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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/f^{ɛ}-like sub-Ohmic behavior are considered to imitate realistic scenarios for superconducting qubits. Apart from dynamical features, fidelities of the qubit performance over entire sequences are analyzed as a figure of merit. 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.