Figure 1

(a) Schematic representation for executing the Hadamard rotation. Units are chosen such as $\hslash =1$. The solid lines represent the two levels associated with the qubit. The levels in the ground surface are equally spaced with ${\omega }_g=1$ (for ${\mathrm{L}\mathrm{i}}_2$ in the $A$ state ${\omega }_g=255\mathrm{c}{\mathrm{m}}^{-\mathrm{1}}$) and in the excited surface with ${\omega }_e=0.9$ (for ${\mathrm{L}\mathrm{i}}_2$ in the $E$ state ${\omega }_e=241\mathrm{c}{\mathrm{m}}^{-\mathrm{1}}$). The other model parameters are $\Omega =15$ (for ${\mathrm{L}\mathrm{i}}_2$ the $A$ to $E$ transitions $\Omega =12400\mathrm{c}{\mathrm{m}}^{-\mathrm{1}}$) and ${\mu }_0=0.1$. The arrows are two of the possible transitions induced by the driving field. (b) Optimized field that induces a Hadamard rotation in the qubit at $T=70$ (for ${\mathrm{L}\mathrm{i}}_2$ $T\sim 1.5\mathrm{p}\sec $). (c) Fourier transform of the field.Reuse & Permissions

Figure 2

(a) Schematic representation of the execution of a two qubit Fourier transform. The solid lines represent the levels associated with the qubits. The frequencies are $E_{g{\alpha }_0}=0$, $E_{g{\alpha }_1}=1$, $E_{e{\alpha }_0}=15$, $E_{e{\alpha }_1}=15.8$, $E_{g{\beta }_0}=0$, $E_{g{\beta }_1}=0.9$, $E_{e{\beta }_0}=14.5$, and $E_{e{\beta }_1}=15.2$. The arrows are examples of transitions induced by the driving field in each mode. The other model parameters are ${\mu }_{0\alpha }=0.1$, ${\mu }_{0\beta }=0.08$, and ${\delta }_{\alpha \beta }=0.21$. (b) Fourier transform of the optimal field that induces ${\widehat{\mathrm{O}}}_R^{\mathrm{F}\mathrm{T}}$ at $T=320$.Reuse & Permissions