Quantum random walks: An introductory overview

By Julia Kempe. 2003

1,596 citations recorded by the source corpus.

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/7838c01bdd3319e9061d2078efa1f9d96215d3dc

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum computation and quantum-state engineering driven by dissipation (2009, background): “(errors do not accumulate and the path does not have to be engineered carefully) and implementing quantum random walk”
Vibrations, quanta and biology (2013, background): “This includes coherence and interference, that is, wave-like features of particles which may lead to faster propagation for example in quantum random walks [9].”
Introduction to Weak Measurements and Weak Values (2013, background): “The following example is a version of an example introduced in [20].”
Quantum Walk Based Search Algorithms (2008, methodology): “The standard way advocated by several papers (see the survey [ 20 ]) is to extend the vertex space X by a coin space C, and define the state space of the walk asX ×C. Then a step of the walk is defined as the product of two unitary operations.”
An Aligned Subtree Kernel for Weighted Graphs (2015, background): “The CTQW represents the quantum counterpart of the continuous-time random walk (CTRW) (Emms et al., 2009).”
Universal quantum computation using the discrete-time quantum walk (2009, background): “ally introduced in two diﬀerent forms [4, 5] and has since been studied extensively. A quantum walk can be deﬁned in both continuous and discrete time in direct analog of their classical counterparts [6]. In the same way that classical random walks are used in computer science for algorithm design, ”
Random walks and diffusion on networks (2016, background): “RWs [4, 70, 71], zero-range processes [72], multiplicative random processes [73, 105 74], adaptive RWs (including reinforced RWs [75]), branching RWs [76], Lévy 106 flights [34, 35], elephant RWs [77], quantum walks [78, 79], intermittent RWs 107 [80], persistent RWs [81], starving RWs [82–84], mort”
Simulating chemistry using quantum computers. (2010, background): “Although we focused on the adiabatic and circuit models, these are not the only universal models of quantum computation and it may be possible to make further algorithmic progress with models such as topological quantum computing (69, 90), one-way quantum computing (108,109), and quantum walks (65,2”
Quantum walks: a comprehensive review (2012, background): “Therefore, we shall devote this section to review the fundamental links between quantum walks and computer science (mainly algorithms) and we strongly recommend the reader to go to both the references provided in this section, as well as to the introductions and reviews of quantum walk-based algorit”
Quantum walk algorithm for element distinctness (2003, methodology): “There has been considerable amount of research on quantum wa lks (surveyed in [30]) and their applications (surveyed in [6]).”
QUANTUM WALKS AND THEIR ALGORITHMIC APPLICATIONS (2003, methodology): “We refer the reader to an excellent survey by Kempe [14] for more information about quantum walks in general.”