Amplitude-Ensemble Quantum-Inspired Tabu Search Algorithm for Solving 0/1 Knapsack Problems

TL;DR

An improved version of Quantum-inspired Tabu Search (QTS) is proposed, called “Amplitude-Ensemble” QTS (AE-QTS), which makes AE-QTS more similar to the real quantum search algorithm, Grover Search Algorithm, in abstract concept, while keeping the simplicity of the algorithm.

Abstract

In this paper, an improved version of QTS (Quantum-inspired Tabu Search) has been proposed, which enhances the utilization of population information, called "amplitude-ensemble" QTS (AE-QTS). This makes AE-QTS more similar to the real quantum search algorithm, Grover Search Algorithm, in abstract concept, while keeping the simplicity of the algorithm. Later, we demonstrate the AE-QTS on the classical combinatorial optimization 0/1 knapsack problem. Experimental results show that the AE-QTS outperforms other algorithms, including the QTS, by at least an average of 20% in all cases and even by 30% in some cases. Even as the problem complexity increases, the quality of the solutions found by our method remains superior to that of the QTS. These results prove that our method has better search performance.

Figures (7)

• Figure 1: Polar plot of the rotation matrix on a qubit.
• Figure 2: The selection pair in $P(t)$.
• Figure 3: Case I: 100, 250, and 500 items.
• Figure 4: Case II: 100, 250, and 500 items.
• Figure 5: Case III: 100, 250, and 500 items.