Kenta Kasai

Collaboration

Open problems

Concrete questions connecting explicit QLDPC construction, distance, decoding, and implementability.

Problem 1

Construction theory for regular quantum LDPC codes

Several explicit regular constructions exhibit unusually favorable combinations of rate, girth, finite-length distance evidence, and decoding performance. A unified theory explaining which algebraic and combinatorial structures are responsible is still missing.

Questions

  • Can the successful (3,12), (3,8), and (3,6) designs be derived from a common construction principle?
  • Can one systematically build smaller high-rate, large-girth instances rather than discovering them through extensive screening?
  • Can rigorous lower bounds approach the explicit upper-bound witnesses for the same code family?

Starting points: Kasai codes, other constructions, and the live catalog.

Problem 2

Finite-degree QLDPC codes reaching the GV bound

Finite-degree constructions can achieve strong distance-theoretic guarantees, but this does not automatically yield sparse practical syndrome measurement or favorable decoding dynamics.

Questions

  • How far can syndrome-extraction circuits or measurement operators be sparsified while retaining the distance behavior?
  • Can spatially coupled versions preserve finite degree, strong distance, and practical decoding performance at the same time?
  • Which structural conditions connect the asymptotic distance result to finite-length implementability?

Starting point: Finite-Degree Quantum LDPC Codes Reaching the Gilbert–Varshamov Bound and its proof material on GitHub.

Problem 3

Constructible ensembles with predictable sum-product BP performance

There is no fully satisfactory model that simultaneously supplies explicit constructible QLDPC families and an ensemble-level theory accurately predicting their sum-product BP performance by density evolution.

Questions

  • Can randomness be introduced without sacrificing the large-girth structure needed by finite constructions?
  • Can density evolution be made predictive for a genuinely constructible ensemble rather than only an idealized random model?
  • Can the same framework explain both waterfall behavior and low-error-rate failures?

Starting points: arXiv:2511.04634, the degree-distribution benchmark, and the FAQ.

Collaboration. If one of these questions overlaps with your work, please contact kenta@ict.eng.isct.ac.jp. Online seminar and informal research-meeting invitations are also welcome.