Fig. 7: Rate of increase of \(\overline{{{{{\mathscr{E}}}}}_{{{{\rm{b}}}},n}}({{{{\mathcal{E}}}}}_{z})={c}_{{{{\rm{b}}}},n}(\{{L}_{k}\})\gamma t\) as a function of Hilbert Space dimension d = 2n.
From: Noisy qudit vs multiple qubits: conditions on gate efficiency for enhancing fidelity

The data shown was generated for \(H={{\mathbb{0}}}_{{2}^{n}}\) and γt ∈ [0, 10−4]. The {Lk} collapse operators are the ones defined in (18). The circled dots show the numerical results. The solid curve presents the expected theoretical result according to (20). The dashed line shows \({{{{\mathscr{E}}}}}_{{{{\rm{b}}}},n}^{{{{\rm{(p)}}}}}({{{{\mathcal{E}}}}}_{z})\) given in (31) which is linear in \(n={\log }_{2}(d)\).