Theory seminar
A quantum mechanical road-coloring theorem
Speaker: Ion Wood-Thanan ()
Date: Wednesday 26 March 2025
Time: 14:00
Venue: N/1.32
The road-coloring theorem is a statement that, for certain type of directed graphs, it is always possible to color the graph as to permit a synchronizing instruction. A synchronizing instruction allows one to start at any vertex on the graph and travel to the same final vertex. Inspired by this theorem, we attempted to create quantum tight-binding models – models which are naturally represented on a graph – endowed with a synchronizing instruction. In the context of mechanics, a synchronizing instruction allows one to evolve a set of initial states to the same final states using the same time-dependent potential. The required irreversible time-evolution necessitates that the quantum system has a non-Hermitian Hamiltonian; the system is open and can have gain and loss from the environment. The talk will be centered around two attempts at creating these quantum road-colored systems: one attempt based on ancilla qubits used in quantum computing and one attempt based on the Hatano-Nelson model, a foundational non-Hermitian tight-binding model.