Gate Operations for Superconducting Qubits and Non-Markovianity: Fidelities, Long-range Time Correlations, and Suppression of Decoherence

While the accuracy of qubit operations has been greatly improved in the last decade, further development is demanded to achieve the ultimate goal: a fault-tolerant quantum computer that can solve real-world problems more efficiently than classical computers. With growing fidelities even subtle effects of environmental noise such as qubit-reservoir correlations and non-Markovian dynamics turn into the focus for both circuit design and control. To guide progress, we disclose, in a numerically rigorous manner, a comprehensive picture of the single-qubit dynamics in presence of a broad class of noise sources and for entire sequences of gate operations. Thermal reservoirs ranging from Ohmic to deep 1/fε-like sub-Ohmic behavior are considered to imitate realistic scenarios for superconducting qubits. Apart from dynamical features, two figures of merit are analyzed, namely, fidelities of the qubit performance over entire sequences and coherence times in presence of quantum control schemes such as the Hahn echo and dynamical decoupling. The relevance of retarded feedback and long-range qubit-reservoir correlations is demonstrated on a quantitative level, thus, providing a deeper understanding of the limitations of performances for current devices and guiding the design of future ones.