  Computing disconnected diagrams in Lattice QCD (operator insertion in a quark
loop) entails the computationally demanding problem of taking the trace of the
all to all quark propagator. We first outline the basic algorithm used to
compute a quark loop as well as improvements to this method. Then, we motivate
and introduce an algorithm based on the synergy between hierarchical probing
and singular value deflation. We present results for the chiral condensate
using a 2+1-flavor clover ensemble and compare estimates of the nucleon charges
with the basic algorithm.
