### Abstract

Language | English |
---|---|

Pages | 50-62 |

Number of pages | 13 |

Journal | Electronic Proceedings in Theoretical Computer Science |

Volume | 171 |

DOIs | |

Publication status | Published - 27 Dec 2014 |

### Fingerprint

### Keywords

- quantum physics
- stabilizer quantum mechanics
- ZX-calculus

### Cite this

*Electronic Proceedings in Theoretical Computer Science*,

*171*, 50-62. https://doi.org/10.4204/EPTCS.171.5

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*Electronic Proceedings in Theoretical Computer Science*, vol. 171, pp. 50-62. https://doi.org/10.4204/EPTCS.171.5

**Pivoting makes the ZX-calculus complete for real stabilizers.** / Duncan, Ross; Perdrix, Simon.

Research output: Contribution to journal › Conference Contribution

TY - JOUR

T1 - Pivoting makes the ZX-calculus complete for real stabilizers

AU - Duncan, Ross

AU - Perdrix, Simon

PY - 2014/12/27

Y1 - 2014/12/27

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

VL - 171

SP - 50

EP - 62

JO - Electronic Proceedings in Theoretical Computer Science

T2 - Electronic Proceedings in Theoretical Computer Science

JF - Electronic Proceedings in Theoretical Computer Science

SN - 2075-2180

ER -