  Concordant computation is a circuit-based model of quantum computation for
mixed states, that assumes that all correlations within the register are
discord-free (i.e. the correlations are essentially classical) at every step of
the computation. The question of whether concordant computation always admits
efficient simulation by a classical computer was first considered by B. Eastin
in quant-ph/1006.4402v1, where an answer in the affirmative was given for
circuits consisting only of one- and two-qubit gates. Building on this work, we
develop the theory of classical simulation of concordant computation. We
present a new framework for understanding such computations, argue that a
larger class of concordant computations admit efficient simulation, and provide
alternative proofs for the main results of quant-ph/1006.4402v1 with an
emphasis on the exactness of simulation which is crucial for this model. We
include detailed analysis of the arithmetic complexity for solving equations in
the simulation, as well as extensions to larger gates and qudits. We explore
the limitations of our approach, and discuss the challenges faced in developing
efficient classical simulation algorithms for all concordant computations.
