4 adopted from Ref. [18]. In this range of parameters the coupling between MIs and nuclear spins (Δ$_{j,l}$) is opti- mized to be weak to maximize τ$_{m}$/τ$_{e}$ . However with de- creasing Δ$_{j,l}$, the coupling between two MIs (Δ$_{m}$) lowers and as a result the time required for fundamental gate operations becomes longer. Thus, the gain in coherence time ( τ$_{m}$/τ$_{e}$ ) is offset by a loss in gate operation times (Δ$_{e}$ / Δ$_{m}$). To maximize N$_{m}$/N$_{e}$ we search for a range of parameters that allows simultaneous maximization of τ$_{m}$/τ$_{e}$ and Δ$_{m}$ / Δ$_{e}$. teraction mediated by electrons. Here Λ( ⃗ R$_{1}$, ⃗ R$_{2}$ ) = ∑ 2 j $_{=1}$| ϕ$_{+}$ ( ⃗ R$_{j}$ ) ϕ$_{−}$ ( ⃗ R$_{j}$ ) | describes the spatial dependence of the e-MI exchange interaction, a parameter that de- pends on the electron envelop wavefunction at the MI positions ⃗ R$_{j}$ . Note that in the limit of zero inter-dot tunneling, A$_{e}$ = A$_{m}$ . The ratio of MI and electron co- herence times can be calculated as τ$_{m}$ τ$_{e}$ = Δ$_{e}$ γ $^{2}$J$_{em}$ Λ( ⃗ R$_{1}$, ⃗ R$_{2}$ ) A$_{e}$ A$_{m}$ . (13) In Fig. 2 we show the results for Fe:ZnSe. N$_{m}$ and N$_{e}$ normalized to 2 πA$_{e}$ are plotted as a function of parabolic confining strength ω$_{0}$ for various values of the gate volt- age V$_{g}$ , and the external magnetic field B (inset). Within numerical parameters considered in this calculation we found A$_{e}$ ≈ A$_{m}$ . We observe that N$_{m}$/N$_{e}$ increases with increasing B , V$_{g}$ (inter-dot energy barrier) and ω$_{0}$ (tighter confinement). Within the parameter range con- sidered here, a maximum performance increase of about three orders of magnitude can be achieved over the elec- tron spin coded qubit. It is important to mention that even higher increases of N$_{m}$/N$_{e}$ might be achievable. The maximum B and V$_{g}$ values used for our optimization had to be limited to the range of validity of our two level model. For increasing values of B and V$_{g}$ the system approaches the singlet triplet transition point at which Δ$_{e}$ → 0 and N$_{m}$/N$_{e}$ ∝ 1 / Δ$_{e}$ → ∞ . In this limit our approximation based on the two level model fails, and a more exact analysis becomes necessary. This will be studied in more detail in a follow-up work. Further, the smallest realizable quantum dot size is around 5 nm cor- responding to the maximum ω$_{0}$ in Fig. 2. However, an extrapolation of the numerical results to the atomic scale indicates performances gains N$_{m}$/N$_{e}$ of more than five orders of magnitude. In this limit, our system becomes comparable to Kane’s proposal [8], which demonstrates its favorable performance properties. The advantage of our system is that a compromise can be found between optimizing performance and accommodating technologi- cal limitations. In conclusion the qubit system investigated here opens the possibility for noise and performance optimization. We have found that a combination of active and passive optimization is necessary to obtain appreciable improve- ments; our analysis of the hybrid MI/electron qubit pre- dicts a performance gain of at least three orders of magni- tude over electron spin coded qubits in the limit of small inter-dot coupling. In Eq. (14), N$_{m}$/N$_{e}$ ∝ 1 / Δ$_{e}$. Unlike the other param- eters in Eq. (14), Δ$_{e}$ decays to zero very rapidly by in- creasing the external magnetic field and inter-dot energy barrier that lowers the inter-dot coupling. Therefore one expects to observe decay in performance of the electron spin coded qubit due to variations in B and V$_{g}$ . Un- like the electrons, MIs show a robust increase in their quantum operation performance. To gain the optimum performance of MIs over electrons we employ a numerical calculation based on exact diagonalization of Eq.(1) from which the input parameters for Eq.(14) are obtained [11]. The DQD is chosen to be double Gaussian along the axis and parabolic in the perpendicular direction and each MI is centered at one of the QDs. We perform our calcula- tion for three different materials, Gd:PbTe, Fe:CdSe, and Fe:ZnSe where they show τ$_{m}$/τ$_{e}$ ≈ 300 , 20 , 2 respectively at V$_{g}$ = 154 meV and B = 0. The values for J$_{em}$ are The MI and electron spin swap times are given by Δ − 1 m , and Δ − 1 e modulus π ¯ h , assuming that the gate voltage and therewith exchange coupling is controlled by a square pulse [4]. Here, Δ$_{m}$ ≡ Δ$_{jj}$ ′ is the cou- pling coefficient between the two MIs. As a result, N$_{e}$ = Δ$_{e}$ / (2 πA$_{e}$ ), N$_{m}$ = [ J$_{em}$U/ (2Λ)] / (2 πA$_{m}$ ) where U = ϕ$_{+}$ ( ⃗ R$_{1}$ ) ϕ$_{−}$ ( ⃗ R$_{1}$ ) ϕ$_{+}$ ( ⃗ R$_{2}$ ) ϕ$_{−}$ ( ⃗ R$_{2}$ ) and ⃗ R$_{1}$ , ⃗ R$_{2}$ are MI coordinates. The ratio of the maximum number of el- ementary operations (per coherence time) is given by N$_{m}$/N$_{e}$ = ( τ$_{m}$/τ$_{e}$ )(Δ$_{m}$ / Δ$_{e}$), which finally gives The performance of a quantum computing setup is given by the maximum number of operations N$_{i}$ = τ$_{i}$/T$_{i}$ with i = e, m for electrons and MI qubits, respectively. Here, τ is the coherence time and T is the time required for the elementary gate operations. Our system is com- pared to the original proposal in Ref. [4], where an XOR gate control in a two-electron DQD is analyzed. The el- ementary gate operations needed for the XOR gate are: (i) a correlated spin swap from |↑↓〉 →|↓↑〉 , where the first and second position refers to the left and right dot, respectively, and (ii) single qubit operations with an ex- ternal pulsed magnetic field. The second operation has to be done within the time of one spin swap. Therefore, the time for one XOR gate is determined by the correlated spin swap time T . N$_{m}$ N$_{e}$ = J$_{em}$ Δ$_{e}$ U 2Λ A$_{e}$ A$_{m}$ . (14) [1] L. Jacak et al. , Quantum Dots (Springer, Berlin, 1998); D. Bimberg et al., Quantum Dot Heterostructures (John Wiley & Sons, Chichester, 1999). S. M. Reimann and M. Manninen, Rev. Mod. Phys. 74 , 1283 (2002), and the references therein.