  Quantum computation strongly relies on the realisation, manipulation and
control of qubits. A central method for realizing qubits is by creating a
double-well potential system with a significant gap between the first two
eigenvalues and the rest. In this work we first revisit the theoretical grounds
underlying the double-well qubit dynamics, then proceed to suggest novel
extensions of these principles to a triple-well qutrit with periodic boundary
conditions, followed by a general d-well analysis of qudits. These analyses are
based on representations of the special unitary groups SU(d) which expose the
systems' symmetry and employ them for performing computations. We conclude with
a few notes on coherence and scalability of d-well systems.
