Quantum Random Walks do not need a Coin Toss

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.

6 pages, 4 figures, RevTeX (v2) Expanded to include relation to quantum walk with a coin. Connection with Dirac equation pointed out. Version to be published in Phys. Rev. A