Pith Number

pith:TWHQNFXL

pith:2026:TWHQNFXLLCVVNBZ73XW5TO7M4O

not attested not anchored not stored refs pending

Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators

Alessandro Roggero, Do\u{g}a Murat K\"urk\c{c}\"uo\u{g}lu, Gabriel N. Perdue, Marina Maneyro, Samuel Godwood

Qudit encodings can cut non-Clifford costs by constant factors over qubits for diagonal quadratic operators at small d in LCU settings, but qubits scale better asymptotically and dominate product formulas.

arxiv:2604.26792 v2 · 2026-04-29 · quant-ph

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\usepackage{pith}
\pithnumber{TWHQNFXLLCVVNBZ73XW5TO7M4O}

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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

Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in d. Nevertheless, the finite-d threshold analysis identifies low dimensional regions in which qudits can yield meaningful constant-factor savings, particularly for LCU-based implementations.

C2weakest assumption

Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU(2) rotations; this modeling choice and the idealized negligible-overhead qubit-qudit code-switching model are load-bearing for the break-even conditions and T-count comparisons.

C3one line summary

Qudit encodings for quadratic diagonal evolutions require exponentially stronger synthesis advantages than qubits to win asymptotically in product formulas but can yield constant-factor savings in LCU at low d.

Receipt and verification

First computed	2026-05-21T02:05:03.597506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9d8f0696eb58ab56873fddedd9bbece3b2ec1ce678d25a567fc2a285b2ba8b08

Aliases

arxiv: 2604.26792 · arxiv_version: 2604.26792v2 · doi: 10.48550/arxiv.2604.26792 · pith_short_12: TWHQNFXLLCVV · pith_short_16: TWHQNFXLLCVVNBZ7 · pith_short_8: TWHQNFXL

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/TWHQNFXLLCVVNBZ73XW5TO7M4O \
  | 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: 9d8f0696eb58ab56873fddedd9bbece3b2ec1ce678d25a567fc2a285b2ba8b08

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3f9710114fc3bda0d27b9ecd5f0ddf8a1667d4a370a611a8462c49c6a87b70d2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-29T15:25:08Z",
    "title_canon_sha256": "c23dd6070d78cabaf2489cd82b3c8e3b1599f2737c3725bf3560f4c707558dd8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.26792",
    "kind": "arxiv",
    "version": 2
  }
}