The Fermilab Holometer, comprised of two co-located but independent and isolated 40-meter interferometers, is obtaining the first measurements of non-local correlations of position variations over an extended volume of space-time with a strain noise power spectral density smaller than a Planck time. These measurements directly test one class of models of quantum geometry, which predict an observable decoherence at this scale as the consequence of a lower-dimensional limit on the number of independent geometrical position states. The two interferometer readout signals, each sensitive to 10-14 m displacements in differential position over 40 m, are sampled at 50 MHz and cross-correlated. Quantum-geometrical effects appear as correlations of the position displacements on time scales shorter than 130 ns, the 40-meter light crossing time, or at frequencies below 7.5 MHz. The Holometer in current and future configurations will provide precision tests of a wide class of models of quantum geometry at the Planck scale, beyond those already constrained by currently operating gravitational wave observatories. In this talk, I will present the constraints on quantum geometry obtained by the Holometer to date, as well as ongoing efforts to develop new experimental tests.