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A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates (1302.7316v1)
Published 28 Feb 2013 in quant-ph and cs.DS
Abstract: We present an extension to the quantum walk search framework that facilitates quantum walks with nested updates. We apply it to give a quantum walk algorithm for 3-Distinctness with query complexity ~O(n{5/7}), matching the best known upper bound (obtained via learning graphs) up to log factors. Furthermore, our algorithm has time complexity ~O(n{5/7}), improving the previous ~O(n{3/4}).