  Tensor networks provide a useful tool to describe low-dimensional complex
many-body systems. Finding efficient algorithms to use these methods for
finite-temperature simulations in two dimensions is a continuing challenge.
Here, we use the class of recently introduced isometric tensor network states,
which can also be directly realized with unitary gates on a quantum computer.
We utilize a purification ansatz to efficiently represent thermal states of the
transverse field Ising model. By performing an imaginary-time evolution
starting from infinite temperature, we find that this approach offers a
different way with low computational complexity to represent states at finite
temperatures.
