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arXiv · 1307.7025

The ZX-calculus is complete for stabilizer quantum mechanics

Miriam Backens
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Abstract

The ZX-calculus is a graphical calculus for reasoning about quantum systems and processes. It is known to be universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation and post-selected pure projective measurement can be expressed in the ZX-calculus. The calculus is also sound, i.e. any equality that can be derived graphically can also be derived using matrix mechanics. Here, we show that the ZX-calculus is complete for pure qubit stabilizer quantum mechanics, meaning any equality that can be derived using matrices can also be derived pictorially. The proof relies on bringing diagrams into a normal form based on graph states and local Clifford operations.

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Miriam Backens. 2013-07-26. The ZX-calculus is complete for stabilizer quantum mechanics. https://doi.org/10.1088/1367-2630/16/9/093021

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