MIT Quantum Information Processing seminar Monday 10/31 at 4:00 in 6C-442 ------------------------------------------------- Pawel Wocjan (University of Central Florida) Quantum Algorithm for Computing the Period Lattice of an Infrastructure Abstract: We present an efficient quantum algorithm for computing the period lattice of infrastructures of fixed dimension. The algorithm applies to infrastructures that satisfy certain conditions. The latter are always fulfilled for infrastructures obtained from global fields, i.e., algebraic number fields and function fields with finite constant fields. The first of our main contributions is a rigorous and complete proof that the running time of the algorithm is polynomial in the logarithm of the determinant of the period lattice and exponential in the dimension n. The second main contribution is the determination of an explicit lower bound on the success probability of our algorithm which improves on the bounds given in the works of Hallgren and Schmidt and Vollmer. The exponential scaling seems inevitable because the best currently known methods for carrying out fundamental arithmetic operations in infrastructures obtained from algebraic number fields take exponential time. In contrast, the problem of computing the period lattice of infrastructures arising from function fields can be solved without the exponential dependence on the dimension n since this problem reduces efficiently to the abelian hidden subgroup problem. This is also true for other important computational problems in algebraic geometry. The running time of the best classical algorithms for infrastructures arising from global fields increases subexponentially with the determinant of the period lattice. The talk is based on two articles: one with Felix Fontein and one with Pradeep Sarvepalli. _______________________________________________ qip mailing list qip(a)mit.edu http://mailman.mit.edu/mailman/listinfo/qip