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<p>This work is intended as an attempt to motivate a novel model of disordering discrete-time quantum walk in a one-dimensional lattice of integers. We construct such a model over max-plus algebra and give the notion of coin operator of the disordered discrete-time quantum walk in a one-dimensional lattice <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10626_2025_409_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">Z</mi> </math></EquationSource> </InlineEquation> to derive a very complicated decision matrix. Furthermore, we investigate the properties of the decision matrix for each state and prove some results for the disordered quantum walk over max-plus algebra that are similar to the conserved quantity of the conventional disordered quantum walk.</p>

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Disordered discrete-time quantum walk over max-plus algebra

  • 期刊论文

  • 发表日期：

    2025年1月25日

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  • Mohamad Ilham Dwi Firmansyah,
  • Muhammad Syifa’ul Mufid,
  • Subiono,
  • Bijan Davvaz

摘要

This work is intended as an attempt to motivate a novel model of disordering discrete-time quantum walk in a one-dimensional lattice of integers. We construct such a model over max-plus algebra and give the notion of coin operator of the disordered discrete-time quantum walk in a one-dimensional lattice \(\mathbb {Z}\) Z to derive a very complicated decision matrix. Furthermore, we investigate the properties of the decision matrix for each state and prove some results for the disordered quantum walk over max-plus algebra that are similar to the conserved quantity of the conventional disordered quantum walk.