Numerical simulation of statistical properties of matchgate shadows

Classical shadows provide a powerful measurement tool which allows the estimation of linear amount observables with a logarithmic amount of quantum measurements. Recently this technique has been adapted for fermionic systems in the form of matchgate shadows, allowing for the efficient estimation of local fermionic observables and overlaps of arbitrary states and fermionic gaussian states. This has found application in proposed near-term algorithms like QC-AFQMC, motivating further investigation into the behaviour of these measurement techniques. We study statistical properties of this scheme in numerical experiments for different systems, give evidence to justify a Gaussian noise model when simulating measurements of computational basis states and non-orthonal Slater determinants as used in AFQMC and compare with theoretical bounds of the variance.