Realization of qudits in coupled potential wells

Abstract

Quantum computation strongly relies on the realization, 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 [Formula: see text]-well analysis of qudits. These analyses are based on representations of the special unitary groups SU[Formula: see text] which expose the systems’ symmetry and employ them for performing computations. We conclude with a few notes on coherence and scalability of [Formula: see text]-well systems.