Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies.Recent results showing quantum walks are "universal for quantum computation" relate to algorithms, to be run on quantum computers.We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies.Recent results showing quantum walks are "universal for quantum computation" relate to algorithms, to be run on quantum computers.We consider whether an experimental implementation of a quantum walk could provide useful computation before we have a universal quantum computer.
Quantum versions of random walks have diverse applications that are motivating experimental implementations as well as theoretical studies. However, the main impetus behind this interest is their use in quantum algorithms, which have always employed the quantum walk in the form of a program running on a quantum computer. Recent results showing that quantum walks are "universal for quantum computation" relate entirely to algorithms, and do not imply that a physical quantum walk could provide a new architecture for quantum computers. Nonetheless, quantum walks used to model transport phenomena in spin chains and biomolecules broaden their scope well beyond algorithms, and reopen the question of when a physical implementation might provide useful computational outputs. In this article we determine the conditions under which a physical quantum walk experiment could provide useful results beyond the reach of classical computation.
The classical random walk formalism plays an important role in a wide range of applications. Its quantum counterpart, the quantum walk, is proposed as an important theoretical model for quantum computing. By exploiting quantum effects such as superposition, interference, and entanglement, quantum walks and their variations have been extensively studied for achieving computing power beyond that of classical computing and have been broadly used in designing quantum algorithms for algebraic and optimization problems, graph and network analysis, and quantum Hamiltonian and biochemical process simulations. Moreover, quantum walk models have been proven capable of universal quantum computation. Unlike conventional quantum circuit models, quantum walks provide a feasible path for implementing application-specific quantum computing, particularly in the noisy intermediate-scale quantum era. Recently, remarkable progress has been achieved in implementing a wide variety of quantum walks and quantum walk applications, which demonstrates the great potential of quantum walks. In this review, we provide a thorough summary of quantum walks and quantum walk computing, including theories and characteristics, physical implementations, and applications. We also discuss the challenges facing quantum walk computing, which aims to realize a practical quantum computer in the near future.
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walks in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. In this paper, I explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts.
Abstract A random walk is one of the widely adopted random processes for simulation and approximation in multiple areas of science and engineering. Quantum random walk is an analog version of the classical random walk. It was first introduced in 1993 by Y. Aharonov et al. They presented that, with the nature of quantum characteristic, the average length of the walking path on a line is possible to larger than a classical random walk can produce. Therefore, the quantum random walk can be used as a tool to construct many other quantum algorithms. Moreover, it can solve graph problems that many real-world problems can be formulated. However, quantum algorithms are only useful in practice if we can implement them efficiently on a quantum computer. In this study, we are then interested in designing and implementing a quantum circuit that can be run on a real quantum computing device. We firstly focus on the most straightforward, which is a one-dimension, quantum random walk algorithm. Then, the quantum circuits are developed and implemented on a real quantum computer and a quantum computing simulator using software development kits provided by IBM. Lastly, the performance and results of the quantum circuits tested on both computing platforms are presented.
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entangle-ment as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete-time quantum walks.
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle result than is often appreciated, since it applies to computations run on qubit-based quantum computers in the single walker case, and physical quantum walks in the multi-walker case (quantum cellular automata). Nonetheless, quantum walks are powerful tools for quantum computing when correctly applied. In this paper, I explain the relationship between quantum walks as models and quantum walks as computational tools, and give some examples of their application in both contexts.