A Comparison of Quantum Walk Implementations on NISQ Computers
This paper explores two circuit approaches for quantum walks: the first
consists of generalised controlled inversions, whereas the second one
effectively replaces them with rotation operations around the basis states. We
show the theoretical foundation of the rotational implementation. The
rotational approach nullifies the large amount of ancilla qubits required to
carry out the computation when using the inverter implementation. Our results
concentrate around the comparison of the two architectures in terms of
structure, benefits and detriments, as well as the computational resources
needed for each approach. We show that the inverters approach requires
exponentially fewer gates than the rotations but almost half the number of
qubits in the system. Finally, we execute a number of experiments using an IBM
quantum computer. The experiments show the effects of noise in our circuits.
Small two-qubit quantum walks evolve closer to our expectations, whereas for a
larger number of steps or state space the evolution is severely affected by
noise.
Konstantinos Georgopoulos Clive Emary Paolo Zuliani