  As systems for quantum computing keep growing in size and number of qubits,
challenges in scaling the control capabilities are becoming increasingly
relevant. Efficient schemes to simultaneously mediate coherent interactions
between multiple quantum systems and to reduce decoherence errors can minimize
the control overhead in next-generation quantum processors. Here, we present a
superconducting qubit architecture based on tunable parametric interactions to
perform two-qubit gates, reset, leakage recovery and to read out the qubits. In
this architecture, parametrically driven multi-element couplers selectively
couple qubits to resonators and neighbouring qubits, according to the frequency
of the drive. We consider a system with two qubits and one readout resonator
interacting via a single coupling circuit and experimentally demonstrate a
controlled-Z gate with a fidelity of $98.30\pm 0.23 \%$, a reset operation that
unconditionally prepares the qubit ground state with a fidelity of $99.80\pm
0.02 \%$ and a leakage recovery operation with a $98.5\pm 0.3 \%$ success
probability. Furthermore, we implement a parametric readout with a single-shot
assignment fidelity of $88.0\pm 0.4 \%$. These operations are all realized
using a single tunable coupler, demonstrating the experimental feasibility of
the proposed architecture and its potential for reducing the system complexity
in scalable quantum processors.
