
Low Rank Approximation in Simulations of Quantum Algorithms
Simulating quantum algorithms on classical computers is challenging when...
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Nonsmooth FrankWolfe using Uniform Affine Approximations
FrankWolfe methods (FW) have gained significant interest in the machine...
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Nice latent variable models have logrank
Matrices of low rank are pervasive in big data, appearing in recommender...
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Local Asymptotic Normality and Optimal Estimation of lowrank Quantum Systems
In classical statistics, a statistical experiment consisting of n i.i.d ...
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New error bounds for Legendre approximations of differentiable functions
In this paper we present a new perspective on error analysis of Legendre...
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Quantum Algorithm for Matrix Logarithm by Integral Formula
The matrix logarithm is one of the important matrix functions. Recently,...
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An improved analysis and unified perspective on deterministic and randomized low rank matrix approximations
We introduce a Generalized LUFactorization (GLU) for lowrank matrix ap...
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Entanglement Properties of Quantum Superpositions of Smooth, Differentiable Functions
We present an entanglement analysis of quantum superpositions corresponding to smooth, differentiable, realvalued (SDR) univariate functions. SDR functions are shown to be scalably approximated by lowrank matrix product states, for large system discretizations. We show that the maximum vonNeumann bipartite entropy of these functions grows logarithmically with the system size. This implies that efficient lowrank approximations to these functions exist in a matrix product state (MPS) for large systems. As a corollary, we show an upper bound on tracedistance approximation accuracy for a rank2 MPS as Ω(log N/N), implying that these lowrank approximations can scale accurately for large quantum systems.
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