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Center for Nonlinear Studies |
Graphical models refer to a broad family of frameworks that represent multivariate probability distributions via their conditional dependence structure. In this talk I will show how undirected graphical models can be used as powerful tools for representing quantum states. In the first part of the talk I will focus on quantum tomography and demonstrate how undirected graphical models can be used to learn an informationally complete representation for any quantum state given measurement samples produced from the state. In the context of this problem, graphical models provide us with a flexible framework that allows us to incorporate various symmetries of the state and prior information directly in the learning process. In the absence of any such information, universal function approximators like neural nets can also be used within the graphical model framework to learn quantum states. In the second part of the talk I will discuss how a graphical model can be used as a variational ansatz to find representations for the ground states of stochastic Hamiltonians. In another demonstration of the flexibility of graphical models, we will use a graphical model factorized in an autoregressive form as the ansatz in this application. This type of factorization allows for exact sampling from the model and leads to succinct representations for the ground states of a variety of local Hamiltonians.
Host: Andrey Lokhov