TY - JOUR
T1 - Exponential algorithmic speedup by quantum walk
Y1 - 2002
A1 - Andrew M. Childs
A1 - Richard Cleve
A1 - Enrico Deotto
A1 - Edward Farhi
A1 - Sam Gutmann
A1 - Daniel A. Spielman
AB - We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different technique from previous quantum algorithms based on quantum Fourier transforms. We show how to implement the quantum walk efficiently in our oracular setting. We then show how this quantum walk can be used to solve our problem by rapidly traversing a graph. Finally, we prove that no classical algorithm can solve this problem with high probability in subexponential time.
UR - http://arxiv.org/abs/quant-ph/0209131v2
J1 - Proc. 35th ACM Symposium on Theory of Computing (STOC 2003)
U5 - 10.1145/780542.780552
ER -