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Quantum Physics

arXiv:1910.06818 (quant-ph)
[Submitted on 15 Oct 2019 (v1), last revised 6 Sep 2021 (this version, v3)]

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

Authors:Anthony Munson (University of Oxford), Bob Coecke (Cambridge Quantum Computing Ltd.), Quanlong Wang (Cambridge Quantum Computing Ltd.)
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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.
Comments: In Proceedings QPL 2020, arXiv:2109.01534
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:1910.06818 [quant-ph]
  (or arXiv:1910.06818v3 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1910.06818
Journal reference: EPTCS 340, 2021, pp. 230-255
Related DOI: https://doi.org/10.4204/EPTCS.340.12

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 15 Oct 2019 14:40:39 UTC (139 KB)
[v2] Sun, 13 Dec 2020 23:59:34 UTC (145 KB)
[v3] Mon, 6 Sep 2021 01:00:45 UTC (78 KB)
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