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A quantum advection-diffusion solver using the quantum singular value transform

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Gard Olav Helle, Tommaso Benacchio, Anna Bomme Ousager, J{o}rgen Ellegaard Andersen

Quantum Physics · Submitted 16 Dec 2025

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy.

how it is stated · asserted 1.00 read the record →

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arXiv ID2512.22163 (version 3)
Pith IDNEFXB5UP, Pith's permanent record of this paper and its review
CitationAnna Bomme Ousager, Gard Olav Helle, J{\o}rgen Ellegaard Andersen, Tommaso Benacchio. "A quantum advection-diffusion solver using the quantum singular value transform." arXiv:2512.22163 (2025). https://pith.science/paper/NEFXB5UP
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,899 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.02 · controlled comparison 0.11 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.31 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. contribution 0.90 0.93 0.23 asserted 1.00
s1 Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. result 0.95 0.94 0.50 asserted 1.00
s2 The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks. result 0.80 0.92 0.12 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.61.

What was examined, and what was not

sources read
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not examined
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  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We present a quantum algorithm for the simulation of the linear advection-diffusion equation based on block encodings of high order finite-difference operators and the quantum singular value transform. Our complexity analysis shows that the higher order methods significantly reduce the number of gates and qubits required to reach a given accuracy. The theoretical results are supported by numerical simulations of one- and two-dimensional benchmarks.

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What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 1 sentence without a confident label

Uses the method or tool of 3 papers
  • The basic idea is to use a modular adder [ref] and the linear combinations of unitaries (LCU) method originally introduced in [ref] .

    Addition on a Quantum Computer · Block encoding of finite-difference operators · 0.96

  • The code is written in qiskit [ref] and is available in an accompanying https://github.com/GOHelle/QC_advection-diffusion_simGithub repository [ref] .

    Quantum computing with Qiskit · Numerical results · 1.00

  • Their method is also implemented in the python package pyqsp introduced in [ref] .

    A Grand Unification of Quantum Algorithms · The Quantum Singular Value Transform · 0.82

Cites as background 3 papers

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