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Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

Authors Stacey Jeffery , Galina Pass

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Author Details

Stacey Jeffery
  • QuSoft, CWI, Amsterdam, The Netherlands
  • University of Amsterdam, The Netherlands
Galina Pass
  • QuSoft, Amsterdam, The Netherlands
  • University of Amsterdam, The Netherlands

Funding

  • Jeffery, Stacey: Supported by ERC STG grant 101040624-ASC-Q, NWO Klein project number OCENW.Klein.061. SJ is a CIFAR Fellow in the Quantum Information Science Program.
  • Pass, Galina: Supported by the National Agenda for Quantum Technologies (NAQT), as part of the Quantum Delta NL programme.

Cite As Get BibTex

Stacey Jeffery and Galina Pass. Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer. In 42nd International Symposium on Theoretical Aspects of Computer Science (STACS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 327, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.STACS.2025.54

Abstract

We introduce an object called a subspace graph that formalizes the technique of multidimensional quantum walks. Composing subspace graphs allows one to seamlessly combine quantum and classical reasoning, keeping a classical structure in mind, while abstracting quantum parts into subgraphs with simple boundaries as needed. As an example, we show how to combine a switching network with arbitrary quantum subroutines, to compute a composed function. As another application, we give a time-efficient implementation of quantum Divide & Conquer when the sub-problems are combined via a Boolean formula. We use this to quadratically speed up Savitch’s algorithm for directed st-connectivity.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Quantum Divide & Conquer
  • Time-Efficient
  • Subspace Graphs
  • Quantum Walks
  • Switching Networks
  • Directed st-Connectivity

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References

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