Sponsor: THALES
Context
The problem of inverting a matrix that represents group convolution and/or cross-correlation has been studied by Seth Lloyd team at MIT and at Waterloo University. The algorithm’s complexity does not depend on the sparsity of the matrix. Quantum Group Convolution is used to solve linear partial differential equations (PDEs) over domains that contain a certain symmetry (periodic PDE questions can be reformulated as cross-correlations). Achievements of polynomial speedups with respect to the dimension of the problem, while enjoying from a polylogarithmic dependence on the inverse precision.
Objectives
Study of Quantum Group Convolution for PDE to solve:
- Poisson equation (to formulate the stationary state of a heat equation)
- Elliptic equation (generalizing the Poisson equation)
Extension of study of Quantum Group Convolution for Quantum Equivariant Neural Network.