Interacting electrons in silicon quantum interconnects

Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We show that one-dimensional electron channels formed in the silicon quantum well of a Si/SiGe heterostructure exhibit strong Coulomb interactions and realize exotic Luttinger liquid physics. At low electron densities and temperatures, the system enters a Wigner regime characterized by dominant $4k_F$ correlations. Via bosonization, we show that increasing the electron density leads to a crossover from Wigner regime to Friedel-dominated $2k_F$ correlations. We support these results through large-scale density matrix renormalization group (DMRG) simulations of the interacting ground state under both screened and unscreened Coulomb potentials. We propose experimental signatures of the Wigner crystal via charge transport and charge-sensing in both zero and high magnetic field limits. Furthermore, we analyze the role of short-range correlated disorder — including random alloy fluctuations and valley splitting variations — and identify thresholds below which Wigner crystal signatures remain robust. Finally, we show that the Wigner regime leads to long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to create long-range entanglement mediated by a Wigner crystal. Our results position silicon interconnects as a new platform for studying Luttinger liquid physics and enabling architectures for non-local quantum error correction and quantum simulation.