be matched with a common continuum scheme, such as the MS-bar scheme, otherwise the results cannot be compared. The expansion has to be carried out to the same order in the continuum scheme and the lattice one. The lattice regularization was initially introduced by Wilson as a framework for studying strongly coupled theories non-perturbatively. However, it was found to be a regularization suitable also for perturbative calculations. Perturbation theory involves an expansion in the coupling constant, and is well-justified in high-energy QCD where the coupling constant is small, while it fails completely when the coupling is large and higher order corrections are larger than lower orders in the perturbative series. In this region non-perturbative methods, such as Monte-Carlo sampling of the correlation function, are necessary. Lattice perturbation theory can also provide results for condensed matter theory. One can use the lattice to represent the real atomic crystal. In this case the lattice spacing is a real physical value, and not an artifact of the calculation which has to be removed (a UV regulator), and a quantum field theory can be formulated and solved on the physical lattice. Quantum computing In 2005 researchers of the National Institute of Informatics reformulated the U(1), SU(2), and SU(3) lattice gauge theories into a form that can be simulated using "spin qubit manipulations" on a universal quantum computer. Limitations The method suffers from a few limitations: Currently there is no formulation of lattice QCD that allows us to simulate the real-time dynamics of a quark-gluon system such as quark–gluon plasma. It is computationally intensive, with the bottleneck not being flops but the bandwidth of memory access. It provides reliable predictions only for hadrons containing heavy quarks, such as hyperons, which have one or more strange quarks. See also Lattice model (physics) Lattice field theory Lattice gauge theory QCD matter SU(2) color superconductivity QCD sum rules Wilson action References Further reading M. Creutz, Quarks, gluons and lattices, Cambridge University Press 1985. I. Montvay and G. Münster, Quantum Fields on a Lattice, Cambridge University Press 1997. J. Smit, Introduction to Quantum Fields on a Lattice, Cambridge University Press 2002. H. Rothe, Lattice Gauge Theories, An Introduction, World Scientific 2005. T. DeGrand and C. DeTar, Lattice Methods for Quantum Chromodynamics, World Scientific 2006. C. Gattringer and C. B. Lang, Quantum Chromodynamics on the Lattice, Springer 2010. External links Gupta - Introduction to Lattice QCD Lombardo - Lattice QCD