|DATE||February 26 (Mon), 2018|
|INSTITUTE||Korea Institute for Advanced Study|
|TITLE||Axiomatization for complexity in quantum field theories and its properties|
By considering on the foundations of circuit complexity, three axioms are abstracted. With two assumptions on unitary processes, I will show that the complexity for SU(n) groups is given by bi-invariant Finsler manifolds and is determined up to a total factor. I will show a complexity principle which has a direct connection to Schrodinger's equation for isolated system. By using density matrix operators to replace the state vectors, we generalize the complexity of SU(n) groups to describe the complexity between states. For pure states, it contains the proposal of Fubini-Study metric and proves the conjecture between the ``path-integral complexity'' and minimal Euclidean action.