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arXiv · 2108.02723

Quantum Computing: Implementing Hitting Time for Coined Quantum Walks on Regular Graphs

Ellinor Wanzambi·Stina Andersson
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Abstract

In recent years, quantum walks have been widely researched and have shown exciting properties. One such is a quadratic speed-up in hitting time compared to its classical counterpart. In this paper, we design a quantum circuit for the MNRS algorithm, which finds a marked node in a graph with a quantum walk, and use it to find a hitting time for the marked nodes in the walk. We do this by implementing the circuit on IBM quantum simulators and show that the execution on a noise-free simulator results in hitting times that agree with the theoretical expectations. We also run the algorithm on a mock backend that simulates the noise of the IBM Melbourne computer. As expected, the noise has an extensive impact on the output, resulting in outcomes far from the noise-free simulation.

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Ellinor Wanzambi, Stina Andersson. 2021-08-05. Quantum Computing: Implementing Hitting Time for Coined Quantum Walks on Regular Graphs. https://arxiv.org/abs/2108.02723

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