LDGM codes enable syndrome measurement for QLDPC codes with controlled constant-weight stabilizers, yielding lower logical error rates than repeated extraction on a distance-5 surface code.
Projective plane and planar quantum codes
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abstract
Cellulations of the projective plane RP^2 define single qubit topological quantum error correcting codes since there is a unique essential cycle in H_1(RP^2;Z_2). We construct three of the smallest such codes, show they are inequivalent, and identify one of them as Shor's original 9 qubit repetition code. We observe that Shor's code can be constructed in a planar domain and generalize to planar constructions of higher genus codes for multiple qubits.
fields
quant-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
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Fault-Tolerant QLDPC Syndrome Measurement via LDGM Encoding
LDGM codes enable syndrome measurement for QLDPC codes with controlled constant-weight stabilizers, yielding lower logical error rates than repeated extraction on a distance-5 surface code.