  According to the hypothesis of Penrose and Diosi, quantum state reduction is
a manifestation of the incompatibilty of general relativity and the unitary
time evolution of quantum physics. Dimensional analysis suggests that
Schrodinger cat type states should collapse on measurable time scales when
masses and lengths of the order of bacterial scales are involved. We analyze
this hypothesis in the context of modern developments in condensed matter and
cold atoms physics, aimed at realizing macroscopic quantum states. We first
consider 'micromechanical' quantum states, analyzing the capacity of an atomic
force microscopy based single spin detector to measure the gravitational state
reduction, but we conclude that it seems impossible to suppress environmental
decoherence to the required degree. We subsequently discuss 'split' cold atom
condensates to find out that these are at present lacking the required mass
scale by many orders of magnitude. We then extent Penrose's analysis to
superpositions of mass current carrying states, and we apply this to the flux
quantum bits realized in superconducting circuits. We find that the flux qubits
approach the scale where gravitational state reduction should become
measurable, but bridging the few remaining orders of magnitude appears to be
very difficult with present day technology.
