{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/161208000","title":"Efficient tomography of a quantum many-body system","arxiv_id":"1612.08000","date":"2016-12-23","proceeding":null,"authors":["B. P. Lanyon","C. Maier","M. Holzäpfel","T. Baumgratz","C. Hempel","P. Jurcevic","I. Dhand","A. S. Buyskikh","A. J. Daley","M. Cramer","M. B. Plenio","R. Blatt","C. F. Roos"],"abstract":"Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the effort required grows exponentially in the number of constituents. Developing more efficient techniques is particularly pressing as precisely-controllable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing effort to develop new characterisation tools for quantum many-body systems. Here we demonstrate Matrix Product State (MPS) tomography, which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an effort that increases efficiently with constituent number. We first prove that this broad class includes the out-of-equilbrium states produced by 1D systems with finite-range interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled spins (qubits): a size far beyond the reach of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyond-classical performance. MPS tomography should find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers.","url_abs":"http://arxiv.org/abs/1612.08000v1","url_pdf":"http://arxiv.org/pdf/1612.08000v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"161208000","repo_url":"https://github.com/dseuss/mpnum","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1612.08000","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1612.08000"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/dseuss/mpnum","reach":{"status":"ok","spdx":"BSD-3-Clause"}}],"summary":{"unverified":18},"by_repo_kind":{"listed":{"samples":18,"ran":0,"repositories":1}},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":0,"samples":[{"code_sha256_prefix":"29ebd00f4660174a","entry":"block_diag","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/utils/extmath.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/utils/extmath.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"29ebd00f4660174a"}},{"code_sha256_prefix":"21cb757bf23dd482","entry":"compression_svd","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/_testing.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/_testing.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"21cb757bf23dd482"}},{"code_sha256_prefix":"cc16f373661bb4dd","entry":"dot","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/mparray.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/mparray.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"cc16f373661bb4dd"}},{"code_sha256_prefix":"5d91caa1c0ca73bb","entry":"eig","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/linalg.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/linalg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"5d91caa1c0ca73bb"}},{"code_sha256_prefix":"8a2fd1108ff52242","entry":"eig_sum","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/linalg.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/linalg.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"8a2fd1108ff52242"}},{"code_sha256_prefix":"7b77b57b12e40387","entry":"eye","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/factory.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/factory.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"7b77b57b12e40387"}},{"code_sha256_prefix":"e509a0e471bb4ffd","entry":"global_to_local","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/utils/array_transforms.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/utils/array_transforms.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"e509a0e471bb4ffd"}},{"code_sha256_prefix":"ade9bbea619a1083","entry":"inner_prod_mps","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/special.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/special.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"ade9bbea619a1083"}},{"code_sha256_prefix":"3e545d13d087d896","entry":"local_to_global","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/utils/array_transforms.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/utils/array_transforms.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"3e545d13d087d896"}},{"code_sha256_prefix":"fe8b8f6432e3d2c4","entry":"matdot","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/utils/extmath.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/utils/extmath.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"fe8b8f6432e3d2c4"}},{"code_sha256_prefix":"95b069fa64cae200","entry":"partial_trace","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/utils/extmath.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/utils/extmath.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"95b069fa64cae200"}},{"code_sha256_prefix":"dd63f719e206161c","entry":"pmps_dm_to_array","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/mpsmpo.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/mpsmpo.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"dd63f719e206161c"}},{"code_sha256_prefix":"3819b6ccee572f3e","entry":"pmps_reduction","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/mpsmpo.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/mpsmpo.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"3819b6ccee572f3e"}},{"code_sha256_prefix":"57526b72877bff30","entry":"reductions_mpo","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/mpsmpo.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/mpsmpo.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"57526b72877bff30"}},{"code_sha256_prefix":"8825b938194fec94","entry":"x_povm","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/povm/localpovm.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/povm/localpovm.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"8825b938194fec94"}},{"code_sha256_prefix":"e081d948047e136d","entry":"y_povm","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/povm/localpovm.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/povm/localpovm.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"e081d948047e136d"}},{"code_sha256_prefix":"5638b2dc453b951e","entry":"z_povm","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/povm/localpovm.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/povm/localpovm.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"5638b2dc453b951e"}},{"code_sha256_prefix":"91f6e476b96a966b","entry":"zero","repo":"dseuss/mpnum","repo_kind":"listed","path":"mpnum/factory.py","file_url":"https://github.com/dseuss/mpnum/blob/HEAD/mpnum/factory.py","link_basis":"harvester_set","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":"BSD-3-Clause","inline_ok":true,"mcp_get_code":{"code_sha256":"91f6e476b96a966b"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}