The dynamics of a quantum system is generated by Hamiltonians whose exponentials produce unitary time evolution. When multiple Hamiltonians are available, the commutators of these generators produce a Lie algebra known as the dynamical Lie algebra of the system. This algebra determines the set of reachable quantum operations and therefore characterizes the controllability and expressive power of quantum circuits. Dynamical Lie algebras play an important role in quantum control, Hamiltonian simulation, and the theoretical analysis of variational quantum algorithms. In this master project, you will study the dynamical Lie algebras generated by families of Hamiltonians relevant to quantum computing. The project may involve computing Lie closures of sets of operators, analyzing the structure and dimension of the resulting Lie algebras.
Prerequisite knowledge:
Recommended knowledge: