Non-Local Multi-Qubit Quantum Gates via a Driven Bosonic Mode

Native Non-Local quantum gates are essential for efficient implementation of quantum circuits in the Noisy-Intermediate-Scale-Quantum(NISQ) era quantum devices, and for Quantum Error Correction in the future. In this regard, we present two protocols for implementing deterministic non-local multi-qubit quantum gates on qubits coupled to a common bosonic mode e.g. a cavity field. In contrast to previous proposals, our protocols only rely on a classical drive of the bosonic mode, while no external drive of the qubits is required. In the first protocol, the state of the bosonic mode follows a closed trajectory in phase space and accumulates a geometric phase depending on the state of the qubits. The second protocol instead uses an adiabatic evolution of the combined qubit and bosonic mode system to accumulate a dynamical phase. For both protocols, we provide analytic solutions for the error rates in the presence of losses. Our protocols are applicable to a variety of systems, including cold atoms and molecules in cavities, trapped ions coupled via a motional mode, and superconducting qubits coupled to a microwave resonator.