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- 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)

- 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)

- 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)

- Colin P. Williams, Tad Hogg
- AAAI
- 1992

One usually writes A.I. programs to be used on a range of examples which, although similar in kind, differ in detail. This paper shows how 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 sophisticated algorithms… (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)

Classical, interferometric, optical lithography is diffraction limited to writing features of a size λ/4 or greater, where λ is the optical wavelength. Using nonclassical photon-number states, entangled N at a time, we show that it is possible to write features of minimum size λ/(4N) in an N-photon absorbing substrate. This result surpasses the usual… (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, Tad Hogg
- AAAI
- 1993