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Article: Quantum compression of tensor network states
Title | Quantum compression of tensor network states |
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Authors | |
Keywords | Matrix product states Quantum data compression Quantum machine learning Quantum many-body systems Tensor networks |
Issue Date | 2020 |
Publisher | IOP Publishing: Open Access Journals. The Journal's web site is located at http://iopscience.iop.org/1367-2630/ |
Citation | New Journal of Physics, 2020, v. 22 n. 4, article no. 043015 How to Cite? |
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. |
Persistent Identifier | http://hdl.handle.net/10722/284902 |
ISSN | 2023 Impact Factor: 2.8 2023 SCImago Journal Rankings: 1.090 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bai, G | - |
dc.contributor.author | Yang, Y | - |
dc.contributor.author | Chiribella, G | - |
dc.date.accessioned | 2020-08-07T09:04:07Z | - |
dc.date.available | 2020-08-07T09:04:07Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | New Journal of Physics, 2020, v. 22 n. 4, article no. 043015 | - |
dc.identifier.issn | 1367-2630 | - |
dc.identifier.uri | http://hdl.handle.net/10722/284902 | - |
dc.description.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. | - |
dc.language | eng | - |
dc.publisher | IOP Publishing: Open Access Journals. The Journal's web site is located at http://iopscience.iop.org/1367-2630/ | - |
dc.relation.ispartof | New Journal of Physics | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Matrix product states | - |
dc.subject | Quantum data compression | - |
dc.subject | Quantum machine learning | - |
dc.subject | Quantum many-body systems | - |
dc.subject | Tensor networks | - |
dc.title | Quantum compression of tensor network states | - |
dc.type | Article | - |
dc.identifier.email | Chiribella, G: giulio@cs.hku.hk | - |
dc.identifier.authority | Chiribella, G=rp02035 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1088/1367-2630/ab7a34 | - |
dc.identifier.scopus | eid_2-s2.0-85085249491 | - |
dc.identifier.hkuros | 312270 | - |
dc.identifier.volume | 22 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | article no. 043015 | - |
dc.identifier.epage | article no. 043015 | - |
dc.identifier.isi | WOS:000529230500001 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 1367-2630 | - |