Resonators: Classical Treatment

Resonators play an important role in superconducting quantum computers. The qubits themselves are nonlinear resonators, and in many architectures, the qubits are coupled to other qubits and to external circuits through transmission line segments functioning as resonators. Ultimately, to excite or measure the properties of a lumped‐element resonator, it must be connected to an external circuit. The gaps create discontinuities causing reflections and the standing wave characteristic of the resonance, but also provide capacitive coupling to an external circuit. Circuits important to quantum computing also include qubits coupled to resonators, and qubits coupled to one another. The coupled‐resonator model can be used to describe a transmission line resonator coupled to a qubit, provided we only allow the resonator representing the qubit to have two states. The gaps create discontinuities causing reflections and the standing wave characteristic of the resonance, but also provide capacitive coupling to an external circuit.