We present a complete and detailed discussion of the finite lattice spacing corrections to staggered fermion matrix elements. Expanding upon arguments of Sharpe, we explicitly implement the Symanzik improvement program demonstrating the absence of order a terms in the Symanzik improved action. We propose a general program to improve fermion operators to remove all O(a) corrections from their matrix elements, and demonstrate this program for the examples of matrix elements of fermion bilinears and B K . We find the former does have O(a) corrections while the latter does not. Also, we give an explicit form of lattice currents which are accurate to order a 2 at the tree level. ͓S0556-2821͑97͒03301-8͔

By using Symanzik's improvement program, we study on-shell improved lattice QCD with staggered fermions. We find that there are as many as 15 independent lattice operators of dimension of six (including both gauge and fermion operators) which must be added to the unimproved action to form an O(a 2 ) improved action. Among them, the total number of dimension-6 gauge operators and fermion bilinears is 5. The other 10 terms are four-fermion operators. At the tree-level and tadpole-improved tree-level, all the 10 four fermion operators are absent.

The rst stage in the construction of the 0.8 Tera ops Supercomputer at Columbia, a working, two node parallel computer, has been successfully completed. The next stage, a 512 node, 26 Giga ops prototype, is in its nal construction phase. A general description and current status of the hardware and software is presented.

We describe the completed 8,192-node, 0.4Tflops machine at Columbia as well as the 12,288-node, 0.6Tflops machine assembled at the RIKEN Brookhaven Research Center. Present performance as well as our experience in commissioning these large machines is presented. We outline our on-going physics program and explain how the configuration of the machine is varied to support a wide range of lattice QCD problems, requiring a variety of machine sizes. Finally a brief discussion is given of future prospects for large-scale lattice QCD machines.Comment: LATTICE98(machines), 3 pages, 1 picture, 1 figur

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