  A quantum state is called concordant if it has zero quantum discord with
respect to any part. By extension, a concordant computation is one such that
the state of the computer, at each time step, is concordant. In this paper, I
describe a classical algorithm that, given a product state as input, permits
the efficient simulation of any concordant quantum computation having a
conventional form and composed of gates acting on two or fewer qubits. This
shows that such a quantum computation must generate quantum discord if it is to
efficiently solve a problem that requires super-polynomial time classically.
While I employ the restriction to two-qubit gates sparingly, a crucial
component of the simulation algorithm appears not to be extensible to gates
acting on higher-dimensional systems.
