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IEEE International Conference on Quantum Computing and Engineering (QCE)

Implementation and Viusalization of Quantum Walks

Addie Jordon, Austin Hawkins-Seagram, Ulrike Stege

Published Sep 1, 2022• 3 citations
Publisher

Abstract

Quantum walks (QWs) are the quantum analogue to classical random walks. We explore various implementations of QWs and create visualizations for each, with the goal of increasing educational accessibility. A new QW, called sticky walk, is introduced, where the walker sticks to targets once found. Corresponding pseudocode and Qiskit implementations are provided. Sticky walk helps bridge the gap between non-searching QWs and Quantum Walk Search (which may be an unintuitive search algorithm for those new to QWs).

DOI
10.1109/qce53715.2022.00122

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Quantum walks (QWs) are the quantum analogue to classical random walks. We explore various implementations of QWs and create visualizations for each, with the goal of increasing educational accessibility. A new QW, called sticky walk, is introduced, where the walker sticks to targets once found. Corresponding pseudocode and Qiskit implementations are provided. Sticky walk helps bridge the gap between non-searching QWs and Quantum Walk Search (which may be an unintuitive search algorithm for those new to QWs).
Quantum walks (QWs) are the quantum analogue to classical random walks. We present visualizations for quantum walks and show how they can be used to teach quantum concepts such as superposition and interference. Using our Quantum Walks Visualization Application (QWalkVis) for visualizing quan-tum walks lets the user select the dimensions, number of states, and number of steps in the walk and generates probabilistic plots on-the-fly. Users can view a plot for each step of the walk, allowing them to compare the probability distributions as time progresses. Visualizations share an important space in education; QWalkVis was created to aid students in learning about quantum walks and foundational quantum concepts through an interactive design. We highlight some potential use cases of QWalkVis for both self-directed student learning and the education in a classroom.
Using numerical simulation, we measured the performance of several potential quantum algorithms, based on quantum random walks, to solve Boolean satisfiability (SAT) problems. We develop the fundamentals of quantum computing and the theory of classical algorithms to indicate how these algorithms could be implemented. We also discuss the development of quantum random walks and the principles that go into creating them, presenting existing work on search algorithms using coined discrete-time quantum random walks. Although our quantum algorithms do not solve SAT problems faster than may be done classically, as a step toward that objective, we present the first example of a quantum walk on a directed graph that has a significant increase in speed over the analogous classical walk.
Abstract Quantum walks (QWs) are one of the fundamental concepts in quantum information science, being an essential component for various new applications. Implementing QWs using integrated photonic waveguide lattices allows for realizing long evolution times, for exploring novel lattice geometries, and even for controllable coupling to the environment. This tutorial gives an introduction to the field of on-chip QWs of single photons and photon pairs featuring non-classical two-photon correlations.
In the sub-field of quantum algorithms, physicists and computer scientist take classical computing algorithms and principles and see if there is a more efficient or faster approach implementable on a quantum computer, i.e. a ”quantum advantage”. We take random walks, a widely applicable group of classical algorithms, and move them into the quantum computing paradigm. Additionally, an introduction to a popular quantum search algorithm called Grover’s search is included to guide the reader to the development of a quantum search algorithm using quantum random walks. To close the gap between algorithm and hardware, we will look at using neutral-atom (also known as cold-atom) quantum computing to physically implement two types of quantum random walks and Grover’s algorithm.