Method and System for Solving Optimization Problems

Abstract

The present invention relates to a computer-implemented method 100 and system for solving optimization problems using a quantum processing unit with multiple qubits and quantum gates. The method employs a tree-based optimization approach, for example a branch-and-bound or cut technique, integrated with a bias-field digitized counter-diabatic quantum optimization algorithm. It involves encoding the optimization problem into a problem Hamiltonian, initializing a time- dependent Hamiltonian, and applying a bias field. The quantum processing unit evolves the quantum state to reach the ground state of the problem Hamiltonian, followed by measuring and computing expectation values. The present invention constructs a tree of branches based on selected qubits, applying constraints to explore configurations that yield the lowest expectation values. Ultimately, it determines the optimal solution by extracting a bitstring from the final probability distribution, enhancing the efficiency and accuracy of solving complex optimization problems.