@article {1258, title = {A Time-Efficient Quantum Walk for 3-Distinctness Using Nested Updates}, year = {2013}, month = {2013/02/28}, 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}). }, url = {http://arxiv.org/abs/1302.7316v1}, author = {Andrew M. Childs and Stacey Jeffery and Robin Kothari and Frederic Magniez} }