bibkey: cowtanburton2024csssurgery
authors: "Alexander Cowtan; Simon Burton"
year: 2024
title: "CSS code surgery as a universal construction"
doi: 10.22331/q-2024-05-14-1344
url: https://arxiv.org/abs/2301.13738v6
claim: "Appendix D, Conjecture D.1 asks whether pushouts of basis-preserving monic spans of LDPC CSS complexes remain LDPC."
strata_touched:
  - D5/S3/Quantum/Information/CssMonicPushoutLdpc
license: citation-only
triage: anchor

CSS code surgery as a universal construction

Alexander Cowtan and Simon Burton, “CSS code surgery as a universal construction,” Quantum 8 (2024), 1344, arXiv:2301.13738v6.

Definition 3.4 says that a chain map is basis-preserving when every matrix at each component maps basis elements to basis elements. Definition 5.1 describes the componentwise pushout and Lemma 5.4 gives a basis-preserving choice. Section 4.1 defines LDPC families by bounded row and column Hamming weights. Appendix D, Conjecture D.1 asks whether a family of basis-preserving monic spans of Z-type complexes of quantum LDPC codes has an LDPC pushout family.

Appendix D, Conjecture D.1 (Appendix D) states: “Let C• ←f• A• →g• D• be a basis-preserving monic span in Ch(MatF2), and let Q• be the pushout chain complex of this monic span. Further, let the monic span be a representative of a family of monic spans which are parameterised by some n ∈ ℕ, and let A•, C• and D• be the Z-type complexes of quantum LDPC codes. Then (Q•, Q•) is also LDPC.”

The formal statement uses length-two complexes over ZMod 2, basis functions on Fin dimensions, the quotient basis from Lemma 5.4, and the row and column weight definitions from Section 4.1. The source’s parameterisation phrase is read as an arbitrary natural-indexed family. The settlement proves the explicit single-span row and column bounds and therefore the family conclusion. The literature screen recorded in issue #19488 is incomplete; the thesis check and full novelty status remain ASSUMED-UNVERIFIED.

Verified locator

• DOI: 10.22331/q-2024-05-14-1344
• Source: https://arxiv.org/abs/2301.13738v6