Analysis of quantum error correction with symmetric hypergraph states

Abstract

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.

18 pages, 2 figures; corrected number of figures; 16.02.2018: removed minor inconsistencies in font choice, added supplemental files 23.02.2018: added journal ref

References in corpus (8)

• Quantum Error Correcting Codes Using Qudit Graph States
• Entanglement and nonclassical properties of hypergraph states
• Encoding Hypergraphs into Quantum States
• Local unitary symmetries of hypergraph states
• Graphical description of unitary transformations on hypergraph states
• Analysis of quantum error correction with symmetric hypergraph states
• Local Pauli stabilizers of symmetric hypergraph states
• Quantum Error-Correcting Codes with Preexisting Protected Qubits

Cited by in corpus (7)

• Analysis of quantum error correction with symmetric hypergraph states
• Entanglement Purification of Hypergraph States
• Phase Squeezing of Quantum Hypergraph States
• Multipartite entanglement sudden death and birth in randomized hypergraph states
• Graphical Framework for Non-Gaussian Quantum States
• Randomized hypergraph states and their entanglement properties
• Geometric Graph-Theoretic Aspects of Quantum Stabilizer Codes