Pith Number

pith:AH37TN4U

pith:2026:AH37TN4U7DLXRUGECFWV667WIC

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Feedback-based quantum optimization and its classical counterpart: quantum advantage and the power of classical algorithms

Takuya Hatomura, Tomohiro Hattori

Quantum optimization produces higher-quality solutions than classical counterparts but converges more slowly

arxiv:2605.13082 v1 · 2026-05-13 · quant-ph

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Claims

C1strongest claim

Quantum algorithms can be advantageous to classical algorithms in terms of the quality of solutions, while classical algorithms tend to show faster convergence than quantum ones, and one classical algorithm shows significant scalability for higher-order unconstrained binary optimization problems.

C2weakest assumption

That the quantum-classical correspondence of spin systems preserves the relative performance ranking between the quantum and classical feedback algorithms on the tested instances.

C3one line summary

Classical feedback-based optimization matches or exceeds quantum performance in speed and scalability while quantum retains an edge in final solution quality on tested instances.

References

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[1] The single parameterβ X(t) is given by βX(t) = i⟨Ψ(t)| " ˆHP, NX i=1 ˆXi # |Ψ(t)⟩,(6) which guarantees the reduction of the cost function (4)

[2] [49], we can introduce multiple parameters

[3] CC-FALQON We introduce the classical counterpart of FALQON (CC-FALQON). In CC-FALQON, we consider the fol- lowing Hamiltonian Ht =H P +β X(t) NX i=1 mX i , (12) 4 with the parameter βX(t) =−2 NX i=1 m

[4] CC-iFALQON We also introduce the classical counterpart of iFALQON (CC-iFALQON). In CC-iFALQON, we con- sider the following Hamiltonian Ht =H P + NX i=1 βX i (t)mX i , (14) with the parameters βX i (t)

[5] CACAO In CACAO [63], which was derived from the theory of FALQON, we consider the following Hamiltonian Ht = NX i=1 βY i (t)mY i , (16) with the parameters βY i (t) = 2mX i ∂HP ∂mZ i .(17) In the prev

Receipt and verification

First computed	2026-05-18T03:08:58.656334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

01f7f9b794f8d778d0c4116d5f7bf640872cf33e183030b6f48ca0869592267c

Aliases

arxiv: 2605.13082 · arxiv_version: 2605.13082v1 · doi: 10.48550/arxiv.2605.13082 · pith_short_12: AH37TN4U7DLX · pith_short_16: AH37TN4U7DLXRUGE · pith_short_8: AH37TN4U

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AH37TN4U7DLXRUGECFWV667WIC \
  | 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: 01f7f9b794f8d778d0c4116d5f7bf640872cf33e183030b6f48ca0869592267c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c31bc5e5befb1fbcc70470c70e351bcaa8235a48560fd829b946f1450a5d2d33",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-13T06:54:28Z",
    "title_canon_sha256": "8950dd77b79665ae03ef5d6dec32a9728b2aafebd9123e1e421810bc62fbab91"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13082",
    "kind": "arxiv",
    "version": 1
  }
}