。鉴于它们的几何性质，完整门对几种扰动和缺陷是鲁棒的。这一事实，以及绝热的方式，其中执行门，使在原则上HQC的一个有吸引力的方式向通用容错QC。

英文摘要：

Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of Hamiltonians. The computational network of unitary quantum gates is realized by driving adiabatically the Hamiltonian parameters along loops in a control manifold. By properly designing such loops the non-trivial curvature of the underlying bundle geometry gives rise to unitary transformations i.e., holonomies that implement the desired unitary transformations. Conditions necessary for universal QC are stated in terms of the curvature associated to the non-abelian gauge potential (connection) over the control manifold. In view of their geometrical nature the holonomic gates are robust against several kind of perturbations and imperfections. This fact along with the adiabatic fashion in which gates are performed makes in principle HQC an appealing way towards universal fault-tolerant QC.

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