CEPI Seminar Abstract

Wednesday, May 03, 2006 • 3:30 PM • Robert N. Noyce Conference Room

Joseph Traub Computer Science Dept., Columbia University

Qubit Complexity of Continuous Problems

For the foreseeable future the number of qubits will be a crucial computational resource. We show how to lower bound the qubit complexity using the classical query complexity. We use this result to present a simple problem which cannot be solved on a quantum computer in the standard quantum setting with deterministic queries but can be solved on a classical computer using randomized queries (Monte Carlo). This suggests introducing a quantum setting with randomized queries. We apply this setting to high dimensional integration and to path integration. In particular, there is an exponential improvement in the qubit complexity of path integration using the quantum setting with randomized queries. We end by discussing future directions and where to learn more.

Joseph F. Traub is the Edwin Howard Armstrong Professor at Columbia University and External Professor at the Santa Fe Institute. In 1959 he started his pioneering research on what is now called information-based complexity. He is the author of ten books and some one hundred and twenty research papers in which he has applied complexity theory to fields as diverse as physics, economics, and finance. A major focus of his current work is quantum computing.

From 1971 to 1979 Traub was Head of the Computer Science Department at Carnegie Mellon University. He served as founding chairman of the Computer Science Department at Columbia University from 1979 to 1989. He started the Journal of Complexity in 1985 and has been Editor-in-Chief since. He was founding Chair of the Computer Science and Telecommunications Board of the National Academies from 1986 to 1992 and is again serving as Chair.

Traub has received numerous honors including election to the National Academy of Engineering in 1985, the Emanuel R. Piore Gold Medal from IEEE, and the 1992 Distinguished Service Award, Computer Research Association. He is a Fellow of the American Association for the Advancement of Science, the Association of Computing Machinery, and the New York Academy of Sciences. He has been Sherman Fairchild Distinguished Scholar at the California Institute of Technology and received a Distinguished Senior Scientist Award from the Alexander Van Humboldt Foundation. He was selected by the Academia Nazionale dei Lincei in Rome to present the 1993 Lezione Lincei. Traub received the 1999 Mayor's Award for Excellence in Science and Technology. The Award was presented by Mayor Rudy Giuliani at a ceremony in New York City. In 2001 he received an honorary Doctorate of Science from the University of Central Florida.