Error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering

We propose a scheme to realize error-resistant nonadiabatic binomial-code geometric quantum computation using reverse engineering. A strong Kerr nonlinearity restricts the evolution in a computational subspace of the binomial code and a two-photon squeezing drive provides the connections between the logical states. The effective Hamiltonian possesses SU(2) dynamic structure and is analyzed through reverse engineering based on a dynamic invariant. By combining reverse engineering with the optimal control method, we find the evolution paths for nonadiabatic geometric quantum computation and derive the control field robust against the systematic error. Numerical simulations show that the scheme holds excellent resistance to the systematic error and is still well implemented in the presence of resonator leakage with the current superconducting nonlinear resonator technology. Therefore, the scheme may provide a promising approach for accurate nonadiabatic binomial-code geometric quantum computation.