Simulating the Impact of Noise on Quantum Walk Algorithm

Abstract: Quantum computing has recently shown promise for improving the efficiency of some classical algorithms. However, quantum computing suffers from issues in reliability due to the fundamental problem of quantum mechanics called decoherence. Having reliable algorithms is crucial if the industry and our society is going to dare adopt this new, potentially world-altering, technology. Quantum walk is the quantum equivalent of the classical random walk. It is exponentially faster and its utility in practice can have tremendous impact. It is interesting to understand to what extent the quantum walk algorithm is robust against the problems of quantum computing. Therefore, this thesis examines the impact of noise on the quantum walk algorithm on a hypercube. This is done by using IBM Qiskit to simulate different noise models’ effects on a quantum walk’s accuracy, while walking on the 4-dimensional hypercube. The simulator is configured with calibration data gathered from the 7-bit quantum computer IBM Nairobi. The results are clear. At worst, the algorithm produces an incorrect result approximately one in five times. It is also the case that walking from some nodes in the graph cause more error than other nodes. Depending on what path is walked, different levels of error are observed.