Pith Number

pith:JPXPUA5S

pith:2026:JPXPUA5SQ2ZLWR675WDTDAD47P

not attested not anchored not stored refs pending

Quantum Data Loading for Carleman Linearized Systems: Application to the Lattice-Boltzmann Equation

Abeynaya Gnanasekaran, Amit Surana, Daniel Gunlycke, Reuben Demirdjian, Thomas Hogancamp

A decomposition of any square matrix into non-unitaries yields an LCU for Carleman-linearized systems whose term count depends only on truncation order and velocity count.

arxiv:2605.00302 v3 · 2026-05-01 · quant-ph

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\pithnumber{JPXPUA5SQ2ZLWR675WDTDAD47P}

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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

we construct a generalized LCU framework for any Carleman linearized autonomous dynamical system with a polynomial nonlinearity. This framework is then used to construct an LCU for the 3-dimensional Carleman linearized lattice Boltzmann equation (LBE) in which the number of terms scales like Ns ∼ O(α² Q²), where α is the Carleman truncation order and Q is the number of discrete velocities from the LBE. Importantly, Ns is completely independent of both the number of temporal and spatial discretization points.

C2weakest assumption

That an arbitrary square matrix representing the Carleman-linearized system can be decomposed into a linear combination of non-unitaries whose count scales as O(α² Q²) and that each non-unitary can be embedded into a unitary without introducing discretization-dependent overheads that would invalidate the claimed independence.

C3one line summary

A new LCNU-to-LCU decomposition enables a generalized quantum framework for Carleman-linearized polynomial systems like the lattice Boltzmann equation, with Ns scaling as O(α² Q²) independent of spatial and temporal discretization points.

Receipt and verification

First computed	2026-05-20T00:02:12.064004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4beefa03b286b2bb47dfed8731807cfbeaa0003f3a7097be61b3a708a9b4ba92

Aliases

arxiv: 2605.00302 · arxiv_version: 2605.00302v3 · doi: 10.48550/arxiv.2605.00302 · pith_short_12: JPXPUA5SQ2ZL · pith_short_16: JPXPUA5SQ2ZLWR67 · pith_short_8: JPXPUA5S

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/JPXPUA5SQ2ZLWR675WDTDAD47P \
  | 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: 4beefa03b286b2bb47dfed8731807cfbeaa0003f3a7097be61b3a708a9b4ba92

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "235f92f3a613b3d1a549b1de1eaa983560f0c66575e31dc98314d76b3bda540b",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-01T00:10:50Z",
    "title_canon_sha256": "aa8d54cceece9af84fc41aa0d84b713f18ddcdee27c2491742a09281483f86f5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.00302",
    "kind": "arxiv",
    "version": 3
  }
}