Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.
Stabilizer codes can be realized as graph codes
4 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
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UNVERDICTED 4representative citing papers
A systematic graph-state protocol yields a family of [[n,1,3]] non-CSS codes that preserve bare-ancilla fault tolerance against hook errors and includes one code with higher rate than prior examples under depolarizing noise.
A graph-based bounded distance decoder corrects all errors up to a chosen weight in arbitrary stabilizer codes by representing stabilizers and syndromes as graphs and pruning the search space with a feed-forward structure.
New building block and protocol for all-photonic quantum repeaters using repeater graph states that reduces emissive memories at end nodes and integrates with memory-based systems.
citing papers explorer
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Fun with Graph States: Nonlocal Bell Pairs and the Arf Invariant
Graph-state inner products are governed by the F2-rank of the adjacency matrix and the Arf invariant, yielding a nonlocal Bell-pair factorization of the Hilbert space.
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Fault-tolerant syndrome extraction in [[n,1,3]] non-CSS code family generated using measurements on graph states
A systematic graph-state protocol yields a family of [[n,1,3]] non-CSS codes that preserve bare-ancilla fault tolerance against hook errors and includes one code with higher rate than prior examples under depolarizing noise.
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A graph-aware bounded distance decoder for all stabilizer codes
A graph-based bounded distance decoder corrects all errors up to a chosen weight in arbitrary stabilizer codes by representing stabilizers and syndromes as graphs and pruning the search space with a feed-forward structure.
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Architecture and protocols for all-photonic quantum repeaters
New building block and protocol for all-photonic quantum repeaters using repeater graph states that reduces emissive memories at end nodes and integrates with memory-based systems.