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The distribution of hard graph coloring problems as a function of graph connectivity is shown to have two distinct transition behaviors. The first, previously recognized, is a peak in the median search cost near the connectivity at which half the graphs have solutions. This region contains a high proportion of relatively hard problem instances. However, the(More)
We describe how techniques that were originally developed in statistical mechanics can be applied to search problems that arise commonly in artificial intelligence. This approach is useful for understanding the typical behavior of classes of problems. In particular, these techniques predict that abrupt changes in computational cost, analogous to physical(More)
We discuss quantum algorithms that calculate numerical integrals and descriptive statistics of stochastic processes. With either of two distinct approaches , one obtains an exponential speed increase in comparison to the fastest known classical deterministic algorithms and a quadratic speed increase in comparison to classical Monte Carlo (probabilistic)(More)
The quantum Fourier transform (QFT), a quantum analog of the classical Fourier transform, has been shown to be a powerful tool in developing quantum algorithms. However, in classical computing there is another class of unitary transforms, the wavelet transforms, which are every bit as useful as the Fourier transform. Wavelet transforms are used to expose(More)
A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order ͱd, where d is the dimension of the search space, whereas any classical algorithm necessarily scales as O(d). It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting one(More)