Adiabatic Simulation of the Hydrogen Molecule with Superconducting Qubits

Superconducting circuits are well suited for the adiabatic simulation of Hamiltonians with bosonic as well as fermionic degrees of freedom. Here, we present analytical and numerical results, which demonstrate the feasibility of simulating the groundstate of the hydrogen molecule using two superconducting qubits. In our proposal tunable two-qubit interactions are realised by parametrically modulating the frequency of a tunable bus element with an external magnetic flux. We derive the effective Hamiltonian of the device with tunable XX and YY type interactions using a time-dependent Schrieffer-Wolff transformation. Numerical simulations of a quantum annealing protocol for the groundstate of the hydrogen molecule demonstrate that the time required to reach chemical accuracy lies in the few microsecond range for typical device coherence.