Speaker
Description
In this talk, we present a quantum algorithm for numerically solving the Fokker-Planck equation that describes the stochastic processes in cosmology. In particular, we consider the discretization in which time evolution is represented via (sub-)stochastic transition matrices. Based on this discretization, the computation of time evolution of the numerical solution to the Fokker-Planck equation becomes repeated multiplication of the transition matrices, suggesting the possibility of an implementation via quantum algorithms. We present a method to implement this repeated matrix multiplication using a quantum matrix inversion algorithm [1] based on Quantum Singular Value Transformation (QSVT) [2]. As an application, we demonstrate how this method can be used to analyze the phase transition to eternal inflation in cosmic inflation [3].
