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Advances in numerical methods applied to quantum systems move at a rapid pace, as do increases in available computing power. For a given problem a variety of numerical techniques are available; some are outdated and some not. What techniques should one use? This question is of special urgency given the realization of 100,000+ core petaflop machines that will require a shift in computing paradigms. We shall focus our workshop on quantum condensed matter since there are a wealth of new algorithms and codes being developed in this area, including significant advances in dynamical mean field theory (DMFT); quantum Monte Carlo (QMC); density matrix renormalization group (DMRG); matrix product state (MPS), projected entangled pair state (PEPS) and related methods; diagonalization methods; series expansion methods; petaflop computing; and computational provenance. The organization and analysis of resources designed to numerically tackle problems in quantum condensed matter is an important area of study with the potential for broad impact. Our workshop will address three general topics to streamline access to such methods:
i) We will first collect and critically analyze state-of-the-art numerical methods and identify specific scientific problems that can
be addressed with these methods.
ii) We will then identify relevant problems and look ahead to the design of new algorithms that may significantly advance petaflop simulations in quantum condensed matter.
iii) And finally, we will discuss and lay out guidelines for standards of computational provenance that should be met to ensure reproducibility and reliability of published computational research.
Our workshop will result in a written report summarizing our conclusions and recommendations for each of these three areas.