Reducing computations in quantum walk algorithms
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Abstract
Quantum walks (QWs) are of interest as examples of uniquely quantum behavior and are applicable in a variety of quantum search and simulation models. Implementing QWs on quantum devices is useful from both points of view. We describe a prototype one-dimensional QW algorithm that economizes resources required in its implementation. Our algorithm needs only a single shift (increment) operation. It also allows complete flexibility in choosing the shift circuit, a resource intensive part of QW implementations. This is desirable for Noisy Intermediate-Scale Quantum (NISQ) devices, in which fewer computations implies faster execution and reduced effects of noise and decoherence. We implement versions of the algorithm, with two different shift circuit structures, on publicly accessible IBM quantum computers.