Quantum compression of tensor network states
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Date
2020-04
Publication Type
Journal Article
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yes
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Abstract
We design quantum compression algorithms for parametric families of tensor network states. We first establish an upper bound on the amount of memory needed to store an arbitrary state from a given state family. The bound is determined by the minimum cut of a suitable flow network, and is related to the flow of information from the manifold of parameters that specify the states to the physical systems in which the states are embodied. For given network topology and given edge dimensions, our upper bound is tight when all edge dimensions are powers of the same integer. When this condition is not met, the bound is optimal up to a multiplicative factor smaller than 1.585. We then provide a compression algorithm for general state families, and show that the algorithm runs in polynomial time for matrix product states.
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published
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Journal / series
Volume
22 (4)
Pages / Article No.
43015
Publisher
IOP Publishing
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Edition / version
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Software
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Date collected
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Subject
quantum data compression; tensor networks; matrix product states; quantum machine learning; quantum many-body systems
Organisational unit
03781 - Renner, Renato / Renner, Renato