  A noncommutative deformation of a quadric surface is usually described by a
three-dimensional cubic Artin-Schelter regular algebra. In this paper we show
that for such an algebra its bounded derived category embeds into the bounded
derived category of a commutative deformation of the Hilbert scheme of two
points on the quadric. This is the second example in support of a conjecture by
Orlov. Based on this example, we formulate an infinitesimal version of the
conjecture, and provide some evidence in the case of smooth projective
surfaces.
