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

Quantum circuits for the realization of equivalent forms of one-dimensional discrete-time quantum walks on near-term quantum hardware