Pith Number

pith:T3UTLKWI

pith:2026:T3UTLKWI6WO3XLPXE5626MGFMH

not attested not anchored not stored refs resolved

Univariate Bicycle Quantum LDPC Codes: Explicit Logical Structure and Distance Bounds

Hessam Mahdavifar, Sheida Rabeti

Univariate bicycle codes reduce quantum LDPC design to a single polynomial while providing an explicit basis for logical operators and upper bounds on distance.

arxiv:2605.14173 v1 · 2026-05-13 · cs.IT · math.IT

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Claims

C1strongest claim

We provide an explicit algebraic characterization of the logical coset spaces by constructing a basis for the logical quotient space, yielding a complete parametrization of logical operators. Leveraging this structure, we derive upper bounds on the minimum distance by relating structured logical representatives to cycle-density properties of associated circulant matrices.

C2weakest assumption

The Frobenius relation applied to the defining polynomials preserves the sparsity, the quantum CSS structure, and the low-density parity-check property of the original generalized bicycle codes.

C3one line summary

Univariate bicycle codes give an explicit basis for logical operators and distance upper bounds in a restricted class of quantum LDPC codes while matching the performance of less constrained generalized and bivariate bicycle codes in simulations.

References

23 extracted · 23 resolved · 2 Pith anchors

[1] R. Gallager, “Low-density parity-check codes,”IRE Transactions on information theory, vol. 8, no. 1, pp. 21–28, 1962 1962

[2] Fifteen years of quantum LDPC coding and improved decoding strategies, 2015

[3] Quantum low-density parity- check codes, 2021

[4] Quantum low-density parity-check codes 2025

[5] Quantum kronecker sum-product low- density parity-check codes with finite rate, 2013

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:11.332228Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ee935aac8f59dbbadf7277daf30c561c4bb74b07d19a500396ba91d5c250575

Aliases

arxiv: 2605.14173 · arxiv_version: 2605.14173v1 · doi: 10.48550/arxiv.2605.14173 · pith_short_12: T3UTLKWI6WO3 · pith_short_16: T3UTLKWI6WO3XLPX · pith_short_8: T3UTLKWI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/T3UTLKWI6WO3XLPXE5626MGFMH \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 9ee935aac8f59dbbadf7277daf30c561c4bb74b07d19a500396ba91d5c250575

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6c1cba1f6b0a796308208d241e5fa85ce301ba8f22d4bde736cbc52b60fff54",
    "cross_cats_sorted": [
      "math.IT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-13T22:52:01Z",
    "title_canon_sha256": "e05b3e3f67066f86f1f796a8e24cf6464a4be98dc4289759e591529cefcc4f91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.14173",
    "kind": "arxiv",
    "version": 1
  }
}