Quantum Algorithms and Oracles with the Scalable ZX-calculus

Titouan Carette
(Université de Lorraine, CNRS, Inria, LORIA)
Yohann D'Anello
(Université de Lorraine, CNRS, Inria, LORIA)
Simon Perdrix
(Université de Lorraine, CNRS, Inria, LORIA)

The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum processes. However, in practice, such approaches are limited by the intrinsic low level nature of ZX calculus. The scalable notations have been proposed as an attempt to recover an higher level point of view while maintaining the topological rewriting rules of a graphical language. We demonstrate that the scalable ZX-calculus provides a formal, intuitive, and compact framework to describe and prove quantum algorithms. As a proof of concept, we consider the standard oracle-based quantum algorithms: Deutsch-Jozsa, Bernstein-Vazirani, Simon, and Grover algorithms, and we show they can be described and proved graphically.

In Chris Heunen and Miriam Backens: Proceedings 18th International Conference on Quantum Physics and Logic (QPL 2021), Gdansk, Poland, and online, 7-11 June 2021, Electronic Proceedings in Theoretical Computer Science 343, pp. 193–209.
Published: 18th September 2021.

ArXived at: http://dx.doi.org/10.4204/EPTCS.343.10 bibtex PDF
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