Pith Number

pith:OESEHZXP

pith:2026:OESEHZXPALL5BCP4LNKJZHA4VX

not attested not anchored not stored refs resolved

A QPINN Framework with Quantum Trainable Embeddings for the Lid-Driven Cavity Problem

A. Pedro Aguiar, Ban Q. Tran, Nahid Binandeh Dehaghani, Rafal Wisniewski, Susan Mengel

A quantum neural network with trainable embeddings solves the lid-driven cavity flow using fewer parameters than classical PINNs while keeping competitive accuracy.

arxiv:2605.13892 v1 · 2026-05-12 · quant-ph · physics.flu-dyn

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\pithnumber{OESEHZXPALL5BCP4LNKJZHA4VX}

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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

The proposed QNN-TE-QPINN exhibits stable training behavior and competitive solution accuracy compared with classical PINNs and hybrid quantum models using classical embeddings, while requiring significantly fewer trainable parameters.

C2weakest assumption

That the reported numerical experiments on the lid-driven cavity generalize beyond the specific test cases and that the observed parameter reduction and stability arise from the trainable quantum embeddings rather than from unstated implementation choices or hyperparameter tuning.

C3one line summary

QPINN framework with QNN-based trainable embeddings solves the lid-driven cavity problem with stable training, competitive accuracy, and fewer parameters than classical PINNs.

References

12 extracted · 12 resolved · 1 Pith anchors

[1] High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method, 1982

[2] A detailed study of lid-driven cavity flow at moderate reynolds numbers using incompressible sph, 2014

[3] Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, 2019

[4] Variational quantum algorithms 2021

[5] Solving nonlinear differential equations with differentiable quantum circuits, 2021

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:39:19.041746Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

712443e6ef02d7d089fc5b549c9c1cadc84782dc235898364e29a2bf590d1536

Aliases

arxiv: 2605.13892 · arxiv_version: 2605.13892v1 · doi: 10.48550/arxiv.2605.13892 · pith_short_12: OESEHZXPALL5 · pith_short_16: OESEHZXPALL5BCP4 · pith_short_8: OESEHZXP

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OESEHZXPALL5BCP4LNKJZHA4VX \
  | 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: 712443e6ef02d7d089fc5b549c9c1cadc84782dc235898364e29a2bf590d1536

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "608dc103f8bf5945af95b64d1c12868a94da72f4d42a3bd5b6364e537d339512",
    "cross_cats_sorted": [
      "physics.flu-dyn"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-12T10:03:45Z",
    "title_canon_sha256": "1cdc54c682d2bae0a057062fa823bdbd947f24a82a2bc46299b547f795038eaa"
  },
  "schema_version": "1.0",
  "source": {
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    "kind": "arxiv",
    "version": 1
  }
}