Resistive silicon spin qubit interconnects as platforms for mesoscopic physics

Large-scale quantum computers built from silicon spin qubits will require medium- and long-range interconnects. We consider an interconnect between two dots consisting of a quasi-1D channel created by a resistive topgate. In the absence of interactions, a single electron moves independently with its spin through the channel. If the channel hosts a finite density of electrons, however, Coulomb interactions between those electrons can dramatically change the nature of the ground state, e.g., to form a Luttinger-liquid state. We investigate how this physics is changed by the details of such a channel in an Si/SiGe quantum well. We consider the effect of phenomenological disorder, valley-splitting disorder due to Ge alloy disorder at the Si/SiGe interface, screening by the resistive topgate. We also consider coupling to quantum dots on each end of the channel, as opposed to the non-interacting (or Fermi liquid) leads commonly studied in mesoscopic physics.