  This paper generalizes and expands upon the work [Phys. Rev. Lett. 102,
070502 (2009)] where we introduced a scheme for fault-tolerant holonomic
quantum computation (HQC) on stabilizer codes. HQC is an all-geometric strategy
based on non-Abelian adiabatic holonomies, which is known to be robust against
various types of errors in the control parameters. The scheme we present shows
that HQC is a scalable method of computation, and opens the possibility for
combining the benefits of error correction with the inherent resilience of the
holonomic approach. We show that with the Bacon-Shor code the scheme can be
implemented using Hamiltonian operators of weight 2 and 3.
