Research Interest

- Applied Linear Algebra (specially, problems involving structured matrices)
- Complex Networks (specially, mathematical models of complex networks, strategic network formation, and diffusion phenomena)
- Quantum Information Theory (specially, quantum entanglement, and graph theoretic aspects of quantum theory)
- Quantum Machine Learning (Quantum Walks, Parameterized Quantum Circuits, Quantum Neural Networks)

Current Research Interest:

Research Projects

- (as PI) Theory and Numerical Algorithms for Interval Linear System and Interval Eigenvalue Problem, Funded by BNRS, BARC Mumbai, 2013 - 2017
- (as PI from April 2013-December 2014 and as Co-PI from December 2014-2017) Graph Theoretic Aspects in Quantum Information Processing, Funded by CSIR, Delhi, 2013- 2017

Research Experience

- Visiting Scientist, January - May 2019, Simons Institute for the Theory of Computing, University of California Berkeley, USA
- Visiting Researcher, September - December 2018, Institute for Computational and Experimental Research in Mathematics, Brown University, USA
- Assistant Professor, December 2009 - January 2015, IIT Jodhpur
- Visiting Scientist, May-July 2013, TU Berlin and Berlin Mathematical School, Germany
- Institute Postdoctoral Fellow, January-December 2009, Department of Electrical Engineering, IIT Bombay
- Visiting Ph. D. student, April-May 2008, ETH Zurich, Switzerland

Publications

- Edited Book
- Vijay V., Yadav S. K., Adhikari B., Seshadri H., and Fulwani D. K., (eds.) Systems Thinking Approach for Social Problems: Proceedings of 37th National Systems Conference, December 2013. Vol. 327. Springer, 2015
- Journal Papers
- Mandal A., Sarkar R.S., and Adhikari B., Localization of two dimensional quantum walks defined by generalized Grover coins, Journal of Physics A: Mathematical and Theoretical, 56(2), p.025303, 2023
- Adhikari B., Singh A., and Yadav S.K., Corona product of signed graphs and its application to modeling signed networks, Discrete Mathematics, Algorithms and Applications, 15(1), 2250062, 2023
- Mandal A., Sarkar R.S., Chakraborty S., and Adhikari B., Limit theorems and localization of three-state quantum walks on a line defined by generalized Grover coins, Physical Review A, 106, 042405, 2022
- Mandal A., and Adhikari B., A characterization of orthogonal permutative matrices of order 4, Linear Algebra and its Applications, 654, pp. 102-124, 2022
- Pandey P.K., Adhikari B., Mazumdar M., and Ganguly N.,Modeling signed networks as 2-layer growing networks, IEEE Trans. on Knowledge and Data Engineering, 34(7) pp. 3377-3390, 2022
- Ganai T., and Adhikari B., Eigenvalue embedding problem for quadratic regular matrix polynomials with symmetry structures, Linear Algebra and its Applications, 640, pp. 118-148, 2022
- Ganai T., and Adhikari B., Preserving spectral properties of structured matrices under structured perturbations, Linear Algebra and its Applications, 629, pp. 168-191, 2021
- Adhikari B., Datta B.N., Ganai T., and Karow M., Updating structured matrix pencils with no spillover effect on unmeasured spectral data and deflating pair, Linear Algebra and its Applications, 624, pp. 318-348, 2021
- Singh S., Adhikari B., Dutta S., and Zueco D., Perfect state transfer on hypercubes and its implementation using superconducting qubits, Physical Review A, 102, 062609, 2020
- Sarkar R.S., Mandal A., and Adhikari B., Periodicity of lively quantum walks on cycles with generalized Grover coin, Linear Algebra and its Applications, 604, pp. 399-424, 2020
- Dutta S. and Adhikari B., Construction of cospectral graphs, Journal of Algebraic Combinatorics, 52, pp. 215–235, 2020
- Pandey P.K., Adhikari B., and Chakraborty S., A diffusion protocol for detection of link failure and utilization of resources in multi-agent systems, IEEE Trans. on Network Science and Engineering, 7(3), pp. 1493-1507, 2020
- Sharma R., Adhikari B., and Krueger T., Self-organized corona graphs: a deterministic complex network model with hierarchical structure, Advances in Complex Systems, 22 (5), 1950019 2019
- Dutta S., Adhikari B. and Banerjee S., Condition for zero and nonzero discord in graph Laplacian quantum states, International Journal of Quantum Information, 17(02), pp. 1950018, 2019
- Maitra A., Adhikari B. and Adhikari S., Proposal for dimensionality testing in quantum private query (QPQ), Quantum Information and Computation, 18(13&14), pp. 1125–1142, 2018
- Pandey P.K., Adhikari B. and Chakraborty J., Interpreting nucleation as a network formation process, Journal of Mathematical Chemistry, 56(5), pp. 1467-1480, 2018
- Pandey P.K. and Adhikari B., A parametric model approach for structural reconstruction of scale-free networks, IEEE Trans. on Knowledge and Data Engineering, 29(10), pp. 2072-2085, 2017
- Jajoo G., Kumar Y., Yadav SK, Adhikari B. and Kumar A.,Blind signal modulation recognition through clustering analysis of constellation signature, Expert Syst. With Appls, 90, pp.13-22, 2017
- Singh R. and Adhikari B., Measuring the balance of signed networks and its application to sign prediction, Journal of Statistical Mechanics:Theory and Experiment, 063302, pp. 1-16, 2017
- Dutta S., Adhikari B. and Banerjee S., Quantum discord of states arising from graphs, Quantum Information Processing, 16:183, pp. 1-17, 2017
- Sharma R., Adhikari B. and Mishra A., Structural and spectral properties of corona graphs, Discrete Applied Mathematics, 228, pp. 14-31, 2017
- Adhikari B., Banerjee S., Adhikari S. and Kumar A., Laplacian matrices of weighted digraphs represented as quantum states, Quantum Information Processing, 16:79, pp. 1-22, 2017
- Dutta S., Adhikari B., Banerjee S. and Srikanth R., Bipartite separability and nonlocal quantum operations on graphs, Physical Review A, 94, 012306, pp. 1-10, 2016
- Dutta S., Adhikari B. and Banerjee S., A graph theoretical approach to states and unitary operations, Quantum Information Processing, 15(5), pp. 2193-2212, 2016
- Adhikari B. and Alam R., Structured Procrustes problem, Linear Algebra and its Applications, 490, pp. 145-161, 2016
- Pandey P.K. and Adhikari B., Context dependent preferential attachment model for complex networks, Physica A: Statistical Mechanics and its Applications, 436, pp. 499-508, 2015
- Adhikari B. and Alam R., Structured mapping problems for linearly structured matrices, Linear Algebra and its Applications, 444, pp. 132-145, 2014
- Adhikari B., Vector space of linearizations for the quadratic two-parameter matrix polynomial, Linear and Multilinear Algebra, 61(5), pp. 603-616, 2013
- Adhikari B. and Alam R., On backward errors of structured polynomial eigenproblems solved by structure preserving linearizations, Linear Algebra and its Appls., 434(9), pp. 1989-2017, 2011
- Adhikari B., Alam R. and Kressner D., Structured eigenvalue condition numbers and linearizations for matrix polynomials, Linear Algebra and its Applications, 435(9), pp. 2193-2221, 2011
- Adhikari B. and Alam R., Structured backward errors and pseudospectra of structured matrix pencils, SIAM Journal on Matrix Analysis and Applications, 31(2), pp. 331-359, 2009
- Conference Papers
- Hazra R., Singh M., Goyal P., Adhikari B., Mukherjee A., The Rise and Rise of Interdisciplinary Research: Understanding the Interaction Dynamics of Three Major Fields – Physics, Mathematics and Computer Science., ICADL 2019, Lecture Notes in Comput. Sci., 11853, Springer
- Pal D., and Adhikari B., Games on Network Involving Social Relations: Enmity and Friendship, 13th Meeting of the Society for Social Choice and Welfare, Lund Sweden 2016
- Pandey P.K., Adhikari B. and Gupta R., Measuring diversity of network models using distorted information diffusion process, Social Networking Workshop, COMSNETS 2015
- Pal D., Adhikari B. and Mazumdar M., Strategic network formation involving social relations: Enmity and friendship, Social Networking Workshop, COMSNETS 2015
- Sharma R., Adhikari B., and Mishra A., On Spectra of Corona Graphs, CALDAM 2015, Lecture Notes in Comput. Sci., 8959, Springer