Implementation of controlled-controlled-phase gates by refocusing three-body interactions

Many applications for noisy intermediate scale quantum (NISQ) computing devices require entanglement over a large number of qubits, which is typically generated using two-qubit gates. However, being able to access and control strong multi-qubit interactions could significantly improve the capabilities of a device by allowing for more efficient generation of entanglement. For this purpose, we investigate a system of three superconducting qubits connected to a single tunable coupling element, in which conditional frequency shifts can be controlled by adiabatic flux pulses applied to the coupler. Using appropriate refocusing pulses and flux pulse timings, all accumulated phases of the computational states can be controlled leading to the implementation of the full family of pairwise controlled-phase (CPHASE) and controlled-controlled-phase (CCPHASE) gates. Numerical simulations, including decoherence effects, result in gate fidelities above 99% for realistic experimental parameter settings and gate times between 200ns and 300ns.