**Spherical configurations, exponential sums, and quantum computation (joint work with Martin Roeteller).** - Igor Shparlinski

We describe two types of vector systems on the n-dimensional sphere over C, which are useful for quantum computation. For one type, such configurations can be obtained from Gaussian sums for every prime n. Configurations of the other type are not known to exist for infinitely many n. We show that using bounds of exponential sums with polynomials one can achieve certain approximate solutions. The results are based on both the Weil and Weyl bounds and also the result of Baker-Harman-Pintz about gaps between consecutive primes.