Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

Stacey Jeffery; Galina Pass

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arXiv · 2401.08355

Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer

Stacey Jeffery·Galina Pass

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Abstract

We introduce an object called a \emph{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 \emph{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.

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Stacey Jeffery, Galina Pass. 2024-01-16. Multidimensional Quantum Walks, Recursion, and Quantum Divide & Conquer. https://arxiv.org/abs/2401.08355

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