  Resonant transverse driving of a two-level system as viewed in the rotating
frame couples two degenerate states at the Rabi frequency, an amazing
equivalence that emerges in quantum mechanics. While spectacularly successful
at controlling natural and artificial quantum systems, certain limitations may
arise (e.g., the achievable gate speed) due to non-idealities like the
counter-rotating term. Here, we explore a complementary approach to quantum
control based on non-resonant, non-adiabatic driving of a longitudinal
parameter in the presence of a fixed transverse coupling. We introduce a
superconducting composite qubit (CQB), formed from two capacitively coupled
transmon qubits, which features a small avoided crossing -- smaller than the
environmental temperature -- between two energy levels. We control this
low-frequency CQB using solely baseband pulses, non-adiabatic transitions, and
coherent Landau-Zener interference to achieve fast, high-fidelity, single-qubit
operations with Clifford fidelities exceeding $99.7\%$. We also perform coupled
qubit operations between two low-frequency CQBs. This work demonstrates that
universal non-adiabatic control of low-frequency qubits is feasible using
solely baseband pulses.
