Pith Number

pith:WOQMSQAQ

pith:2026:WOQMSQAQWRGS5U6JJVTFLV7MU4

not attested not anchored not stored refs pending

Simpler Presentations for Many Fragments of Quantum Circuits

Colin Blake

Treating wire permutations as structural yields minimal rewrite rules for six near-Clifford quantum circuit fragments.

arxiv:2602.09874 v2 · 2026-02-10 · quant-ph · cs.LO

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\usepackage{pith}
\pithnumber{WOQMSQAQWRGS5U6JJVTFLV7MU4}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

The resulting presentations are minimal in all arities for qubit Clifford, real Clifford, and CNOT-dihedral, minimal in bounded ranges for the remaining fragments, and comparable by one transfer-and-separation pattern.

C2weakest assumption

That the prior completeness theorems can be transferred into the PROP setting while preserving completeness and allowing removal of non-structural rules without losing any equivalences.

C3one line summary

Simpler minimal rule sets are derived for qubit Clifford, real Clifford, Clifford+T (up to two qubits), Clifford+CS (up to three qubits), CNOT-dihedral, and qutrit Clifford by transferring completeness from prior theorems and removing redundant non-structural rules.

Receipt and verification

First computed	2026-07-16T01:22:34.713708Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3a0c94010b44d2ed3c94d6655d7eca72351fe6996f37f6c49b6270a91f6970c

Aliases

arxiv: 2602.09874 · arxiv_version: 2602.09874v2 · doi: 10.48550/arxiv.2602.09874 · pith_short_12: WOQMSQAQWRGS · pith_short_16: WOQMSQAQWRGS5U6J · pith_short_8: WOQMSQAQ

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/WOQMSQAQWRGS5U6JJVTFLV7MU4 \
  | 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: b3a0c94010b44d2ed3c94d6655d7eca72351fe6996f37f6c49b6270a91f6970c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c32588cb280ea1e946baa152bf108a50b426482cf69e567a5331ef9479f21cc2",
    "cross_cats_sorted": [
      "cs.LO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-02-10T15:17:24Z",
    "title_canon_sha256": "1e82049b9138b5fccabfdbfb9f669b9bad0e019b91be6c7808e8c66769880447"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.09874",
    "kind": "arxiv",
    "version": 2
  }
}