Improving Algorithms to Compute All Elements of the Lattice Quark Propagator

The discovery of exactly chirally symmetric fermions on the lattice has triggered intensive research in the development of algorithms to simulate dynamical Ginsparg-Wilson fermions on the lattice. In light of recent work in this area, we anticipate that there will be a limited number of expensive, full QCD configurations in the near future. One would like to extract all the information that one can from these lattices without being restricted by point propagators, which would appear highly wasteful considering the cost to generate the configurations. Point propagators do not require massive computing power but restrict the physics one has access to, mainly the flavour non-singlet spectrum. They also restrict the interpolating operator basis used to produce early plateaux in effective masses, for instance, since a new inversion must be performed for every operator that is not restricted to a single lattice point. Variational methods would be much more powerful with the use of all-to-all propagators. All-to-all propagators [1,2,3,4,5,6] provide a solution to these problems, but are usually too expensive to compute exactly as this requires an unrealistic number of quark inversions. Stochastic estimates tend to be very noisy and variance reduction techniques are crucial in order to separate the signal from the noise. In this paper we propose an exact algorithm to compute the all-to-all