Pith Number

pith:Y4DEUJWA

pith:2026:Y4DEUJWAWTBUVLA5327TRFLMEN

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Geometric Preconditioning and Curriculum Optimization for Trainable Variational Quantum Regression

Qingyu Meng, Yangshuai Wang

A capacity-controlled classical embedding acts as a learnable geometric preconditioner to improve trainability of variational quantum circuits for regression.

arxiv:2601.11942 v3 · 2026-01-17 · cs.LG · quant-ph

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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

Across finite-size statevector audits on PDE-informed regression benchmarks and small-data tabular tasks, the Hybrid QNN lowers error relative to Pure QNN baselines under matched quantum-model budgets.

C2weakest assumption

The classical embedding successfully acts as a learnable geometric preconditioner that reshapes the empirical Gram matrix to improve residual contraction in the linearized quantum-parameter dynamics, without the capacity control introducing new ill-conditioning that offsets the benefit.

C3one line summary

A hybrid variational quantum regression design with classical geometric preconditioning and curriculum optimization improves trainability over pure quantum models while remaining behind strong classical baselines.

References

36 extracted · 36 resolved · 0 Pith anchors

[1] The power of quantum neural networks.Nature Computa- tional Science, 1(6):403–409, 2021

[2] UCI machine learning repository, 2007

[3] Training deep quan- tum neural networks.Nature communications, 11(1):808, 2020

[4] Trainable embedding quantum physics informed neural networks for solving nonlinear pdes.Sci- entific Reports, 15(1):18823, 2025

[5] J., Farkas, M., Killoran, N 2023

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-18T03:09:24.385650Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c7064a26c0b4c34aac1ddebf38956c2370f17c9e96a135f36805133a5584f500

Aliases

arxiv: 2601.11942 · arxiv_version: 2601.11942v3 · doi: 10.48550/arxiv.2601.11942 · pith_short_12: Y4DEUJWAWTBU · pith_short_16: Y4DEUJWAWTBUVLA5 · pith_short_8: Y4DEUJWA

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/Y4DEUJWAWTBUVLA5327TRFLMEN \
  | 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: c7064a26c0b4c34aac1ddebf38956c2370f17c9e96a135f36805133a5584f500

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e48866d9a1718a2c13f71a2bf4bc1c8434fd27946911f195c469996268aaf6b3",
    "cross_cats_sorted": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "cs.LG",
    "submitted_at": "2026-01-17T07:32:18Z",
    "title_canon_sha256": "cc05d6ae44c146deef6d82166ac1ae397e2c197d2dec1a8ffcd73d3b1b22f0c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.11942",
    "kind": "arxiv",
    "version": 3
  }
}