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Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

Authors Stacey Jeffery , Galina Pass

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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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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.

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

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.

References

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