Pivoting makes the ZX-calculus complete for real stabilizers

Ross Duncan; Simon Perdrix

doi:10.4204/EPTCS.171.5

Pivoting makes the ZX-calculus complete for real stabilizers

Ross Duncan, Simon Perdrix

Research output: Contribution to journal › Conference Contribution › peer-review

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Abstract

We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.

Original language	English
Pages (from-to)	50-62
Number of pages	13
Journal	Electronic Proceedings in Theoretical Computer Science
Volume	171
DOIs	https://doi.org/10.4204/EPTCS.171.5
Publication status	Published - 27 Dec 2014

Keywords

quantum physics
stabilizer quantum mechanics
ZX-calculus

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10.4204/EPTCS.171.5

Duncan-Perdrix-EPTCS-2014-Pivoting-makes-the-ZX-calculus-complete-forFinal published version, 138 KBLicence: CC BY-ND 4.0

http://eptcs.web.cse.unsw.edu.au/paper.cgi?QPLX.5

Cite this

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title = "Pivoting makes the ZX-calculus complete for real stabilizers",

abstract = "We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics. ",

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AU - Perdrix, Simon

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N2 - We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.

AB - We show that pivoting property of graph states cannot be derived from the axioms of the ZX-calculus, and that pivoting does not imply local complementation of graph states. Therefore the ZX-calculus augmented with pivoting is strictly weaker than the calculus augmented with the Euler decomposition of the Hadamard gate. We derive an angle-free version of the ZX-calculus and show that it is complete for real stabilizer quantum mechanics.

KW - quantum physics

KW - stabilizer quantum mechanics

KW - ZX-calculus

U2 - 10.4204/EPTCS.171.5

DO - 10.4204/EPTCS.171.5

M3 - Conference Contribution

SN - 2075-2180

VL - 171

SP - 50

EP - 62

JO - Electronic Proceedings in Theoretical Computer Science

JF - Electronic Proceedings in Theoretical Computer Science

ER -

Pivoting makes the ZX-calculus complete for real stabilizers

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Keywords

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