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

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.

arXiv commentIn Proceedings QPL 2020, arXiv:2109.01534

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Cited by in corpus (5)

• Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences
• Algebraic complete axiomatisation of ZX-calculus with a normal form via elementary matrix operations
• Lower T-count with faster algorithms
• Differentiating and Integrating ZX Diagrams with Applications to Quantum Machine Learning
• Scalable Spider Nests (...Or How to Graphically Grok Transversal Non-Clifford Gates)