Quantum Walks in a Superconducting Quantum Computer - Santos, Jaime; Chagas, Bruno; Chaves, Rodrigo (Anais do Workshop de Comunicação e Computação Quântica (WQuantum), 2021)
Quantum Walks are among the most widely used techniques with which we can construct new quantum algorithms. This paper aims to outline how to construct a circuit for the continuous-time quantum walk (CTQW) over circulant graphs using the Quantum Fourier Transform (QFT) due to the spectral properties of those graphs. Furthermore, we examine how the Approximate Quantum Fourier Transform (AQFT) allows us to shorten the size of the circuit by reducing the number of controlled rotation gates. The contributions of this paper consist of the development of a general circuit implementation of the CTQW for an important class of graphs that does not scale up with time, and the study of the cases where the AQFT decreases the error by controlling the approximation. Finally, we provide a statistical analysis for several circulant graphs, running experiments in a IBM's superconducting quantum computer, and we also explore the pretty good state transfer (PGST) for some graphs.