Computational study of all-electrical quantum operations on molecular spin qubits

We solve the problem of a single electron scattering from two decoupled spin-1/2 magnetic impurities with a single-particle Green's function treatment. We show that this treatment can map the scattering problem onto a quantum operation on the two impurities, and that for certain forms of the scattering potential this operation can be made unitary in order to realize two-qubit gates. We demonstrate that when the scattering potential is the sd exchange model, we can achieve a SWAP gate in a completely time-independent manner and without ever directly coupling the two impurities by appropriate location of a real-space barrier voltage term. We subsequently apply the same treatment to a SWAP^1/2 gate. We next examine whether even when the barrier location is fixed the momentum of the scattered electron can modulate the nature of the gate in a time-independent manner. We find that this more experimentally attainable scheme suffers from reduced gate fidelity. Finally, we explore beyond the single-particle picture by performing a many-body quantum mechanical simulation of our system of interest.