Pith Number

pith:7HKE4SIT

pith:2026:7HKE4SITYQLHRQ2W7AAECTMASR

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Quantum Precoded Polar Codes

Matthieu R. Bloch, Shrinivas Kudekar, Tyler Kann

Rate-1 precoded polar codes yield CSS quantum codes with logical error rates matching a much larger surface code.

arxiv:2605.12796 v1 · 2026-05-12 · cs.IT · math.IT · quant-ph

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\pithnumber{7HKE4SITYQLHRQ2W7AAECTMASR}

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We present codes of dimension [[256, 2]] and [[512, 2]] that have logical error rates similar to the [[1201, 1, 25]] surface code over the depolarizing channel.

C2weakest assumption

The benefits of classical rate-1 precoding for short-blocklength polar codes transfer directly to the quantum CSS setting after genetic-algorithm optimization of the rate profile and precoder.

C3one line summary

Quantum CSS codes derived from precoded polar codes match the logical error performance of a large surface code at small block lengths [[256,2]] and [[512,2]] over depolarizing noise.

References

26 extracted · 26 resolved · 0 Pith anchors

[1] Gottesman,Stabilizer codes and quantum error correction 1997

[2] Good Quantum Error-Correcting Codes Exist, 1996

[3] Multiple-particle interference and quantum error correction, 1954

[4] Efficient Polar Coding of Quantum Information, 2012

[5] Fault-tolerant preparation of quantum polar codes encoding one logical qubit, 2023

Receipt and verification

First computed	2026-05-18T03:09:12.792277Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9d44e4913c41678c356f800414d809451fb5e150c151092328449f62ca1c13f

Aliases

arxiv: 2605.12796 · arxiv_version: 2605.12796v1 · doi: 10.48550/arxiv.2605.12796 · pith_short_12: 7HKE4SITYQLH · pith_short_16: 7HKE4SITYQLHRQ2W · pith_short_8: 7HKE4SIT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7HKE4SITYQLHRQ2W7AAECTMASR \
  | 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: f9d44e4913c41678c356f800414d809451fb5e150c151092328449f62ca1c13f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "26940ee96b33df98e7e9565fcb10841de3ce34b9a660d5eed529d1ff6454fc45",
    "cross_cats_sorted": [
      "math.IT",
      "quant-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.IT",
    "submitted_at": "2026-05-12T22:25:00Z",
    "title_canon_sha256": "fb08a9c8d73b130615470f7c06132c4df5dd5e8360e82159c31c8f4fdc56bb57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.12796",
    "kind": "arxiv",
    "version": 1
  }
}