Exponential algorithmic speedup by quantum walk

Details Exponential algorithmic speedup by quantum walk Exponential algorithmic speedup by quantum walk

2002-09-24

arxiv.org/abs/quant-ph/0209131v2

Proc. 35th ACM Symposium on Theory of Computing (STOC 2003), pp. 59-68

Physics

Quantum Physics

24 pages, 7 figures; minor corrections and clarifications

Scientific paper

10.1145/780542.780552

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.

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