
At the Interface of Algebra and Statistics
This thesis takes inspiration from quantum physics to investigate mathem...
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Tossing Quantum Coins and Dice
The procedure of tossing quantum coins and dice is described. This case ...
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Universal discriminative quantum neural networks
Quantum mechanics fundamentally forbids deterministic discrimination of ...
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Constraints on Multipartite Quantum Entropies
The von Neumann entropy plays a vital role in quantum information theory...
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Distances between States and between Predicates
This paper gives a systematic account of various metrics on probability ...
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Probabilistic Modeling with Matrix Product States
Inspired by the possibility that generative models based on quantum circ...
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Quantum Clique Gossiping
This paper establishes a framework for the acceleration of quantum gossi...
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Modeling Sequences with Quantum States: A Look Under the Hood
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry information about the complementary subsystem. This is in contrast to the classical marginal distributions on a subsystem in which information about the complementary system has been integrated out and lost. A training algorithm based on the density matrix renormalization group (DMRG) procedure uses the extra information contained in the reduced densities and organizes it into a tensor network model. An understanding of the extra information contained in the reduced densities allow us to examine the mechanics of this DMRG algorithm and study the generalization error of the resulting model. As an illustration, we work with the evenparity dataset and produce an estimate for the generalization error as a function of the fraction of the dataset used in training.
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