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Adaptive mutation, the phenomenon where organisms appear to increase beneficial mutation rates in response to environmental stress, has challenged the traditional understanding of random mutations in evolutionary biology. Here, we present a novel computational model, the Entangled Evolution Model, which integrates quantum game theory and quantum walks to provide a new approach to understanding mutation dynamics. By applying the Clauser-Horne-Shimony-Holt (CHSH) quantum game within a modified Lotka-Volterra framework, we simulate how quantum entanglement can accelerate the rate of adaptive mutations in Escherichia coli populations. Our simulations reveal that entangled bacterial populations achieve successful adaptive mutations with an 85% probability, significantly surpassing the classical theoretical maximum. These results introduce a new perspective on computational approaches to evolutionary adaptation, offering an efficient algorithmic framework to explore the role of quantum effects in biological systems.