Measurement-Based Quantum Walks on High-Dimensional Graphs

Abstract

Quantum walks (QWs) on high-dimensional and reconfigurable graphs can invoke the full potential of quantum simulation and information processing tasks. However, experimental realization of such large-scale and programmable quantum walks is quite challenging, owing to the significantly increased complexity of the existing schemes. Overcoming this limitation, we here demonstrate Grover walks on four-dimensional hypercubes with high similarities above 95%, and 400-step quantum walks on circles and finite lines with similarities of 98%. This is rendered possible by a novel measurement-based approach to quantum walks where measurements on appropriately rotated bases implement the targeted evolution unitaries. Our results open a new path towards the implementation of scalable and programmable quantum networks that can find application in complex tasks, such as Gaussian Boson Sampling.