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International Conference on Reversible Computation

RC 2018: Reversible Computation pp 144–161Cite as

ZX-Rules for 2-Qubit Clifford+T Quantum Circuits

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11106))

Abstract

ZX-calculus is a high-level graphical formalism for qubit computation. In this paper we give the ZX-rules that enable one to derive all equations between 2-qubit Clifford+T quantum circuits. Our rule set is only a small extension of the rules of stabiliser ZX-calculus, and substantially less than those needed for the recently achieved universal completeness. One of our rules is new, and we expect it to also have other utilities.

These ZX-rules are much simpler than the complete of set Clifford+T circuit equations due to Selinger and Bian, which indicates that ZX-calculus provides a more convenient arena for quantum circuit rewriting than restricting oneself to circuit equations. The reason for this is that ZX-calculus is not constrained by a fixed unitary gate set for performing intermediate computations.

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Acknowledgements

This work was sponsored by Cambridge Quantum Computing Inc. for which we are grateful. QW also thanks Kang Feng Ng for useful discussions.

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Authors and Affiliations

  1. University of Oxford, Oxford, UK

    Bob Coecke & Quanlong Wang

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  1. Bob Coecke
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  2. Quanlong Wang
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Correspondence to Quanlong Wang .

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Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. University of Leicester, Leicester, United Kingdom

    Irek Ulidowski

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Coecke, B., Wang, Q. (2018). ZX-Rules for 2-Qubit Clifford+T Quantum Circuits. In: Kari, J., Ulidowski, I. (eds) Reversible Computation. RC 2018. Lecture Notes in Computer Science(), vol 11106. Springer, Cham. https://doi.org/10.1007/978-3-319-99498-7_10

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  • DOI: https://doi.org/10.1007/978-3-319-99498-7_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99497-0

  • Online ISBN: 978-3-319-99498-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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