  Ying conceived of using two or more small-capacity quantum computers to
produce a larger-capacity quantum computing system by quantum parallel
programming ([M. S. Ying, Morgan-Kaufmann, 2016]). In doing so, the main
obstacle is separating the quantum gates in the whole circuit to produce a
tensor product of the local gates. It has been showed that there are few
separable multipartite quantum gates, so the approximate separation problem
involves finding local quantum gates that approximate a given inseparable gate.
We propose and study a problem involving the approximate separation of
multipartite gates based on quantum-gate fidelity. For given multipartite and
local gates, we conclude that the smaller is the maximal distance between the
products of an arbitrary pair of eigenvalues, the greater is their gate
fidelity. This provides a criterion for approximate separation. Lastly, we
discuss the optimal approximate separation of the CNOT gate.
