Quantum computing for modular iterative solvers

Our project focuses on exploring options for an efficient use of quantum computing to accelerate iterative solvers for sparse (non-) linear systems of equations as they typically arise in the discretization of partial differential equations. We target hybrid hardware systems, where the ’outer’ part of the overall solver is executed on a classical CPU or GPU and selected ’inner’ numerical kernels are executed on a connected quantum computer. We investigate options for numerical kernels, for which the complexity is reduced from n to log(n) on a quantum computer and that require only a few input and output data. For common low-order methods, it is well known that sparse solvers are a half-solved problem, and some approaches scale with the number of expected qubits. This naturally lends itself to pursuing preconditioning or more general convergence acceleration (e.g., quasi-Newton) on the quantum computer.