Incorporation of Constraints in Optimization Problems via Normalization Condition in Hilbert Space

Resumo

In this work, we introduce a technique for incorporating constraints into the structure of quantum mechanics through the normalization condition of quantum states. We present a method for constructing Hamiltonians for optimization problems directly from the problem’s own constraints, eliminating the need to insert penalty terms into the Hamiltonian and ensuring that the search space matches the feasible solution space of the problem. We demonstrate the validity of the proposal with a theoretical proof of concept, discuss its possibilities and limitations, and explore potential applications.