Hamiltonian Forging of a Thermofield Double

We address the variational preparation of the Thermofield Double as the ground state of a suitably engineered Hamiltonian acting on the doubled Hilbert space. Through the use of the Entanglement Forging ansatz, we propose a solution that involves only circuits of width $N$. We illustrate the method with generic fermionic Hamiltonians. The free fermion case can be solved in closed form, and yields a warm start state for the variational circuits whenever interactions are present. As an important side product, this method returns the complete energy spectrum and eigenbasis of the system.