Performance Gains for Superconducting Qubits by Means of Optimal Control Theory

Superconducting circuits are promising candidates for the successful implementation of qubit--arrays and qubit--gates within solid--state systems. However, despite recent progress within coherent control of charge, phase and flux qubits, considerable improvement in gate fidelities is needed to build large--scale quantum information processing devices. We present an optimal control scheme based on process tomography, capable of taking into account relaxation, dephasing and unwanted state--leakage within the qubit (array). We apply this theory to explore the performance limits of Josephson charge qubits within current experimental means. Environmental effects, as well as state--leakage, are modeled microscopically, using a full quantum mechanical description and taking into account 1/f and Ohmic fluctuations based on experimental noise spectra. Within time--optimal control theory, we show that under typical conditions gate fidelities of $F=1-10^{-3}$ should be possible for a Josephson charge qubit.