Identifying a Quadratically Constrained Program (QCP) explained that the quadratic matrix in each constraint must be positive semi-definite (PSD), thus providing convexity. A matrix Qi is PSD if xTQix 
0 for every vector x, whether or not x is feasible. Other issues pertaining to positive semi-definiteness are discussed in the context of a quadratic objective function in Identifying Convex QPs.
When you call the barrier optimizer, your quadratic constraints will be checked for the necessary PSD property, and an error status 5002 will be returned if any of them violate it.
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