  Semiconductor platforms are emerging as a promising architecture for storing
and processing quantum information, e.g., in quantum dot spin qubits. However,
charge noise coming from interactions between the electrons is a major limiting
factor, along with the scalability of many qubits, for a quantum computer. We
show that a magnetic field gradient can be implemented in a semiconductor
quantum dot array to induce a local quantum coherent dynamical $\ell-$bit
exhibiting the potential to be used as logical qubits. These dynamical
$\ell-$bits are responsible for the model being many-body localized. We show
that these dynamical $\ell-$bits and the corresponding many-body localization
are protected from all noises, including phonons, for sufficiently long times
if electron-phonon interaction is not non-local. We further show the
implementation of thermalization-based self-correcting logical gates. This
thermalization-based error correction goes beyond the standard paradigm of
decoherence-free and noiseless subsystems. Our work thus opens a new venue for
passive quantum error correction in semiconductor-based quantum computers.
