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An efficient algorithm to recognize local Clifford equivalence of graph states

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arxiv quant-ph/0405023 v2 pith:ODPCB5RX submitted 2004-05-05 quant-ph

An efficient algorithm to recognize local Clifford equivalence of graph states

classification quant-ph
keywords localgraphcliffordstatesalgorithmcomplementationsefficientequivalence
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In [Phys. Rev. A 69, 022316 (2004)] we presented a description of the action of local Clifford operations on graph states in terms of a graph transformation rule, known in graph theory as \emph{local complementation}. It was shown that two graph states are equivalent under the local Clifford group if and only if there exists a sequence of local complementations which relates their associated graphs. In this short note we report the existence of a polynomial time algorithm, published in [Combinatorica 11 (4), 315 (1991)], which decides whether two given graphs are related by a sequence of local complementations. Hence an efficient algorithm to detect local Clifford equivalence of graph states is obtained.

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Cited by 3 Pith papers

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

  1. Local Equivalences of Graph States

    quant-ph 2025-11 conditional novelty 8.0

    Graph states are LU-equivalent if and only if they are linked by r-local complementations for some integer r; LU-equivalence is decidable in quasi-polynomial time, and LU=LC holds on at most 19 qubits.

  2. The Structure of Circle Graph States

    quant-ph 2026-03 unverdicted novelty 7.0

    Circle graphs are closed under r-local complementation and bipartite circle graph states correspond one-to-one with planar code states whose MBQC is classically simulable.

  3. Adaptive Framework for Failure-Aware Protocols in Fusion-Based Graph-State Generation

    quant-ph 2026-01 conditional novelty 6.0

    Adaptive reuse of partially built graph states after failed fusion measurements, combined with graph-theoretic ordering, can cut expected fusion overhead by orders of magnitude relative to repeat-until-success.