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Analysis of quantum error correction with symmetric hypergraph states
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Graph states have been used to construct quantum error correction codes for independent errors. Hypergraph states generalize graph states, and symmetric hypergraph states have been shown to allow for the correction of correlated errors. In this paper, it is shown that symmetric hypergraph states are not useful for the correction of independent errors, at least for up to 30 qubits. Furthermore, error correction for error models with protected qubits is explored. A class of known graph codes for this scenario is generalized to hypergraph codes.
Forward citations
Cited by 2 Pith papers
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Calibrated hypergraph states: II calibrated hypergraph state construction and applications
Calibrated hypergraph states over Galois rings generalize weighted hypergraph states, are stabilizer and locally maximally entangleable, and reduce to the weighted class in the qubit case only.
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Calibrated hypergraph states: I calibrated hypergraph and multi qudit state monads
Calibrated hypergraphs and multi-qudit states are shown to form graded Ω monads, providing a categorical foundation for a broad generalization of hypergraph states.
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