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<p>We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer using the spectral properties of a Hermitian-weighted digraph obtained from the underlying graph. We then provide a polynomial-time algorithm that tests whether pointwise perfect subspace state transfer occurs at an integer step, given that the subspace and coins are rational. Finally, we construct several infinite families of examples that admit pointwise perfect <i>d</i>-dimensional subspace state transfer where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(d\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Subspace state transfer in coined quantum walks

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Yichi Xu,
  • Hanmeng Zhan

摘要

We study a transport phenomenon in certain coined quantum walks where a subspace of states localized at a vertex gets transferred to another vertex. We first develop characterizations for perfect and pretty good subspace state transfer using the spectral properties of a Hermitian-weighted digraph obtained from the underlying graph. We then provide a polynomial-time algorithm that tests whether pointwise perfect subspace state transfer occurs at an integer step, given that the subspace and coins are rational. Finally, we construct several infinite families of examples that admit pointwise perfect d-dimensional subspace state transfer where \(d\ge 2\) d ≥ 2 .