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arxiv: 1310.6813 · v4 · submitted 2013-10-25 · 🪐 quant-ph · cs.ET· cs.LO

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Generators and relations for n-qubit Clifford operators

Peter Selinger (Dalhousie University , Canada)
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classification 🪐 quant-ph cs.ETcs.LO
keywords cliffordformnormalgeneratorsoperatorsrelationscircuitcircuits
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We define a normal form for Clifford circuits, and we prove that every Clifford operator has a unique normal form. Moreover, we present a rewrite system by which any Clifford circuit can be reduced to normal form. This yields a presentation of Clifford operators in terms of generators and relations.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Magic and Non-Clifford Gates in Topological Quantum Field Theory

    hep-th 2026-04 unverdicted novelty 5.0

    Non-Clifford gates including Ising, Toffoli, and T arise as exact path integrals in Chern-Simons and Dijkgraaf-Witten topological quantum field theories.