Calculation of Weak Transitions in Lattice QCD

We propose the use of Monte Carlo simulations of QCD to evaluate hadronic matrix elements of local operators encountered in electroweak and grand-unified-theory transitions. Preliminary Monte Carlo estimates are made of the $\Delta S=2\mathrm{}$ matrix elements responsible for the $K_L-K_S$ mass difference and the $\Delta S=1\mathrm{}$ operators believed to explain the $\Delta I=\frac{1}{2}$ enhancement.