ZX-calculus for the working quantum computer scientist
- URL: http://arxiv.org/abs/2012.13966v1
- Date: Sun, 27 Dec 2020 15:54:25 GMT
- Title: ZX-calculus for the working quantum computer scientist
- Authors: John van de Wetering
- Abstract summary: The ZX-calculus is a graphical language for reasoning about quantum computation.
This review gives a gentle introduction to the ZX-calculus suitable for those familiar with the basics of quantum computing.
The latter sections give a condensed overview of the literature on the ZX-calculus.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: The ZX-calculus is a graphical language for reasoning about quantum
computation that has recently seen an increased usage in a variety of areas
such as quantum circuit optimisation, surface codes and lattice surgery,
measurement-based quantum computation, and quantum foundations. The first half
of this review gives a gentle introduction to the ZX-calculus suitable for
those familiar with the basics of quantum computing. The aim here is to make
the reader comfortable enough with the ZX-calculus that they could use it in
their daily work for small computations on quantum circuits and states. The
latter sections give a condensed overview of the literature on the ZX-calculus.
We discuss Clifford computation and graphically prove the Gottesman-Knill
theorem, we discuss a recently introduced extension of the ZX-calculus that
allows for convenient reasoning about Toffoli gates, and we discuss the recent
completeness theorems for the ZX-calculus that show that, in principle, all
reasoning about quantum computation can be done using ZX-diagrams.
Additionally, we discuss the categorical and algebraic origins of the
ZX-calculus and we discuss several extensions of the language which can
represent mixed states, measurement, classical control and higher-dimensional
qudits.
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