My primary research interest concerns the understanding and analysis of complex network systems and quantum systems, in which, matrix theory/computations plays an important role. I primarily work on theory and numerical algorithms for problems involving structured matrices.
Many real world systems can be viewed as systems of interconnected systems. These systems can be considered as networks, the vertices represent individual systems and edges manifest dependencies between the systems. Often, these edges in a real network are known but dynamic or not known. This half-known dependencies contribute to complexities in understanding the conduct of the entire system. Networks can be represented by (structured) matrices and hence properties of these matrices become increasingly important for the analysis of the corresponding network systems.
The phenomena of entanglement in multipartite quantum mechanical systems has no classical analogue. In general, measures of quantum correlations of multipartite systems is an exciting topic in quantum information and computation. I am interested in such problems for mixed states which are represented by especially structured matrices.
Condition for zero and nonzero discord in graph Laplacian quantum states by Dutta S., Adhikari B. , Banerjee S. International Journal of Quantum Information 17(02) - (2019)
Proposal for dimensionality testing in QPQ by Maitra A., Adhikari B. , Adhikari S. Quantum Information & Computation 18 1125-1142 (2018)
A parametric model approach for structural reconstruction of scale-free networks by Pandey P. K., Adhikari B. IEEE Transactions on Knowledge and Data Engineering 29 2072-2085 (2017)
Bipartite separability and nonlocal quantum operations on graphs by Dutta S., Adhikari B., Banerjee S. and Srikanth R. Physical Review A American Physical Society, 94 (1) 1-10 (2016)
Context dependent preferential attachment model for complex networks by Pandey P.K. and Adhikari B. Physica A Elsevier, 436 499-508 (2015)
Md Aminur Hossain
Area of Research: Quantum Graphs
Area of Research: Applied Linear Algebra
Area of Research: Matrix Theory
Area of Research: Citation Networks
Area of Research: Computational Linear Algebra
Rohit Sarma Sarkar
Area of Research: Quantum Computing