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Quantum Random Walks do not need a Coin Toss

Apoorva Patel·K. S. Raghunathan·Pranaw Rungta
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Abstract

Classical randomized algorithms use a coin toss instruction to explore different evolutionary branches of a problem. Quantum algorithms, on the other hand, can explore multiple evolutionary branches by mere superposition of states. Discrete quantum random walks, studied in the literature, have nonetheless used both superposition and a quantum coin toss instruction. This is not necessary, and a discrete quantum random walk without a quantum coin toss instruction is defined and analyzed here. Our construction eliminates quantum entanglement from the algorithm, and the results match those obtained with a quantum coin toss instruction.

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Apoorva Patel, K. S. Raghunathan, Pranaw Rungta. 2005-01-19. Quantum Random Walks do not need a Coin Toss. https://doi.org/10.1103/physreva.71.032347

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