  Applications for noisy intermediate-scale quantum computing devices rely on
the efficient entanglement of many qubits to reach a potential quantum
advantage. Although entanglement is typically generated using two-qubit gates,
direct control of strong multi-qubit interactions can improve the efficiency of
the process. Here, we investigate a system of three superconducting
transmon-type qubits coupled via a single flux-tunable coupler. Tuning the
frequency of the coupler by adiabatic flux pulses enables us to control the
conditional energy shifts between the qubits and directly realize multi-qubit
interactions. To accurately adjust the resulting controlled relative phases, we
describe a gate protocol involving refocusing pulses and adjustable interaction
times. This enables the implementation of the full family of pairwise
controlled-phase (CPHASE) and controlled-controlled-phase (CCPHASE) gates.
Numerical simulations result in fidelities around 99 % and gate times below 300
ns using currently achievable system parameters and decoherence rates.
