  An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto
qubit degrees of freedom is presented. This new mapping allows for a reduced
unphysical Hilbert space. Insensitivity to interactions within this unphysical
space is exploited to design more efficient quantum circuits. Local gauge
symmetry is used to analytically incorporate the angular momentum alignment,
leading to qubit registers encoding the total angular momentum on each link.
The results of a multi-plaquette calculation on IBM's quantum hardware are
presented.
