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Electrical resonators are widely used in quantum information processing, byengineering an electromagnetic interaction with qubits based on real or virtualexchange of microwave photons. This interaction relies on strong couplingbetween the qubits' transition dipole moments and the vacuum fluctuations ofthe resonator in the same manner as cavity QED, and has consequently come to becalled "circuit QED" (cQED). Great strides in the control of quantuminformation have already been made experimentally using this idea. However, thecentral role played by photon exchange induced by quantum fluctuations in cQEDdoes result in some characteristic limitations. In this paper, we discuss analternative method for coupling qubits electromagnetically via a resonator, inwhich no photons are exchanged, and where the resonator need not have strongquantum fluctuations. Instead, the interaction can be viewed in terms ofclassical, effective "forces" exerted by the qubits on the resonator, and theresulting resonator dynamics used to produce qubit entanglement are purelyclassical in nature. We show how this type of interaction is similar to thatencountered in the manipulation of atomic ion qubits, and we exploit thisanalogy to construct two-qubit entangling operations that are largelyinsensitive to thermal or other noise in the resonator, and to its qualityfactor. These operations are also extensible to larger numbers of qubits,allowing interactions to be selectively generated among any desired subset ofthose coupled to a single resonator. Our proposal is potentially applicable toa variety of physical qubit modalities, including superconducting andsemiconducting solid-state qubits, trapped molecular ions, and possibly evenelectron spins in solids.

Quantum information processing using quasiclassical electromagnetic interactions between qubits and electrical resonators