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Complexity analysis of quantum walk based search algorithms

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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B. L. Douglas, J. B. Wang

Quantum Physics · Submitted 7 Aug 2014

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

The authors' main claim We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms.

how it is stated · asserted 1.00 read the record →

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arXiv ID1408.1616 (version 1)
Pith IDGFHJPKP3, Pith's permanent record of this paper and its review
CitationB. L. Douglas, J. B. Wang. "Complexity analysis of quantum walk based search algorithms." arXiv:1408.1616 (2014). https://pith.science/paper/GFHJPKP3
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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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,595 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.21 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.09 · mentions code or data availability 0.04.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We present several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk search algorithm, without reference to a `black box' oracle. These circuits provide a practically implementable method to explore quantum walk based search algorithms with the aim of eventual real-world applications. We also provide a numerical analysis of a quantum walk based search along a twisted toroid family of graphs, which requires O($\sqrt{n}$ log($n$)) elementary 2-qubit quantum gate operations to find a marked node.

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 several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. contribution 0.98 0.87 0.46 asserted 1.00
s1 For these graphs, we construct quantum circuits that explicitly implement the full quantum walk search algorithm, without reference to a `black box' oracle. method 0.59 0.95 0.17 asserted 1.00
s2 These circuits provide a practically implementable method to explore quantum walk based search algorithms with the aim of eventual real-world applications. interpretation 0.56 0.77 0.18 asserted 0.92
s3 We also provide a numerical analysis of a quantum walk based search along a twisted toroid family of graphs, which requires O($\sqrt{n}$ log($n$)) elementary 2-qubit quantum gate operations to find a marked node. result 0.92 0.95 0.26 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.94 · evidence from simulation or computation 0.55.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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 several families of graphs that allow both efficient quantum walk implementations and efficient quantum walk based search algorithms. For these graphs, we construct quantum circuits that explicitly implement the full quantum walk search algorithm, without reference to a `black box' oracle. These circuits provide a practically implementable method to explore quantum walk based search algorithms with the aim of eventual real-world applications. We also provide a numerical analysis of a quantum walk based search along a twisted toroid family of graphs, which requires O($\sqrt{n}$ log($n$)) elementary 2-qubit quantum gate operations to find a marked node.

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