Sequences of Bivariate Bicycle Codes from Covering Graphs

Sequences of Bivariate Bicycle Codes from Covering Graphs

by Abhishek Rajput

Formal & Physical Sciences Science — General & History PDScience: general issues
🎙 Abhishek Rajput 👥 137 📅 February 18, 2026 ⏱ 46 min 👁 81 📄 original study 🧭 2026-08-16
Available in: English (current) Français

Keywords

bivariate bicycle codescovering graphsquantum LDPChomologychain maps

Summary

This talk presents a method to generate infinite sequences of bivariate bicycle (BB) codes from a given BB code using covering graphs. The speaker defines h-cover codes, where the Tanner graph of the new code is an h-fold cover of the base code’s Tanner graph. They establish algebraic conditions on lattice parameters and defining polynomials for a BB code to be an h-cover code. By extending the covering map to a chain map, they induce projection and lifting maps on (co)homology, enabling the transfer of logical operators and automorphisms. The search space for cover codes is reduced, and they demonstrate that notable codes like the [[144,12,12]] gross code are cover codes. They also find new codes with weight-8 checks, including [[64,14,8]] and [[144,14,14]]. The talk proves bounds on parameters: for odd h, k_h ≥ k and d_h ≤ hd, and if k_h = k, then d ≤ d_h. They conjecture that for any h-cover BB code, parameters satisfy [[n_h = hn, k_h ≥ k, d ≤ d_h ≤ hd]]. The methods are expected to generalize to other group algebra codes.

180 words

Critical Evaluation

Value of the Information & Strength of the Argument

The talk provides significant value by introducing a systematic method to construct families of BB codes, which is crucial for practical quantum error correction. The argumentation is rigorous, with clear definitions, theorems, and proofs. The speaker builds on established concepts like chain complexes and covering graphs, and the logical flow is well-structured. The examples, such as the gross code, illustrate the applicability of the method. The conjectures and open questions are clearly stated, indicating a forward-looking perspective.

Scientific Rigor, Source Quality, Title Accuracy

The scientific rigor is high, with formal definitions, theorems, and proofs. The speaker references prior work, such as the IBM paper introducing BB codes and a paper by Virgil G. on lifted quantum CSS codes, but does not provide explicit citations or URLs. The title accurately reflects the content, focusing on sequences of BB codes from covering graphs. The talk is self-contained, providing necessary background on chain complexes and graph theory.

163 words

Title / Content Match

The title accurately reflects the content, which focuses on constructing sequences of bivariate bicycle codes via covering graphs.

Quality & Reliability

8/10

The talk presents original research with rigorous mathematical proofs, building on established concepts in quantum error correction and algebraic topology. The speaker is from Oxford, and the work is collaborative with researchers from University of Edinburgh and UCL. The presentation is clear and well-structured, with technical depth appropriate for a specialized audience.

Key Moments

Markers derived by PSI from the transcript: the creator did not define chapters.

Cited Sources

  • IBM paper on bivariate bicycle codes — Introduced BB codes
  • Paper by Virgil G. on lifted quantum CSS codes — Related work on lifted codes

Concurring Sources

  • IBM paper on bivariate bicycle codes — The talk builds on the BB code framework introduced by IBM.

Contribution & Novelties

The talk introduces a novel method to generate sequences of BB codes via covering graphs, which is a significant contribution to the field. It provides a systematic way to construct families of codes with controlled parameters, which is crucial for practical implementations. The method also reduces the search space for new codes, as demonstrated by finding new codes with weight-8 checks. The theoretical bounds on parameters are valuable for understanding the trade-offs in code design.

Pour aller plus loin :

111 words

Radar Profile

The radar profile shows high scores in information quantity, quality, and technical level, with a slightly lower but still strong reliability score. This indicates a technically dense and reliable presentation, suitable for a specialized audience.

Reliability 8/10