Realisation of Qudits in Coupled Potential Wells

TL;DR

This paper explores the theoretical foundations and extensions of double-well potential systems for realizing qubits, proposing new models for qutrits and qudits using SU(d) symmetries, with considerations on coherence and scalability.

Contribution

It introduces novel extensions from double-well qubits to triple-well qutrits and general d-well qudits, utilizing SU(d) group representations for quantum computation.

Findings

Theoretical analysis of double-well qubit dynamics

Extension to triple-well qutrit systems with periodic boundary conditions

General framework for d-well qudits based on SU(d) symmetries

Abstract

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.