Four-junction superconducting circuit in both flux and phase regimes

We develop a theory for the quantum circuit consisting of a superconducting loop interrupted by four Josephson junctions and pierced by a magnetic flux (either static or time-dependent). In addition to the similarity with the typical three-junction flux qubit, we demonstrate the difference of the four-junction circuit from its three-junction analogue, especially its distinct advantages over the latter. Moreover, the four-junction circuit in the phase regime is also investigated. Our theory provides a tool to explore the physical properties of this four-junction superconducting circuit.