Group Theory in Quantum Computation

Efficient compilation of algorithms in quantum computation requires a good understanding of the group theory underlying the allowed logical operations. If the physical system is composite, as all proposed quantum computers have been to date, then this compilation problem quickly becomes very complex, and group-theoretic tools become an indispensable part of describing computation. This project will examine the structure of unitary matrix groups and their finite discrete subgroups, and will explore variations on how to present the relevant mathematical and computational information. 

 

References: 

[1] J. Tolar, On Clifford groups in quantum computing, J. Phys.: Conf. Series 1071 (2018) 012022, [arXiv:1810.10259 [quant-ph]].

[2] M. Korbelar and J. Tolar, Symmetries of finite Heisenberg groups for multipartite systems, J. Phys. A: Math. Theor. 45 (2012) 285305, [arXiv:1210.6167 [math-ph]].

[3] J. Tolar, A classification of finite quantum kinematics, J. Phys: Conf. Series 538 (2014) 012020, [arXiv:1411.6390 [quant-ph]].