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Stabilizer codes can be realized as graph codes
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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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Cited by 5 Pith papers
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Local Equivalences of Graph States
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.
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Symmetry-guided constructions of absolutely maximally entangled states in five open cases
New explicit Hermitian self-dual MDS codes yield AME(12,5), AME(18,11), AME(18,13), and their 17-party projections.
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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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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.
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