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Lecture Notes in Computer Science
We consider the problem of testing the commutativity of a black-box group specified by its k generators. The complexity (in terms of k) of this problem was first considered by Pak, who gave a randomized algorithm involving O(k) group operations. We construct a quite optimal quantum algorithm for this problem whose complexity is inÕ(k 2/3 ). The algorithm uses and highlights the power of the quantization method of Szegedy. For the lower bound of Ω(k 2/3 ), we introduce a new technique ofdoi:10.1007/11523468_106 fatcat:owywrsgi6zfrnkzcab2p5ohwmq