Graph-theoretic simplification of quantum circuits with the ZX-calculus
Duncan, Ross and Kissinger, Aleks and Perdrix, Simon and van de Wetering, John (2020) Graph-theoretic simplification of quantum circuits with the ZX-calculus. Quantum, 4. 279. ISSN 2521-327X
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Abstract
We present a completely new approach to quantum circuit optimisation, based on the ZX-calculus. We first interpret quantum circuits as ZX-diagrams, which provide a flexible, lower-level language for describing quantum computations graphically. Then, using the rules of the ZX-calculus, we give a simplification strategy for ZX-diagrams based on the two graph transformations of local complementation and pivoting and show that the resulting reduced diagram can be transformed back into a quantum circuit. While little is known about extracting circuits from arbitrary ZX-diagrams, we show that the underlying graph of our simplified ZX-diagram always has a graph-theoretic property called generalised flow, which in turn yields a deterministic circuit extraction procedure. For Clifford circuits, this extraction procedure yields a new normal form that is both asymptotically optimal in size and gives a new, smaller upper bound on gate depth for nearest-neighbour architectures. For Clifford+T and more general circuits, our technique enables us to to `see around' gates that obstruct the Clifford structure and produce smaller circuits than naïve `cut-and-resynthesise' methods.
Creators(s): |
Duncan, Ross ![]() | Item type: | Article |
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ID code: | 73158 |
Keywords: | quantum science, ZX-calculus, quantum circuits, ZX-diagrams, graph, Electronic computers. Computer science, Computational Theory and Mathematics |
Subjects: | Science > Mathematics > Electronic computers. Computer science |
Department: | Faculty of Science > Computer and Information Sciences |
Depositing user: | Pure Administrator |
Date deposited: | 09 Jul 2020 15:05 |
Last modified: | 07 Dec 2020 10:55 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/73158 |
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