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

Autor: Anthony Munson, Quanlong Wang, Bob Coecke
Rok vydání: 2021
Předmět:
Zdroj: Electronic Proceedings in Theoretical Computer Science. 340:230-255
ISSN: 2075-2180
DOI: 10.4204/eptcs.340.12
Popis: 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.
Comment: In Proceedings QPL 2020, arXiv:2109.01534
Databáze: OpenAIRE
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