A Quantum-Search-Based Algorithm for the 0-1 Knapsack Problem

The knapsack problem is an important example of a combinatorial optimization problem with a wide range of applications in direct practical applications. In this article, the author considers the classical version of the problem (0-1 knapsack) and proposes a quantum algorithm for solving it based on a hybrid approach that combines the Grover quantum search algorithm with the procedure for finding the Durr–Hoyer minimum. The paper presents an analysis of the computational complexity of the proposed algorithm, and in addition to theoretical analysis, the article contains an explicit description of the quantum circuit implementing the proposed algorithm.