Interacting electrons in silicon quantum interconnects

TL;DR

This paper investigates strongly interacting electron channels in silicon quantum wells, revealing a crossover from Wigner to Friedel regimes and proposing their use for long-range quantum entanglement and scalable quantum computing.

Contribution

It demonstrates the presence of Luttinger liquid physics in silicon interconnects and analyzes the robustness of the Wigner-Friedel crossover under disorder, with implications for quantum information processing.

Findings

Identification of Wigner and Friedel regimes in silicon channels

Robustness of the crossover against disorder up to 400 μeV

Proposal for long-range capacitive coupling enabling quantum entanglement

Abstract

Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We argue that one-dimensional electron channels formed in the silicon quantum well of a Si/SiGe heterostructure exhibit strong Coulomb interactions and realize strongly interacting Luttinger liquid physics. At low electron densities, the system enters a Wigner regime characterized by dominant 4kF correlations; increasing the electron density leads to a crossover from the Wigner regime to a Friedel regime with dominant 2kF 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-Friedel crossover via charge transport and charge sensing in both zero- and high-magnetic field limits. We also analyze the impact of short-range correlated disorder - including random alloy fluctuations and valley splitting variations - and identify that the Wigner-Friedel crossover remains robust until disorder levels of about 400 micro eV. Finally, we show that the Wigner regime enables long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to create long-range entanglement between solid-state qubits. Our results position silicon interconnects as a platform for studying Luttinger liquid physics and for enabling architectures supporting nonlocal quantum error correction and quantum simulation.