Efficient three-qubit entangling (Toffoli) gates via excited states in qubit-cavity systems.

Efficient multi-qubit quantum operations are crucial for further development of quantum information processing using available physical designs. We report our results on efficient three-qubit entangling operations in qubit-cavity systems. The proposed gate design is based on non-commutativity of single-qubit pulse controls that can be achieved for systems in which auxiliary states above the qubit subspace are available. It does not rely on dynamical tuning of energy states, and, unlike traditional decomposition approaches, it provides efficiency comparable to that of a single control-NOT operation. We will focus on the transmon qubit systems, which have recently demonstrated coherence times suitable for multi-qubit computation. Other systems will also be discussed.