Variable Electrostatic Transformer: Controllable Coupling of Two Charge Qubits

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Abstract
We propose and investigate a novel method for the controlled coupling of two Josephson charge qubits by means of a variable electrostatic transformer. The value of the coupling capacitance is given by the discretized curvature of the lowest energy band of a Josephson junction, which can be positive, negative, or zero. We calculate the charging diagram of the two-qubit system that reflects the transition from positive to negative through vanishing coupling. We also discuss how to implement a phase gate making use of the controllable coupling.