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Projective plane and planar quantum codes

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arxiv quant-ph/9810055 v1 pith:5QLD4P4I submitted 1998-10-18 quant-ph

classification quant-ph
keywords codesplanarcodeplaneprojectivequantumqubitshor
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Fault-Tolerant QLDPC Syndrome Measurement via LDGM Encoding

    quant-ph 2026-05 unverdicted novelty 5.0 of 10

    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.

  2. Design Automation in Quantum Error Correction

    quant-ph 2025-07 conditional novelty 2.0 of 10

    A comprehensive review of automated tools and methods for designing quantum error-corrected circuits, with case studies on T-gate optimization, surface-code layout, ML decoders, and verification.

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