Geometric and holonomic quantum computation utilizes intrinsic geometric properties of quantum-mechanical state spaces to realize quantum logic gates. Since both geometric phases and quantum holonomies are global quantities depending only on the evolution paths of quantum systems, quantum gates based on them possess built-in resilience to certain kinds of errors. This review provides an introduction to the topic as well as gives an overview of the theoretical and experimental progress for constructing geometric and holonomic quantum gates and how to combine them with other error-resistant techniques.

中文翻译：

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几何和完整量子计算

几何和完整量子计算利用量子力学状态空间的固有几何特性来实现量子逻辑门。由于几何相位和量子完整性都是全局量，仅取决于量子系统的演化路径，因此基于它们的量子门对某些类型的错误具有内置的弹性。本综述介绍了该主题，并概述了构造几何和完整量子门的理论和实验进展以及如何将它们与其他防错技术相结合。