Coherent-state spin qubits in the presence of spin-orbit coupling

The dynamics of any electron-based qubit in quantum condensed-matter systems will inherently involve both spin and charge degrees of freedom however it is defined. The spin-orbit interaction will cause both spin precession and spin-charge entanglement and the resulting dynamics can be very complex. Here we report a scheme for performing quantum logic operations in quantum condensed-matter systems using coherent-state spin qubits that exploit both the electron's charge and spin degrees of freedom. In addition to the conceptual interest in such qubits, our analytical and numerical techniques have general applicability to many-electron dynamics in spin-orbit systems.

Figure 1

Plot of the gate error $\epsilon$ for a root-of-swap quantum gate as a function of the dimensionless SOI strengh and the initial displacement. The dashed lines indicate integer values of $n$ for the constraint in Eq. (21) which provide the minimal gate error. For half integer $n$, the constraint in Eq. (22) is obeyed which accounts for the slight decrease in error in the intermediate region.

Figure 2

Plot of the gate error for small perturbations in the initial displacement from the constraint in Eq. (21) for a range of normalized SOI strengths for $n=1$.