Scheme for fault-tolerant holonomic computation on stabilizer codes

This paper generalizes and expands upon the work [O. Oreshkov, T. A. Brun, and D. A. Lidar, 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 weights 2 and 3.