  Today, multiple new platforms are implementing qudits, $d$-level quantum
bases of information, for Quantum Information Processing (QIP). It is therefore
crucial to study their efficiencies for QIP compared to more traditional qubit
platforms. We present a comparative study of the infidelity scalings of a qudit
and $n$-qubit systems, both with identical Hilbert space dimensions and noisy
environments. The first-order response of the Average Gate Infidelity (AGI) to
the noise in the Lindblad formalism, which was found to be gate-independent,
was calculated analytically in the two systems being compared. This yielded a
critical curve $O(d^2/\log_2(d))$ of the ratio of their respective gate times
in units of decoherence time. This quantity indicates how time-efficient
operations on these systems are. The curve delineates regions where each system
has a higher rate of increase of the AGI than the other. This condition on gate
efficiency was applied to different existing platforms. It was found that
specific qudit platforms possess gate efficiencies competitive with
state-of-the-art qubit platforms. Numerical simulations complemented this work
and allowed for discussion of the applicability and limits of the linear
response formalism.
