High Energy Theory Seminar

Cayley graphs offer a useful representation of finitely-generated groups, where vertices represent group elements and edges represent group generators. When considering a group acting on a Hilbert space, the orbit of a quantum state admits a similar graph representation known as a reachability graph. Reachability graphs can be dressed to encode entanglement information, making them a useful tool for studying state classification and entropy vector dynamics in quantum circuits. We introduce a quotient procedure on Cayley graphs which reproduces, and generalizes, state reachability graphs. By abstracting to this operator-level construction, our technique can be used to study the evolution of any quantum state, and its entropy vector, under a discrete gate set.  We use our results to derive explicit bounds on the entropy vectors that can be achieved for certain classes of quantum states and gate sets. The generality of our construction enables an analysis of all circuits generated from a finite gate set, including universal gate sets at arbitrary fixed circuit depth. 

The talk is in 469 Lauritsen Laboratory.

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