  Inter-qubit coupling and qubit connectivity in a processor are crucial for
achieving high fidelity multi-qubit gates and efficient implementation of
quantum algorithms. Typical superconducting processors employ relatively weak
transverse inter-qubit coupling which are activated via frequency tuning or
microwave drives. Here, we propose a class of multi-mode superconducting
circuits which realize multiple transmon qubits with all-to-all longitudinal
coupling. These "artificial molecules" directly implement a multi-dimensional
Hilbert space that can be easily manipulated due to the always-on longitudinal
coupling. We describe the basic technique to analyze such circuits, compute the
relevant properties and discuss how to optimize them to create efficient
small-scale quantum processors with universal programmability.
