Non-Local Multi-Qubit Quantum Gates via a Driven Cavity

Abstract

We present two protocols for implementing deterministic non-local multi-qubit quantum gates on qubits coupled to a common cavity mode. The protocols rely only on a classical drive of the cavity modes, while no external drive of the qubits is required. In the first protocol, the state of the cavity follows a closed trajectory in phase space and accumulates a geometric phase depending on the state of the qubits. The second protocol uses an adiabatic evolution of the combined qubit-cavity system to accumulate a dynamical phase. Repeated applications of this protocol allow for the realization of phase gates with arbitrary phases, e.g. phase-rotation gates and multi-controlled-Z gates. For both protocols, we provide analytic solutions for the error rates, which scale as $\sim N/\sqrt{C}$, with $C$ the cooperativity and $N$ the qubit number. Our protocols are applicable to a variety of systems and can be generalized by replacing the cavity by a different bosonic mode, such as a phononic mode. We provide estimates of gate fidelities and durations for atomic and molecular qubits coupled to optical or microwave cavities, and suggest applications for quantum error correction.

arXiv commentv1: 7 pages + 7 pages supplementary information, 3 figures; v2: Updated references, minor edits; v3: 11 pages + 7 pages supplement, clarified and extended derivations

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