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My current research falls into two categories, method development for ab initio quantum chemistry calculations and algorithm design for graph partitioning and mapping problems.
My primary research area is focused upon the development of the Density Matrix Renormalization Group (DMRG) algorithm. The DMRG has shown to be a powerful method as applied to quantum chemistry, but still many questions remain unanswered when one considers applications to molecules. DMRG was developed to treat one dimensional systems with primarily local interactions, however, a problem arises of how to represent and map a higher dimensional system to the 1D lattice structure inherent to the current algorithm. Once a representation and measure of interaction have been defined this mapping problem is closely related to the NP complete problem of Minimum Cut Linear Arrangement. Currently I am looking at using graph theoretic techniques in order to calculate a good mapping in polynomial time.
In order to provide this mapping, one must also define a representation and measure of interaction. In quantum chemistry the molecular wavefunction is usually represented as a function of orbitals. I am currently exploring methods of defining pairwise correlation amongst orbitals using techniques developed in the field of Quantum Information Theory.
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