Pith Number

pith:EHMPTOGA

pith:2026:EHMPTOGAP4TQVG7ZIYHLPFVCG7

not attested not anchored not stored refs pending

Quantitative Universal Approximation for Noisy Quantum Neural Networks

Antoine Jacquier, Lukas Gonon, Marcel Mordarski

Noisy quantum neural networks can approximate continuous functions with explicit quantitative error bounds.

arxiv:2604.02064 v3 · 2026-04-02 · quant-ph · cs.NA · math.NA · q-fin.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{EHMPTOGAP4TQVG7ZIYHLPFVCG7}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

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

We provide here a universal approximation theorem with precise quantitative error bounds for noisy quantum neural networks.

C2weakest assumption

The noise model for the quantum neural networks and the representation of target functions as expectations allow the quantitative error bounds to be derived and hold.

C3one line summary

A quantitative universal approximation theorem with error bounds is established for noisy quantum neural networks applied to expectation targets in finance.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T01:06:09.431165Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

21d8f9b8c07f270a9bf9460eb796a237e00fb9335155e81322e221e12a5884e0

Aliases

arxiv: 2604.02064 · arxiv_version: 2604.02064v3 · doi: 10.48550/arxiv.2604.02064 · pith_short_12: EHMPTOGAP4TQ · pith_short_16: EHMPTOGAP4TQVG7Z · pith_short_8: EHMPTOGA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/EHMPTOGAP4TQVG7ZIYHLPFVCG7 \
  | 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: 21d8f9b8c07f270a9bf9460eb796a237e00fb9335155e81322e221e12a5884e0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eff065cb10b962ed7f4a2482b3308b18edbb01d100587fbbdd1c15e3212234aa",
    "cross_cats_sorted": [
      "cs.NA",
      "math.NA",
      "q-fin.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-02T13:58:49Z",
    "title_canon_sha256": "a079e4c8679e12b3f1653c3c094b4f69b1d2b7f6560f04ff19b2fca7780b3d3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.02064",
    "kind": "arxiv",
    "version": 3
  }
}