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Quantum computing, zeroes of zeta functions, and approximate counting

Algebra & Discrete Mathematics

Speaker: Wim van Dam, UC Santa Barbara
Location: 693 Kerr
Start time: Fri, Dec 9 2005, 1:10PM

In this talk I describe a possible connection between quantum computing and Zeta functions of finite field equations that is inspired by the 'spectral approach' to the Riemann conjecture. The assumption is that the zeroes of such Zeta functions correspond to the eigenvalues of finite dimensional unitary operators of natural quantum mechanical systems. To model the desired quantum systems I use the notion of universal, efficient quantum computation.

Using eigenvalue estimation, such quantum systems are able to approximately count the number of solutions of the specific finite field equations with an accuracy that does not appear to be feasible classically. For certain equations (Fermat hypersurfaces) I show that one can indeed model their Zeta functions with efficient quantum algorithms, which gives some evidence in favor of the proposal.

Reference: arXiv:quant-ph/0405081

There will be lunch with the out-of-town speaker. Meet at 11:55 sharp, at the ground floor of Kerr Hall.