Figure 1: The four-level Lab-frame system and the two-qubit Bell-frame system.
From: Hidden two-qubit dynamics of a four-level Josephson circuit
(a) The phase ϕ of a flux-biased superconducting Josephson qudit is localized in a shallow potential well, giving rise to a number of anharmonically spaced energy levels. The multi-level qudit state is measured by lowering the potential barrier, causing the phase to tunnel out of the shallow well. (b) The states of a four-level qudit can be mapped onto a pair of two-level qubits. For example, the two-qubit state 
depicted here by the Bloch spheres corresponds to the state |0› of the physical Lab-frame qudit. SO(4) rotations in the Lab frame factor exactly into local rotations of the Bell-frame qubits, while SU(4) rotations couple them together. (c) The depicted two-qubit state 
corresponds to the state |2› in the Lab frame. The Pythagorean coupling scheme achieves population inversion between the Lab-frame states |0› and |2› by synchronizing rotations of the Bell-frame qubits.
