Pith Number

pith:HEW4KX4R

pith:2025:HEW4KX4RRIRZXH4APC6MWUDRSB

not attested not anchored not stored refs pending

Learning to Maximize Quantum Neural Network Expressivity via Effective Rank

Juan Yao

Quantum neural networks achieve full expressivity when their circuits, data inputs, and measurements are all optimized to the theoretical maximum.

arxiv:2506.15375 v4 · 2025-06-18 · quant-ph · physics.comp-ph

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\usepackage{pith}
\pithnumber{HEW4KX4RRIRZXH4APC6MWUDRSB}

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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

κ can saturate its theoretical upper bound, d_n=4^n-1, for an n-qubit system when each of the three factors (circuit architecture, input data distributions, and measurement protocols) is optimally expressive.

C2weakest assumption

That the count of effectively independent parameters (κ) directly corresponds to the functional expressivity that determines performance on variational tasks, rather than being a proxy that may miss other limiting factors such as trainability or noise.

C3one line summary

Introduces effective rank κ to quantify QNN expressivity and applies reinforcement learning with a transformer agent to optimize circuit architectures for higher κ.

Receipt and verification

First computed	2026-05-28T01:04:28.731758Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

392dc55f918a239b9f8078bccb5071904f6ed570c54ef3732af0eba81cd73607

Aliases

arxiv: 2506.15375 · arxiv_version: 2506.15375v4 · doi: 10.48550/arxiv.2506.15375 · pith_short_12: HEW4KX4RRIRZ · pith_short_16: HEW4KX4RRIRZXH4A · pith_short_8: HEW4KX4R

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/HEW4KX4RRIRZXH4APC6MWUDRSB \
  | 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: 392dc55f918a239b9f8078bccb5071904f6ed570c54ef3732af0eba81cd73607

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "997a1e8637061037cbf2c14fcf698c48aad66f6ba3156165e4609f3b3bc74a3a",
    "cross_cats_sorted": [
      "physics.comp-ph"
    ],
    "license": "http://creativecommons.org/publicdomain/zero/1.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2025-06-18T11:45:57Z",
    "title_canon_sha256": "f748a3087944e4c4c0609f28706b0c3e7aedef75e562c7afe86648ac2a024af1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.15375",
    "kind": "arxiv",
    "version": 4
  }
}