  We propose an enhanced Time-Dependent Variational Principle (TDVP) algorithm
for Matrix Product States (MPS) that integrates Clifford disentangling
techniques to efficiently manage entanglement growth. By leveraging the
Clifford group, which maps Pauli strings to other Pauli strings while
maintaining low computational complexity, we introduce a Clifford dressed
single-site 1-TDVP scheme. During the TDVP integration, we apply a global
Clifford transformation as needed to reduce entanglement by iteratively
sweeping over two-qubit Clifford unitaries that connect neighboring sites in a
checkerboard pattern. We validate the new algorithm numerically using various
quantum many-body models, including both integrable and non-integrable systems.
Our results demonstrate that the Clifford dressed TDVP significantly improves
entanglement management and computational efficiency, achieving higher
accuracy, extended simulation times, and enhanced precision in computed
observables compared to standard TDVP approaches. Additionally, we propose
incorporating Clifford gates directly within the two-site 2-TDVP scheme.
