论文标题

在那里再次回来:电路提取故事

There and back again: A circuit extraction tale

论文作者

Backens, Miriam, Miller-Bakewell, Hector, de Felice, Giovanni, Lobski, Leo, van de Wetering, John

论文摘要

量子电路模型与基于测量的单向模型之间的翻译可用于验证和优化量子计算。他们至关重要地使用称为Gflow的属性。虽然为单向计算定义了GFlow,允许在Bloch球的三个不同平面中进行测量,但到目前为止,大多数研究都集中在仅包含XY平面中的测量值的计算上。在这里,我们将第一个电路萃取算法用于单向计算,其中包含所有三个平面中的测量和具有GFLOW的测量。该算法是有效的,所得电路不包含Ancillae。单向计算是使用ZX-Calculus表示的,因此该算法也代表了从ZX-DIAGRAM中提取电路的最通用过程。在开发该算法时,我们概括了仅包含XY平面测量的计算以前已知的几个概念和结果。我们汇总了几个已知的重写测量模式的规则,并使用ZX-Calculus以统一的符号形式化它们。这些规则用于通过减少Qubit的数量来简化测量模式,同时保留语义和Gflow的存在。结果可以通过将电路转换为模式并再次返回来应用于电路优化。

Translations between the quantum circuit model and the measurement-based one-way model are useful for verification and optimisation of quantum computations. They make crucial use of a property known as gflow. While gflow is defined for one-way computations allowing measurements in three different planes of the Bloch sphere, most research so far has focused on computations containing only measurements in the XY-plane. Here, we give the first circuit-extraction algorithm to work for one-way computations containing measurements in all three planes and having gflow. The algorithm is efficient and the resulting circuits do not contain ancillae. One-way computations are represented using the ZX-calculus, hence the algorithm also represents the most general known procedure for extracting circuits from ZX-diagrams. In developing this algorithm, we generalise several concepts and results previously known for computations containing only XY-plane measurements. We bring together several known rewrite rules for measurement patterns and formalise them in a unified notation using the ZX-calculus. These rules are used to simplify measurement patterns by reducing the number of qubits while preserving both the semantics and the existence of gflow. The results can be applied to circuit optimisation by translating circuits to patterns and back again.

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