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Quantum Coins for Non-Power-of-Two States - Implementation and Performance on Quantum Walk and Quantum Walk Search Algorithms

Quantum coin is an essential element of the discrete-time quantum walk, the quantum analog of random walk. Most existing papers relating to quantum coin discussed the implementation and performance of the coin on power-of-two states and degrees of graphs. In this paper, I proposed and analyzed three alternative coins–binary state coin, W state coin, and Walsh-Hadamard coin–that possessed the property to perform on all states and degrees of graphs. I discussed the implementation and the performance of the three coins in the application of Quantum Walk and Quantum Walk Search. I compared and discussed the advantages, disadvantages, and errors of the three coins on a quantum simulator and a NISQ computer (i.e. IBM Q). In the end, I presented further applications for the three coins in quantum-walk-based algorithms and other potential topics in quantum computing.