Pith Number

pith:6Q3QHS5F

pith:2026:6Q3QHS5FHDRK42FP4NCDHVLCSV

not attested not anchored not stored refs pending

Polylogarithmic-Weight Dicke States in QAC$^0$ and Arbitrary Symmetric States in QAC$^0_f$

Lucas Gretta, Malvika Raj Joshi, Meghal Gupta

Explicit constant-depth circuits prepare polylog-weight Dicke states using only Toffoli gates.

arxiv:2604.15298 v2 · 2026-04-16 · quant-ph · cs.DS

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\pithnumber{6Q3QHS5FHDRK42FP4NCDHVLCSV}

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3 Author claim open · sign in to claim

4 Citations 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 give explicit constant-depth circuits that prepare n-qubit Dicke states for all k ≤ polylog(n), using only multi-qubit Toffoli gates and single-qubit unitaries. This gives the first QAC^0 construction of super-constant weight Dicke states.

C2weakest assumption

The constructions assume the standard quantum circuit model with unbounded fan-in Toffoli gates allowed in constant depth and the prior definition of QAC^0 that permits only polylogarithmic fanout.

C3one line summary

Explicit constant-depth circuits prepare super-constant weight Dicke states in QAC^0 and extend to arbitrary symmetric states with FANOUT_n.

Cited by

1 paper in Pith

Space-Time Tradeoffs of Pauli-Based Computation in Distributed qLDPC Architectures

Receipt and verification

First computed	2026-07-14T02:22:30.117842Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f43703cba538e2ae68afe34433d5629565ca73e8ab50f54c7f50fc54a8002eb0

Aliases

arxiv: 2604.15298 · arxiv_version: 2604.15298v2 · doi: 10.48550/arxiv.2604.15298 · pith_short_12: 6Q3QHS5FHDRK · pith_short_16: 6Q3QHS5FHDRK42FP · pith_short_8: 6Q3QHS5F

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/6Q3QHS5FHDRK42FP4NCDHVLCSV \
  | 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: f43703cba538e2ae68afe34433d5629565ca73e8ab50f54c7f50fc54a8002eb0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fad714d778beef094f24d95a114231fe933446e1b5da3e437a63fb2d2daa44af",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-16T17:57:08Z",
    "title_canon_sha256": "5d5d24076978ba81ddfd503f6169c2bbb05d7ece4f5d507d708d77c8fd564a07"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.15298",
    "kind": "arxiv",
    "version": 2
  }
}