{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T18:58:50Z","timestamp":1775242730693,"version":"3.50.1"},"reference-count":180,"publisher":"Emerald","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,10,13]]},"abstract":"<jats:p>Constraint satisfaction problems are a central pillar of modern computational complexity theory. This survey provides an introduction to the rapidly growing field of Quantum Hamiltonian Complexity, which includes the study of quantum constraint satisfaction problems. Over the past decade and a half, this field has witnessed fundamental breakthroughs, ranging from the establishment of a \u201cQuantum Cook-Levin Theorem\u201d to deep insights into the structure of 1D low-temperature quantum systems via so-called area laws. Our aim here is to provide a computer science-oriented introduction to the subject in order to help bridge the language barrier between computer scientists and physicists in the field. As such, we include the following in this survey: (1) The motivations and history of the field, (2) a glossary of condensed matter physics terms explained in computer-science friendly language, (3) overviews of central ideas from condensed matter physics, such as indistinguishable particles, mean field theory, tensor networks, and area laws, and (4) brief expositions of selected computer science-based results in the area. For example, as part of the latter, we provide a novel information theoretic presentation of Bravyi\u2019s polynomial time algorithm for Quantum 2-SAT.<\/jats:p>","DOI":"10.1561\/0400000066","type":"journal-article","created":{"date-parts":[[2015,10,13]],"date-time":"2015-10-13T16:45:49Z","timestamp":1444754749000},"page":"159-282","source":"Crossref","is-referenced-by-count":97,"title":["Quantum Hamiltonian Complexity"],"prefix":"10.1561","volume":"10","author":[{"given":"Sevag","family":"Gharibian","sequence":"first","affiliation":[{"name":"University of California Simons Institute for the Theory of Computing, ,","place":["Berkeley"]}]},{"given":"Yichen","family":"Huang","sequence":"additional","affiliation":[{"name":"University of California ,","place":["Berkeley"]}]},{"given":"Zeph","family":"Landau","sequence":"additional","affiliation":[{"name":"Simons Institute for the Theory of Computing, University of California ,","place":["Berkeley"]}]},{"given":"Seung Woo","family":"Shin","sequence":"additional","affiliation":[{"name":"University of California ,","place":["Berkeley"]}]}],"member":"140","published-online":{"date-parts":[[2015,10,13]]},"reference":[{"key":"2026040314121209900_ref001","unstructured":"Superfluid helium\n          . https:\/\/www.youtube.com\/watch?v=2Z6UJbwxBZI."},{"key":"2026040314121209900_ref002","unstructured":"S.\n              Aaronson\n            \n          .\n                        The quantum PCP manifesto, 2006.\n                        http:\/\/scottaaronson.com\/blog\/?p=139."},{"key":"2026040314121209900_ref003","volume-title":"Handbook\n                        of Mathematical Functions with Formulas, Graphs, and Mathematical\n                        Tables","author":"Abramowitz","year":"1964"},{"key":"2026040314121209900_ref004","doi-asserted-by":"crossref","first-page":"170501","DOI":"10.1103\/PhysRevLett.111.170501","article-title":"Entanglement rates and area laws","volume":"111","author":"Van 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         Bose-Hubbard model is QMA-complete","author":"Childs","year":"2013"},{"key":"2026040314121209900_ref050","article-title":"Computing the degenerate ground space of gapped spin chains\n                        in polynomial time","author":"Chubb","year":"2015"},{"issue":"50","key":"2026040314121209900_ref051","doi-asserted-by":"crossref","first-page":"504004","DOI":"10.1088\/1751-8113\/42\/50\/504004","article-title":"Renormalization and tensor product states in spin chains and\n                        lattices","volume":"42","author":"Cirac","year":"2009","journal-title":"Journal of Physics A: Mathematical and\n                        Theoretical"},{"key":"2026040314121209900_ref052","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1038\/nphys2275","article-title":"Goals and opportunities in quantum\n                    simulation","volume":"8","author":"Cirac","year":"2012","journal-title":"Nature 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