Tu Delft Team Introduces Reduced Basis Algorithm for Polynomial Nonlinear Equations

Scientists at TU Delft, in collaboration with the Delft Institute of Applied Mathematics and Delft University of Technology, have developed a new method for addressing nonlinear differential equations using quantum computers, despite the inherent linearity of quantum evolution. Monica Lăcătuş and colleagues present a reduced basis algorithm (RBA) that efficiently solves these equations by composing polynomial updates and constructing a linear operator suitable for implementation on a quantum computer. This approach strategically shifts the primary computational load to a classical preprocessing stage, focused on determining the reduced monomial basis, while crucially maintaining accuracy equivalent to the initial time discretization scheme employed. The algorithm’s qubit requirement scales logarithmically with grid size for partial…