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标题：PBS-Calculus: A Graphical Language for Coherent Control of Quantum Computations
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作者：Alexandre Clment ; Simon Perdrix
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：170
页码：24:1-24:14
DOI：10.4230/LIPIcs.MFCS.2020.24
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We introduce the PBS-calculus to represent and reason on quantum computations involving coherent control of quantum operations. Coherent control, and in particular indefinite causal order, is known to enable multiple computational and communication advantages over classically ordered models like quantum circuits. The PBS-calculus is inspired by quantum optics, in particular the polarising beam splitter (PBS for short). We formalise the syntax and the semantics of the PBS-diagrams, and we equip the language with an equational theory, which is proved to be sound and complete: two diagrams are representing the same quantum evolution if and only if one can be transformed into the other using the rules of the PBS-calculus. Moreover, we show that the equational theory is minimal. Finally, we consider applications like the implementation of controlled permutations and the unrolling of loops.
关键词：Quantum Computing; Diagrammatic Language; Completeness; Quantum Control; Polarising Beam Splitter; Categorical Quantum Mechanics; Quantum Switch