Clifford-Enhanced Matrix Product States: A Classical Path for Scalable Quantum State Simulations

We investigate Clifford-enhanced Matrix Product States (CMPS) as a hybrid framework that combines the efficient entanglement representation provided by Clifford circuits with non-stabilizerness encoded in MPS tensors. By separating the contributions of the two resources, we obtain a more flexible and scalable description of many-body quantum states. This division of computational resources results in a substantial reduction in memory footprint without compromising accuracy, while maintaining high expressibility. We demonstrate the effectiveness of this approach by analyzing the expressibility of Clifford-enhanced MPS, showing that they can approach the Haar-random distribution in terms of magic and entanglement. These results highlight the potential of Clifford-enhanced MPS architectures for scalable and memory-efficient quantum state simulations, with a primary focus on ground-state approximations.