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 composed of gates acting on two or fewer qubits. This shows that a quantum computation composed of two-qubit gates 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.
Physical Review A (Atomic, Molecular and Optical Physics)
Simulating Concordant Computations, Physical Review A (Atomic, Molecular and Optical Physics), [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=904877
(Accessed June 8, 2023)