%0 Journal Article %J Physical Review A %D 2021 %T Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware %A Singh, Shivani %A Alderete, C. Huerta %A Balu, Radhakrishnan %A Monroe, Christopher %A Linke, Norbert M. %A Chandrashekar, C. M. %X

Quantum walks are a promising framework for developing quantum algorithms and quantum simulations. They represent an important test case for the application of quantum computers. Here we present different forms of discrete-time quantum walks (DTQWs) and show their equivalence for physical realizations. Using an appropriate digital mapping of the position space on which a walker evolves to the multiqubit states of a quantum processor, we present different configurations of quantum circuits for the implementation of DTQWs in one-dimensional position space. We provide example circuits for a five-qubit processor and address scalability to higher dimensions as well as larger quantum processors.

%B Physical Review A %V 104 %8 12/8/2021 %G eng %U https://arxiv.org/abs/2001.11197 %R https://doi.org/10.1103/PhysRevA.104.062401