Do quantum wave functions curve spacetime before they are measured? Do wave functions cause spacetime curvature before they are measured, or would curvature only happen upon measurement?  I guess the question becomes, do quantum wavefunctions carry energy while they are not directly measured?  Is this a problem that requires a theory of quantum gravity to solve?
EDIT:  Suppose you do the double slit experiment with a hypothetical extremely massive particle.  Would its gravitational field cease to exists after it is emitted from the source and then come back into existence when the particle is detected at the screen?  Because if its field existed in transit, wouldn't the slits necessarily measure the particle via its gravitational field as it passes through the slits, even if there is no external measurement made at the slits?
 A: Unfortunately, that question's answer depends on the theory of quantum gravity that you chose. But roughly here is the situation : 
If you take a classical spacetime and quantum matter fields ($G_{\mu\nu} = \langle T_{\mu\nu} \rangle_\omega$), also known as semiclassical gravity, then the stress energy tensor varies with the measurement. The standard example is taking the quantum state $\frac{1}{\sqrt 2}\vert A \rangle + \frac{1}{\sqrt 2} \vert B \rangle$, the states A and B in disjoint regions of space. The stress energy tensor will be non-zero in both regions. Once it collapses, the stress energy tensor will collapse as well into being entirely in either the region A or B. That's a pretty bad sign but it is probably not what happens.
If you say that gravity itself is a quantum field, then the situation is that your gravitational field is itself a superposition of various states, linked to the various states of the matter field. Once you measure either the gravitational field or the matter field, the wavefunctions collapse into a particular state.
A: I think it is important to note that the wavefunction of quantum mechanics is not a field like the electric or magnetic field.
It assigns complex numbers to configurations. So it is a function where the domain of the function is not space or even spacetime.
So there is not a value of the field at a point in spacetime, so there isn't a thing to curve it.
You can try to do to quantum field theory where they are fields in space, but then instead of a complex number you get an operator so you don't have an energy or a momentum like you'd want for General Relativity, you just have operators.
A: If our goal is to describe a quantum spacetime curvature then we should start with why gravity exists and how its an illusion.  Time dilation from distributions of matter/mass curve into space creating a time gradient with respect to space.  We should therefore be searching for the quantum time particle.  With our understanding of time in the context of quantum mechanics, time is described as frequency fundamentally.  This means that time is inherently the angle theta where $\tan(\theta) = 2$nd derivative of space with respect to itself $(dz^2/dxdy)$.  This formulation of time should also align with the $2$nd law of Thermodynamics that entropy causes time to go forward and time causes entropy to increase.  http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/gratim.html#c4
