Pith Number

pith:I5TLESTC

pith:2026:I5TLESTCZZBBW42OG5OEW2HEO4

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Diagonal Adaptive Non-local Observables on Quantum Neural Networks

Hsin-Yi Lin, Huan-Hsin Tseng, Samuel Yen-Chi Chen, Yan Li

Diagonal observables in adaptive non-local setups match full ANO power while cutting complexity from O(4^k) to O(2^k).

arxiv:2605.15410 v1 · 2026-05-14 · quant-ph · cs.AI · cs.LG

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Claims

C1strongest claim

Diagonal ANO retains the same capability of full ANO while reducing k-local observable complexity from O(4^k) to O(2^k) and lowering the corresponding measurement-side classical computation. In this sense, diagonal ANO preserves much of the benefit of full ANO while encompassing conventional VQCs as a special case.

C2weakest assumption

That restricting to diagonal observables paired with quantum circuits is mathematically equivalent to the full ANO space because diagonal matrices are canonical representatives modulo unitary similarity, without loss of function-space enlargement in the variational setting.

C3one line summary

Diagonal ANOs are mathematically equivalent to full ANOs modulo unitary similarity, reducing k-local observable complexity from O(4^k) to O(2^k) and lowering measurement-side classical computation while including conventional VQCs as a special case.

References

21 extracted · 21 resolved · 0 Pith anchors

[1] Quantum computing in the nisq era and beyond, 2018

[2] Variational quantum algorithms 2021

[3] Noisy intermediate-scale quantum algorithms, 2022

[4] The theory of variational hybrid quantum-classical algorithms, 2016

[5] A variational eigenvalue solver on a photonic quantum processor 2014

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:57.151513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4766b24a62ce421b734e375c4b68e4770d4b3efb528f5b361c738a2c76f657cd

Aliases

arxiv: 2605.15410 · arxiv_version: 2605.15410v1 · doi: 10.48550/arxiv.2605.15410 · pith_short_12: I5TLESTCZZBB · pith_short_16: I5TLESTCZZBBW42O · pith_short_8: I5TLESTC

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/I5TLESTCZZBBW42OG5OEW2HEO4 \
  | 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: 4766b24a62ce421b734e375c4b68e4770d4b3efb528f5b361c738a2c76f657cd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3504cc838128d8a075c1caa8815e3de06910323adb851218ef2c2a7e6017e81b",
    "cross_cats_sorted": [
      "cs.AI",
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-14T20:50:42Z",
    "title_canon_sha256": "d36ae8141a9063a7111b3e7d5a32e8330245ffea48dc07e32d247c7e99b7c2f9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15410",
    "kind": "arxiv",
    "version": 1
  }
}