Application of the Schwinger Oscillator Construct of Angular Momentum to an Interpretation of the Superconducting Transmon Qubit

The Schwinger oscillator construct of angular momentum, applied to the superconducting transmon and its transmission-line readout, modeled as capacitvely coupled quantum oscillators, provides a natural and robust description of a qubit. The construct defines quantum-entangled, two-photon states that form an angular-momentum-like basis, with symmetry corresponding to physical conservation of total photon number, with respect to the combined transmon and readout. This basis provides a convenient starting point from which to study error-inducing effects of transmon anharmonicity, surrounding-environment decoherence, and random stray fields on qubit state and gate operations. Employing a Lindblad master equation to model dissipation to the surrounding environment, and incorporating the effect of weak transmon anharmonicity, we present examples of the utility of the construct. First, we calculate the frequency response associated with exciting the ground state to a Rabi resonance with the lowest-lying spin-1/2 moment, via a driving external voltage. Second, we calculate the frequency response between the three lowest two-photon states, within a ladder-type excitation scheme. The generality of the Schwinger angular-momentum construct allows it to be applied to other superconducting charge qubits.