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- Colin P. Williams, Tad Hogg
- Artif. Intell.
- 1994

We introduce a technique for analyzing the behavior of sophisticated A.I. search programs working on realistic , large-scale problems. This approach allows us to predict where, in a space of problem instances, the hardest problems are to be found and where the fluctuations in difficulty are greatest. Our key insight is to shift emphasis from modelling… (More)

- Tad Hogg, Colin P. Williams
- Artif. Intell.
- 1994

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)

- Tad Hogg, Bernardo A. Huberman, Colin P. Williams
- Artif. Intell.
- 1996

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)

- Amir Fijany, Colin P. Williams
- QCQC
- 1998

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)

- Colin P. Williams, Alexander G. Gray
- QCQC
- 1998

In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of a sequence of quantum gate operations. To date, such designs have either been found by hand or by exhaustive enumeration of all possible circuit topologies. In this paper… (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)

We prove that a generic three-qubit quantum logic gate can be implemented using at most 67 one-qubit rotations about the y-and z-axes and 43 CNOT gates, beating an earlier bound of 64 CNOT gates.

- B Smit, C P Williams
- 2001

Monte Carlo calculations in the Gibbs ensemble are reported for pure quadrupolar Lennard-Jones fluids. The vapour-liquid equilibrium curves, critical temperatures, and critical densities are calculated for various quadrupolar strengths (e*' = Q'/Eu' = 1.0, 1.5, 2.0 and 2.5). It is shown that as the quadrupolar strength increases both the critical… (More)