CaDS Seminar 2024 - Jan. 30

Orkun Sensebat (Quantum Information Processing Group)

Solving partial differential equations on a D-Wave quantum annealer

Abstract:

Solving linear systems of equations represent an often overlooked opportunity to benchmark problems on quantum computers. While such equations can be efficiently solved using the Gauss algorithm on classical computers, quantum annealers necessitate the formulation of the problem as a Quadratic Unconstrained Binary Optimization (QUBO) problem, generally np-hard. We endeavor to expand the current understanding by investigating strategies for solving discrete partial differential equations. The QUBO coefficients, derived from encoding the problem variables via fixed-point binary representations, exhibit exponential scaling, presenting a significant challenge for D-Wave quantum annealers. We propose a method termed ‘gate-based encoding’, which conceptualizes the problem in a logical circuit format, drawing inspiration from factorization problems. This approach effectively addresses the issue of exponential scaling through the employment of ancilla qubits, leading to enhanced success probabilities and the capability to solve problems of marginally greater complexity compared to conventional QUBO formulations.