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This paper explores two circuit approaches for quantum walks: the firstconsists of generalised controlled inversions, whereas the second oneeffectively replaces them with rotation operations around the basis states. Weshow the theoretical foundation of the rotational implementation. Therotational approach nullifies the large amount of ancilla qubits required tocarry out the computation when using the inverter implementation. Our resultsconcentrate around the comparison of the two architectures in terms ofstructure, benefits and detriments, as well as the computational resourcesneeded for each approach. We show that the inverters approach requiresexponentially fewer gates than the rotations but almost half the number ofqubits in the system. Finally, we execute a number of experiments using an IBMquantum computer. The experiments show the effects of noise in our circuits.Small two-qubit quantum walks evolve closer to our expectations, whereas for alarger number of steps or state space the evolution is severely affected bynoise.

A Comparison of Quantum Walk Implementations on NISQ Computers