  Motivated by recent developments on the fabrication and control of
semiconductor-based quantum dot qubits, we theoretically study a finite system
of tunnel-coupled quantum dots with the electrons interacting through the
long-range Coulomb interaction. When the inter-electron separation is large and
the quantum dot confinement potential is weak, the system behaves as an
effective Wigner crystal with a period determined by the electron average
density with considerable electron hopping throughout the system. For stronger
periodic confinement potentials, however, the system makes a crossover to a
Mott-type strongly correlated ground state where the electrons are completely
localized at the individual dots with little inter-dot tunneling. In between
these two phases, the system is essentially a strongly correlated electron
liquid with inter-site electron hopping constrained by strong Coulomb
interaction. We characterize this Wigner-Mott-liquid quantum crossover with
detailed numerical finite-size diagonalization calculations of the coupled
interacting qubit system, showing that these phases can be smoothly connected
by tuning the system parameters. Experimental feasibility of observing such a
hopping-tuned Wigner-Mott-liquid crossover in currently available semiconductor
quantum dot qubits is discussed. In particular, we connect our theoretical
results to recent quantum-dot-based quantum emulation experiments where
collective Coulomb blockade was demonstrated. One conclusion of our theory is
that currently available realistic quantum dot arrays are unable to explore the
low-density Wigner phase with only the Mott-liquid crossover being accessible
experimentally.
