In this paper we develop a passive strategy to improve index investing, which we call the correlation diversified portfolio strategy. The proposed method adjusts the weight vector of the original index based on the permutation of the assets belonging to the original index. We seek the permutation of these assets such that those assets with a strong correlation to many other assets are placed in the center of the permutation. By reducing the weights of such central assets, we can construct portfolios that are more diversified and have better risk–return characteristics than the original index. We solve this asset-permutation problem by adopting a quantum-inspired approach. Concretely, we convert this permutation problem into a quadratic unconstrained binary optimization problem and use simulated annealing on a personal computer or annealing machine to find a near-optimal solution in a reasonable time. To examine the usefulness and computational feasibility of the proposed method, we apply it to three major indexes of the United States and Japan, and we provide numerical experiments that show portfolios constructed by the proposed method can achieve a higher return with lower volatility compared with the original indexes, while their behaviors are still similar to those of the original indexes.