Quantum computing relies on the implementation of unitary transformations on multi-qubit systems. In practice, these transformations must be decomposed into sequences of elementary quantum gates that can be executed on hardware. A powerful mathematical framework for such decompositions is the Cartan (or KAK) decomposition of Lie groups. For example, any two-qubit unitary operation can be expressed as a sequence of local operations acting on individual qubits and a canonical non-local operation determined by the Cartan subalgebra of SU(4). In this project, you will study Cartan decompositions of unitary groups and their applications to quantum circuit synthesis. The work may combine analytical techniques from Lie theory with computational tools for symbolic algebra and numerical simulation.
Prerequisite knowledge:
Recommended knowledge: