Graph-theoretic Simplification of Quantum Circuits with the ZX-calculus

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 simp...

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Vydáno v:Quantum (Vienna, Austria) Ročník 4; s. 279
Hlavní autoři: Duncan, Ross, Kissinger, Aleks, Perdrix, Simon, van de Wetering, John
Médium: Journal Article
Jazyk:angličtina
Vydáno: Verein 04.06.2020
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
Témata:
Computational Complexity
Computer Science
Data Structures and Algorithms
Discrete Mathematics
Physics
Quantum Physics
ISSN:2521-327X, 2521-327X
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Popis
Shrnutí: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.
ISSN:2521-327X
2521-327X
DOI:10.22331/q-2020-06-04-279