Entanglement-Forged Variational Diagonalisation for Low-Energy Subspaces

We address the variational preparation of Thermofield Doubles (TFD) as ground states of suitably engineered Hamiltonians acting on a doubled Hilbert space with of N qubits.

Through the use of the Entanglement Forging ansatz, we propose a variational method that involves only circuits of width N/2, and 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 interaction are present.

As a result of the variational optimization, the unitary matrix that diagonalises the low-energy spectrum of the local system becomes available.