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Quantum walks with memory on cycles

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Michael Mc Gettrick, Jaros{l}aw Adam Miszczak

Quantum Physics · Submitted 14 Jan 2013

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

The authors' main claim We provide a formula for the probability distribution and the time-averaged limiting probability distribution of the introduced quantum walk.

how it is stated · asserted 1.00 read the record →

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arXiv ID1301.2905 (version 2)
Pith IDQB4K3ZH3, Pith's permanent record of this paper and its review
CitationJaros{\l}aw Adam Miszczak, Michael Mc Gettrick. "Quantum walks with memory on cycles." arXiv:1301.2905 (2013). https://pith.science/paper/QB4K3ZH3
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The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,852 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.06 · human participants 0.01 · controlled comparison 0.66 · randomized assignment 0.01 · states quantitative result 0.31 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We study the model of quantum walks on cycles enriched by the addition of 1-step memory. We provide a formula for the probability distribution and the time-averaged limiting probability distribution of the introduced quantum walk. Using the obtained results, we discuss the properties of the introduced model and the difference in comparison to the memoryless model.

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 study the model of quantum walks on cycles enriched by the addition of 1-step memory. contribution 0.91 0.56 0.06 asserted 0.91
s1 We provide a formula for the probability distribution and the time-averaged limiting probability distribution of the introduced quantum walk. result 0.51 0.96 0.35 asserted 1.00
s2 Using the obtained results, we discuss the properties of the introduced model and the difference in comparison to the memoryless model. interpretation 0.70 0.85 0.21 asserted 0.80

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • C citations
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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 study the model of quantum walks on cycles enriched by the addition of 1-step memory. We provide a formula for the probability distribution and the time-averaged limiting probability distribution of the introduced quantum walk. Using the obtained results, we discuss the properties of the introduced model and the difference in comparison to the memoryless model.

Human review

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How the literature uses it

1 arXiv paper cite this in 1 sentence

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

Papers citing it

Cites it as background 1 paper
  • Quantum walks [ref] , quantum counterparts of classical Markov processes, provide a powerful method for developing new quantum algorithms [ref] and protocols [ref] .

    Lively quantum walks on cycles · Introduction · 1.00

What it cites · 6 sentences without a confident label

Builds on 3 papers
  • In this paper we introduce and study the model of quantum walks on cycle [ref] enriched by the addition of 1-step memory [ref] .

    One Dimensional Quantum Walks with Memory · Introduction · 0.86

  • In this paper we introduce and study the model of quantum walks on cycle [ref] enriched by the addition of 1-step memory [ref] .

    Quantum Walks On Graphs · Introduction · 0.86

  • In this paper we introduce and study the model of quantum walks on cycle [ref] enriched by the addition of 1-step memory [ref] .

    Quantum walks on cycles · Introduction · 0.86

Uses the method or tool of 2 papers
  • In order to obtain the expression for the amplitudes of the quantum walk with memory on cycle we use the method introduced in [ref] and represent time evolution of the walk using the Fourier transform [equation] From the above we get a recursive relation for the time evolution in the Fourier basis [equation] where [equation]

    Quantum Walk on the Line · Fourier analysis · 0.96

  • In order to obtain expression for the probability distribution on the cycle we use Fourier analysis method [ref] .

    Limit theorems for quantum walks with memory · Fourier analysis · 1.00

Cites as background 1 paper

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