[1][2] Analytic or perturbative solutions in low-energy QCD are hard or impossible to obtain due to the highly nonlinear nature of the strong force and the large coupling constant at low energies.
This formulation of QCD in discrete rather than continuous spacetime naturally introduces a momentum cut-off at the order 1/a, where a is the lattice spacing, which regularizes the theory.
Most importantly, lattice QCD provides a framework for investigation of non-perturbative phenomena such as confinement and quark–gluon plasma formation, which are intractable by means of analytic field theories.
Numerical lattice QCD calculations using Monte Carlo methods can be extremely computationally intensive, requiring the use of the largest available supercomputers.
[4][5] At present, lattice QCD is primarily applicable at low densities where the numerical sign problem does not interfere with calculations.
[6] Lattice QCD predicts that the transition from confined quarks to quark–gluon plasma occurs around a temperature of 150 MeV (1.7×1012 K), within the range of experimental measurements.
[7][8] Lattice QCD has also been used as a benchmark for high-performance computing, an approach originally developed in the context of the IBM Blue Gene supercomputer.
The importance sampling technique used to select the gauge configurations in the Monte-Carlo simulation imposes the use of Euclidean time, by a Wick rotation of spacetime.