Stochastic optimization on complex variables and pure-state quantum tomography.

ABSTRACT: Real-valued functions of complex arguments violate the Cauchy-Riemann conditions and, consequently, do not have Taylor series expansion. Therefore, optimization methods based on derivatives cannot be directly applied to this class of functions. This is circumvented by mapping the problem to the field of the real numbers by considering real and imaginary parts of the complex arguments as the new independent variables. We introduce a stochastic optimization method that works within the field of the complex numbers. This has two advantages: Equations on complex arguments are simpler and easy to analyze and the use of the complex structure leads to performance improvements. The method produces a sequence of estimates that converges asymptotically in mean to the optimizer. Each estimate is gene

SUBMITTER: Utreras-Alarcon A 

PROVIDER: S-EPMC6834649 | biostudies-literature | 2019 Nov

REPOSITORIES: biostudies-literature