Preparation of a Bell state in an analogue device hosting the transverse-field Ising model

Abstract: We propose a protocol for preparing the singlet Bell state in an analogue device implementing the transverse-field Ising model with ZZ interactions and local X and Z fields, which can be engineered within the superconducting platform, among others. This protocol is performed by direct control of the terms of the Hamiltonian alone. The method exploits the fact that the singlet state is the first excited state of a symmetric Hamiltonian family, and comprises two steps: an adiabatic interpolation preparing the ground state of said symmetric Hamiltonian, followed by the resonant population transfer between its two lowest energy levels. For realistic parameters, the protocol achieves fidelities comparable to standard gate-based preparation within similar time scales ($\sim$100 ns), and can reach infidelities on the order of $10<sup>{-4}$ with a moderately increased duration. We further analyse robustness against systematic control errors and show that high fidelities are maintained under implementation imperfections.