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**Francis Sullivan **

**Matrix Inequalities, Boolean-valued Functions on S^2, and the Foundations of Quantum Computing**

**Wednesday, December 17, 2003
Building 3 Auditorium - 3:30PM**

(Refreshments at 3:00 PM)

Dr. Francis Sullivan, will talk about *Matrix Inequalities, Boolean-valued Functions on S^2, and the Foundations of Quantum Computing*. The discovery of Deutsch's algorithm was the first indication that concepts from the foundations of quantum mechanics might lead to interesting ideas in the theory of computation. The algorithm uses "entanglement" as the basis of a method for deciding if a function is odd or even and gets the answer in fewer steps than would be possible by classical methods. All quantum algorithms achieve their speed-up through the use of the parallelism inherent in entanglement. Limits on the amount of entanglement achievable per computational step provide lower bounds on the possibilities for quantum speed-ups.

From the purely mathematical point of view, the properties of entanglement are a consequence of the fact that quantum states really are vectors rather than merely scalars. Quantum states shouldn't be thought of as scalars whose actual values are based on certain probabilitiy theory. Measurements satisfy other, more general matrix inequality. The first part of this talk will be an exposition of this remarkable inequality.

Francis Sullivan received a B.S. degree in Physics from the Pennsylvania State University in 1962 and a Ph.D. degree in Mathematics from the University of Pittsburgh in 1968.

From 1982 to February 1993 he was at the National Institute of Standards and Technology, where he was Director of the Computing and Applied Mathematics Laboratory. Since February 1993 he has been Director of the IDA Center for Computing Sciences in Bowie, Maryland.

While in government service, Dr. Sullivan received the Department of Commerce Gold Medal in 1987 and the Presidential Meritorious Executive Rank Award in 1988.

Dr. Sullivan serves on several oversight committees, including the Industrial Advisory Board of Duke University; the Computer Science & Electrical Engineering Advisory Board of the University of Maryland-Baltimore County; and the Mathematical Sciences Advisory Network of the Whiting School of Engineering, Johns Hopkins University. He is also a member of the University of California Laboratory Security Panel and Science and Technology Panel for the Los Alamos, Lawrence Livermore, and Lawrence Berkeley National Laboratories. He is a past member of the NAS Mathematical Sciences Education Board, past Chairman of the IMA Board of Governors and is a past member of the SIAM Board of Trustees.

He is the author of a book and over 80 technical publications in algorithm design, non-linear methods, and computational physics. He serves on several editorial boards and is Editor-in-Chief for COMPUTING IN SCIENCE AND ENGINEERING, a joint publication of the IEEE Computer Society and the American Institute of Physics.

IS&T Colloquium Committee Host: John Dorband