Figure 1

(a) A 2QD dipole charge qubit. Logical states, $\{\mid 0⟩,\mid 1⟩\}$, are defined by an excess electron on the left or right dot, respectively. Symmetry electrodes $\left(V_{0,1}\right)$ control ${\sigma }_z$ rotations, and a barrier electrode $\left(V_{\Omega }\right)$ controls ${\sigma }_x$. An SET (omitted) measures in the logical basis. (b) Temporally and spatially varying potential due to external field. (c) A 2-electron 4QD quadrupole qubit with $\mid 0⟩=a^{†}{c}^{†}\mid \mathrm{vac}⟩,\mid 1⟩=b^{†}{d}^{†}\mid \mathrm{vac}⟩$.Reuse & Permissions

Figure 2

(Color online) Qubit coherence decay. Initial state $(\mid 0⟩+\mid 1⟩)∕\sqrt{2}$ coupled to 100 charge traps; $k_{\mathrm{eff}}^{\left(2\right)}=12.46\times {10}^9\hslash ∕s$ and $k_{\mathrm{eff}}^{\left(4\right)}=0.60\times {10}^9\hslash ∕s$. A total of 200 quantum trajectories were simulated and averaged. For all simulations, the 2QD qubit was 20 nm long and the 4QD qubit was a 20 nm square (e.g., P donors in Si, see Ref. 14). Both were located 20 nm below the layer in which the charge traps were located. Charge trap transition rate was $2\times {10}^8\mathrm{Hz}$.Reuse & Permissions

Figure 3

(Color online) Decoherence of 2QD and 4QD qubits. (a) The decoherence decay times are inversely related to the effective coupling to fluctuators and show the same dependence for the 2QD and 4QD qubits. (b) The ratio of the short-term coherence times for the 2QD and 4QD encodings is inversely proportional to the ratio of the effective coupling constants. Each point represents the average of 200 quantum trajectories of a qubit coupled to 100 randomly distributed fluctuators.Reuse & Permissions

Figure 4

(Color online) Coupling and noise versus charge trap density. Noise suppression of the 4QD vs 2QD qubits was calculated for 100 random charge trap distributions per density, which was then averaged. Coupling strength is in units of ${10}^9\hslash ∕s$, bars indicate the $10-90\%$ ranges. At high densities, the mean charge trap spacing is comparable to the size of the qubit, leading to saturation effects.Reuse & Permissions

Figure 5

(Color online) Decoupling versus placement error. We simultaneously and independently perturbed the positions of all quantum dots by a Gaussian displacement with standard deviation $\sigma$ (expressed as a fraction of the array side length). This was repeated 1000 times for each of 500 fluctuator distributions. We plot of median w.r.t fluctuator distributions of the mean over the perturbations of the decoupling ratios as a function of error magnitude for different effective fluctuator densities. Even with a 10% displacement error (i.e., $\sigma =0.1$), the 4QD qubit is still effective.Reuse & Permissions

Figure 6

(Color online) Populations during ${\sigma }_x^{\pi ∕2}$-gate vertical tunneling. An initial state ∣0⟩ is transformed into $(\mid 0⟩+i\mid 1⟩)∕\sqrt{2}$ with transient population in non-DFS subspace $\mid \epsilon ⟩$. (a) $\Omega$ large: $n=2,m=1$, (b) $\Omega$ small: $n=20,m=19$.Reuse & Permissions

Figure 7

The ${\sigma }_x^{\pi ∕2}$-gate error versus noise coupling. Gate parameters: $t_f\approx 50\mathrm{ps},{\Omega }_2=\pi ∕\left(4t_f\right),\delta =3.84\times {10}^{12}\hslash ∕s,4{\Omega }_4={\delta }_c\sqrt{{(62∕61)}^2-1}$. Fidelity was calculated from 50 trajectories per initial state $\{\mid \pm x⟩,\mid \pm y⟩,\mid \pm z⟩\}$.Reuse & Permissions