Design and Analysis of Quantum Comparator Circuits for Constrained Optimization Problem

Quantum optimization has the potential to be one of the paradigms to solve NP-hard problems. In this paper, we demonstrate the design and implementation of quantum comparator circuits for the four-variable knapsack problem. The problem formulation is subject to a capacity limit on the total weight of items. Furthermore, we compare the Quantum Fourier Transform-based comparator with the Toffoli gate-based comparator. The proposed oracle circuit integrates controlled adders, multi-controlled comparators, and ancilla-assisted feasibility flags to enforce constraints. Simulation results demonstrate that the comparators successfully prune the infeasible states. The solution also identifies the optimal solutions with maximum profit while respecting all constraints.