Augmenting Finite Temperature Tensor Network with Clifford Circuits

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 non-stabilizerness 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 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.