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      A note on AND-gates in ZX-calculus: QBC-completeness and phase gadgets

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          Abstract

          In this note we exploit the utility of the triangle symbol in ZX-calculus, and its role within the ZX-representation of AND-gates in particular. First, we derive a decomposition theorem for large phase gadgets, something that is of key importance to recent developments in quantum circuit optimisation and T-count reduction in particular. Then, using the same rule set, we prove a completeness theorem for quantum Boolean circuits (QBCs), which adds to the plethora of complete reasoning systems under the umbrella of ZX-calculus.

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          A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics

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            Transformation rules for designing CNOT-based quantum circuits

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              Diagrammatic Reasoning beyond Clifford+T Quantum Mechanics

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                Author and article information

                Journal
                15 October 2019
                Article
                1910.06818
                b691ef22-aaf7-4dd2-94d2-50e4dd0cb29a

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                a technique note, 25 pages
                quant-ph

                Quantum physics & Field theory
                Quantum physics & Field theory

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