Pith Number

pith:FZTNL7SG

pith:2026:FZTNL7SGC3KEETXYQ72F4IK3OC

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Quantum algorithm for solving differential equations using SLAC derivatives

Dominic W. Berry, Gavin K. Brennen, Gopikrishnan Muraleedharan, Rakshit M. Gharat

Efficient block-encodings of SLAC derivative operators allow quantum linear solvers to handle partial differential equations on finite lattices.

arxiv:2605.04861 v2 · 2026-05-06 · quant-ph

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\usepackage{pith}
\pithnumber{FZTNL7SGC3KEETXYQ72F4IK3OC}

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Record completeness

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4 Citations open

5 Replications 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

This approach enables the solution of partial differential equations with SLAC-discretised derivative operators on a finite lattice using the quantum linear solving algorithm (QLSA).

C2weakest assumption

The state-preparation techniques designed for smoothly decaying functions can efficiently prepare the dense LCU amplitudes with high success probability and low gate cost, and the diagonal preconditioner reduces the condition number to a small constant in the wavelet basis.

C3one line summary

Efficient quantum block-encodings of SLAC first-order derivative and Laplacian operators are built with LCU, state preparation, wavelet multi-scale transforms, and preconditioning to solve PDEs via QLSA with analyzed complexity and error scaling.

Receipt and verification

First computed	2026-05-26T02:05:10.129452Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e66d5fe4616d4424ef887f45e215b708638d3fab7ff64c8568e2991cc506528

Aliases

arxiv: 2605.04861 · arxiv_version: 2605.04861v2 · doi: 10.48550/arxiv.2605.04861 · pith_short_12: FZTNL7SGC3KE · pith_short_16: FZTNL7SGC3KEETXY · pith_short_8: FZTNL7SG

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FZTNL7SGC3KEETXYQ72F4IK3OC \
  | 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: 2e66d5fe4616d4424ef887f45e215b708638d3fab7ff64c8568e2991cc506528

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7d7617c0f11c2282f7112db52b91dbff3fcbe29d0dbc2df4b33657e1b7daf78d",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-05-06T12:57:36Z",
    "title_canon_sha256": "7fda17e5dc8e0c5d925ab61e54fd258fee6515ac4e7e03aa941189a80ef82dde"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.04861",
    "kind": "arxiv",
    "version": 2
  }
}