Seminar: Quantum complexity of integration in tensor product Besov spaces

Time:

Venue/Location: Phòng C102, VIASM

Báo cáo viên: Bernd Käßemodel (Chemnitz University of Technology)

Tóm tắt: After a brief introduction to quantum information-based complexity for multivariate integration and approximation, we study the worst-case quantum query error for the integration of functions from tensor product Besov classes with mixed smoothness. We discuss characterizations of these spaces via the tensorized Faber-Ciesielski basis with coefficients defined by mixed iterated differences. Based on this decomposition, we develop an algorithm that yields upper bounds for the worst-case quantum query error over this function class. Finally, we discuss the optimality of our results in comparison with known error rates of deterministic and randomized classical algorithms