Review on Quantum Walk Computing: Theory, Implementation, and Application
arxiv(2024)
摘要
Classical random walk formalism shows a significant role across a wide range
of applications. As its quantum counterpart, the quantum walk is proposed as an
important theoretical model for quantum computing. By exploiting the quantum
effects such as superposition, interference and entanglement, quantum walks and
their variety have been extensively studied for achieving beyond classical
computing power, and they have been broadly used in designing quantum
algorithms in fields ranging from algebraic and optimization problems, graph
and network analysis, to quantum Hamiltonian and biochemical process
simulations, and even further quantum walk models have proven their
capabilities for universal quantum computation. Compared to the conventional
quantum circuit models, quantum walks show a feasible path for implementing
application-specific quantum computing in particularly the noisy
intermediate-scale quantum era. Recently remarkable progress has been achieved
in implementing a wide variety of quantum walks and quantum walk applications,
demonstrating the great potential of quantum walks. In this review, we provide
a thorough summary of quantum walks and quantum walk computing, including
aspects of quantum walk theories and characteristics, advances in their
physical implementations and the flourishingly developed quantum walk computing
applications. We also discuss the challenges facing quantum walk computing,
toward realizing a practical quantum computer in the near future.
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