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Intricacies of quantum computational paths

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Abstract

Graph search represents a cornerstone in computer science and is employed when the best algorithmic solution to a problem consists in performing an analysis of a search space representing computational possibilities. Typically, in such problems it is crucial to determine the sequence of transitions performed that led to certain states. In this work we discuss how to adapt generic quantum search procedures, namely quantum random walks and Grover’s algorithm, in order to obtain computational paths. We then compare these approaches in the context of tree graphs. In addition we demonstrate that in a best-case scenario both approaches differ, performance-wise, by a constant factor speedup of two, whilst still providing a quadratic speedup relatively to their classical equivalents. We discuss the different scenarios that are better suited for each approach.

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Authors and Affiliations

  1. GAIPS/INESC-ID, Department of Computer Science, Instituto Superior Técnico, Technical University of Lisbon, 2780-990, Porto Salvo, Portugal

    Luís Tarrataca & Andreas Wichert

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  1. Luís Tarrataca
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  2. Andreas Wichert
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Correspondence to Luís Tarrataca.

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Tarrataca, L., Wichert, A. Intricacies of quantum computational paths. Quantum Inf Process 12, 1365–1378 (2013). https://doi.org/10.1007/s11128-012-0475-7

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