Recent studies have highlighted the combination of tensor-network methods and the stabilizer formalism as a very effective framework for simulating quantum many-body systems, encompassing areas from ground-state to time-evolution simulations. In these approaches, the entanglement associated with stabilizers is transferred to Clifford circuits, which can be efficiently managed due to the Gottesman-Knill theorem. Consequently, only the nonstabilizerness entanglement needs to be handled, thereby reducing the computational resources required for accurate simulations of quantum many-body systems in tensor-network-related methods. In this work, we adapt this paradigm for finite-temperature simulations in the framework of the time-dependent variational principle, in which imaginary-time evolution is performed using the purification scheme. Our numerical results on the one-dimensional Heisenberg model and the two-dimensional $J_1-J_2$ Heisenberg model demonstrate that Clifford circuits can significantly improve the efficiency and accuracy of finite-temperature simulations for quantum many-body systems. This improvement not only provides a useful tool for calculating finite-temperature properties of quantum many-body systems, but also paves the way for further advancements in boosting the finite-temperature tensor-network calculations with Clifford circuits and other quantum circuits.

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• Thermodynamics
• Quantum many-body systems
• Density matrix renormalization group
• Matrix product states
• Tensor network methods