Simplification Strategies for the Qutrit ZX-Calculus

• URL: http://arxiv.org/abs/2103.06914v2
• Date: Tue, 21 Jun 2022 17:03:53 GMT
• Title: Simplification Strategies for the Qutrit ZX-Calculus
• Authors: Alex Townsend-Teague and Konstantinos Meichanetzidis
• Abstract summary: The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. The ZX-calculus has found applications in reasoning about quantum circuits, condensed matter systems, quantum algorithms, quantum error codes, and counting problems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The ZX-calculus is a graphical language for suitably represented tensor networks, called ZX-diagrams. Calculations are performed by transforming ZX-diagrams with rewrite rules. The ZX-calculus has found applications in reasoning about quantum circuits, condensed matter systems, quantum algorithms, quantum error correcting codes, and counting problems. A key notion is the stabiliser fragment of the ZX-calculus, a subfamily of ZX-diagrams for which rewriting can be done efficiently in terms of derived simplifying rewrites. Recently, higher dimensional qudits - in particular, qutrits - have gained prominence within quantum computing research. The main contribution of this work is the derivation of efficient rewrite strategies for the stabiliser fragment of the qutrit ZX-calculus. Notably, this constitutes a first non-trivial step towards the simplification of qutrit quantum circuits. We then give further unexpected areas in which these rewrite strategies provide complexity-theoretic insight; namely, we reinterpret known results about evaluating the Jones polynomial, an important link invariant in knot theory, and counting graph colourings.

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