Systematic Magnus-based approach for suppressing leakage and non-adiabatic errors in quantum dynamics

We present a systematic, perturbative method for correcting quantum gates to suppress errors that take the target system out of a chosen subspace. It addresses the generic problem of non-adiabatic errors in adiabatic evolution and state preparation, as well as general leakage errors due to spurious couplings to undesirable states. The method is based on the Magnus expansion: by correcting control pulses, we modify the Magnus expansion of an initially-given, imperfect unitary in such a way that the desired evolution is obtained. Applications to adiabatic quantum state transfer, superconducting qubits and generalized Landau-Zener problems are discussed.