Quantum compression of tensor network states
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.
 Publication:

New Journal of Physics
 Pub Date:
 April 2020
 DOI:
 10.1088/13672630/ab7a34
 arXiv:
 arXiv:1904.06772
 Bibcode:
 2020NJPh...22d3015B
 Keywords:

 quantum data compression;
 tensor networks;
 matrix product states;
 quantum machine learning;
 quantum manybody systems;
 Quantum Physics
 EPrint:
 30 pages, 16 figures. Improved language and fixed typos