  We introduce a novel hybrid approach combining tensor network methods with
the stabilizer formalism to address the challenges of simulating many-body
quantum systems. By integrating these techniques, we enhance our ability to
accurately model unitary dynamics while mitigating the exponential growth of
entanglement encountered in classical simulations. We demonstrate the
effectiveness of our method through applications to random Clifford T-doped
circuits and Random Clifford Floquet Dynamics. This approach offers promising
prospects for advancing our understanding of complex quantum phenomena and
accelerating progress in quantum simulation.
