Fault tolerance in qudit circuit design

The efficient decomposition of multicontrolled gates is a significant factor in quantum compiling, both circuit depth and $T$-gate count. Recent work has demonstrated that qudits have the potential to reduce resource requirements from linear logarithmic avoid fractional phase rotations. Here, we argue, based on scaling decoherence high-index states, not primary factor, choice entangling gate interaction network topology act together determine spread errors ultimate failure rate circuit. We further show for certain linear-depth circuits, additional error mitigation possible via selective application resources.