Range dependent Hamiltonian algorithms for numerical QUBO formulation

With the advent and development of quantum computers, various quantum algorithms that can solve linear equations and eigenvalues faster than classical computers have been developed. In particular, a hybrid solver provided by D-Wave's Leap quantum cloud service can utilize up to two million variables. Using this technology, quadratic unconstrained binary optimization (QUBO) models have been proposed for linear systems, eigenvalue problems, RSA cryptosystems, and computed tomography (CT) image reconstructions. Generally, QUBO formulation is obtained through simple arithmetic operations, which offers great potential for future development with the progress of quantum computers. A common method here was to binarize the variables and match them to multiple qubits. To achieve the accuracy of 64 bits per variable, 64 logical qubits must be used. Finding the global minimum energy in quantum optimization becomes more difficult as more logical qubits are used; thus, a quantum parallel computing algorithm that can create and compute multiple QUBO models is introduced here. This new algorithm divides the entire domain each variable can have into multiple subranges to generate QUBO models. This paper demonstrates the superior performance of this new algorithm particularly when utilizing an algorithm for binary variables.