Methods for initializing a qubit into a pure state, reading the qubit, and arbitrarily rotating the qubit into any quantum state complete in times shorter than the qubit's typical dephasing and relaxation times. These methods provide universal single-qubit control and may be used to implement quantum gates with high fidelity. The methods may be implemented with superconducting qubits, such as heavy fluxonium, and do not rely on a three-dimensional cavity for suppressing spontaneous emission. Therefore, the methods may be implemented using smaller two-dimensional architectures commonly used for superconducting circuits. The methods also work with low-frequency qubits, i.e., qubits for which the energy spacing between the two quantum-computational states is less than the mean thermal energy of a surrounding bath. This reduces the cooling requirements of the qubit while maintaining fidelity.