  In this note we develop quantum circuits for exactly simulating the thermal
properties of the quantum XY/Ising chain. These circuits are applicable to the
simplest integrable lattice models for which the exact momentum-space
scattering-matrix can be constructed in terms of local two-body gates. We
discuss a circuit analogy for Wilsonian renormalization group flow and show how
it can be used to simulate a global coarse graining transformation. We then
construct a circuit that transforms the ground state of these models into the
thermo-field double state, and show how it can be used to implement a local
scale transformation.
