Quantum

Quantum error correcting codes from quiver moduli: Grassmannians, cyclic monodromy, and argyle collision divisors

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Briefings

A research team constructs exact finite-dimensional quantum error-correcting codes using twisted cyclic and argyle quiver moduli on the projective line. The study establishes that the largest Kostka multiplicity determines the optimal dimension for correcting the full monodromy algebra, achieving a logical dimension of t+1 for a balanced three-cycle with t zeroes per arrow. At t=1, explicit codewords for a qubit on six sheets are provided, and collision-parity ranks are computed. The work also derives a conditional criterion for recovery across splitting types and identifies a higher-rank Grassmannian example.

Key points

• The study constructs exact finite-dimensional quantum error-correcting codes from twisted cyclic and argyle quiver moduli on the projective line.
• The optimal logical dimension for correcting the full monodromy algebra is t+1, uniquely attained by the block indexed by (2t,t) for a balanced three-cycle with t zeroes per arrow.

Context

This research builds on a diagrammatic field-theory programme for quantum error correction proposed by the first author, utilizing quiver moduli on the projective line to create exact finite-dimensional codes. The findings advance the understanding of how spectral zeroes are distributed among arrows and how noiseless recovery is achieved through root monodromy acting on Specht factors.

Limitations

The evidence is limited to the arXiv preprint arXiv:2611.05526v1, which is untrusted data. The study focuses on the projective line and specific quiver moduli; additional background on the broader field-theory programme is not supplied. The results are presented as established facts within the preprint context, though the preprint status and uncertainty remain inherent to the source.

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