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.
Highlights
Quantum data compression [1, 2] is one of the pillars of quantum information theory
In this paper we address the compression of tensor network states, a broad class that includes cluster states [30, 31], matrix product states (MPSs) [32,33,34], projected entangled pair states (PEPS) [35, 36], tree tensor networks [37], and multi-scale entanglement renormalization ansatz (MERA) states [38]
We designed compression protocols for parametric families of tensor network states, in which some of the tensors depend on the parameters, while some others are constant
Summary
We design quantum compression algorithms for parametric families of tensor network states. We first this work must maintain establish an upper bound on the amount of memory needed to store an arbitrary state from a given attribution to the author(s) and the title of state family. The bound is determined by the minimum cut of a suitable flow network, and is related to the work, journal citation and DOI. 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.
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