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arXiv · 1910.06818

AND-gates in ZX-calculus: Spider Nest Identities and QBC-completeness

Anthony Munson·Bob Coecke·Quanlong Wang
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Abstract

In this paper we exploit the utility of the triangle symbol which has a complicated expression in terms of spider diagrams in ZX-calculus, and its role within the ZX-representation of AND-gates in particular. First, we derive spider nest identities which are 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) whose rewriting rules can be directly used for a new method of T-count reduction. We give an algorithm based on this method and show that the results of our algorithm outperform the results of all the previous best non-probabilistic algorithms.

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Anthony Munson, Bob Coecke, Quanlong Wang. 2021-09-06. AND-gates in ZX-calculus: Spider Nest Identities and QBC-completeness. https://doi.org/10.4204/eptcs.340.12

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