Variational Quantum Homotopy Perturbation Method to Solve Nonlinear Partial Differential Equations
The Quantum Homotopy Perturbation Method (QHPM) is a new numerical technique to solve complex nonlinear partial differential equations by transforming them into a linear system. It achieves scalability by keeping the Hilbert space dimension constant during linearization and uses a variational quantum simulation framework to reduce qubit requirements. This method provides accurate solutions similar to traditional numerical methods when optimized.