{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T11:05:29Z","timestamp":1649070329915},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001381","name":"National Research Foundation Singapore","doi-asserted-by":"publisher","award":["R-710-000-012-135"],"id":[{"id":"10.13039\/501100001381","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["Quant Algo"],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002661","name":"Fonds De La Recherche Scientifique - FNRS","doi-asserted-by":"publisher","award":["R.50.05.18.F (Quant Algo)"],"id":[{"id":"10.13039\/501100002661","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2021,1]]},"DOI":"10.1007\/s11128-020-02959-0","type":"journal-article","created":{"date-parts":[[2021,1,13]],"date-time":"2021-01-13T02:06:49Z","timestamp":1610503609000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Total functions in QMA"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"http:\/\/orcid.org\/0000-0002-4381-2485","authenticated-orcid":false,"given":"Serge","family":"Massar","sequence":"first","affiliation":[]},{"given":"Miklos","family":"Santha","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,12]]},"reference":[{"key":"2959_CR1","doi-asserted-by":"crossref","unstructured":"Aaronson, S.: Quantum copy-protection and quantum money. In: 24th Annual IEEE Conference on Computational Complexity, 2009. CCC\u201909, pp. 229\u2013242. IEEE (2009)","DOI":"10.1109\/CCC.2009.42"},{"key":"2959_CR2","first-page":"81","volume":"9","author":"S Aaronson","year":"2009","unstructured":"Aaronson, S.: On perfect completeness for QMA. Quant. Inf. Comput. 9, 81\u201389 (2009)","journal-title":"Quant. Inf. Comput."},{"key":"2959_CR3","unstructured":"Aharonov, D., Ben-Or, M., Brandao, F.G.S.L., Sattath, O.: The pursuit for uniqueness: extending Valiant\u2013Vazirani theorem to the probabilistic and quantum settings. arXiv:0810.4840 (2008)"},{"key":"2959_CR4","unstructured":"Aaronson, S., Kuperberg, G.: Quantum versus classical proofs and advice. In: IEEE Conference on Computational Complexity Twenty-Second Annual, 2007. CCC\u201907, pp. 115\u2013128. IEEE (2007)"},{"key":"2959_CR5","doi-asserted-by":"crossref","unstructured":"Aharonov, D., Eldar, L.: On the complexity of commuting local Hamiltonians, and tight conditions for topological order in such systems. In: 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science (FOCS), pp. 334\u2013343. IEEE (2011)","DOI":"10.1109\/FOCS.2011.58"},{"key":"2959_CR6","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1007\/s11128-014-0877-9","volume":"14","author":"D Aharonov","year":"2015","unstructured":"Aharonov, D., Eldar, L.: The commuting local Hamiltonian problem on locally expanding graphs is approximable in NP. Quant. Inf. Process. 14, 83\u2013101 (2015)","journal-title":"Quant. Inf. Process."},{"issue":"2","key":"2959_CR7","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1090\/S0002-9947-1928-1501429-1","volume":"30","author":"JW Alexander","year":"1928","unstructured":"Alexander, J.W.: Topological invariants of knots and links. Trans. Am. Math. Soc. 30(2), 275\u2013306 (1928)","journal-title":"Trans. Am. Math. Soc."},{"key":"2959_CR8","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1145\/2371656.2371659","volume":"59","author":"A Ambainis","year":"2012","unstructured":"Ambainis, A., Kempe, J., Sattath, O.: A quantum Lov\u00e1sz local lemma. J. ACM (JACM) 59, 24 (2012)","journal-title":"J. ACM (JACM)"},{"key":"2959_CR9","doi-asserted-by":"publisher","first-page":"1572","DOI":"10.1038\/s41467-017-01637-7","volume":"8","author":"Y Atia","year":"2017","unstructured":"Atia, Y., Aharonov, D.: Fast-forwarding of Hamiltonians and exponentially precise measurements. Nat. Commun. 8, 1572 (2017)","journal-title":"Nat. Commun."},{"key":"2959_CR10","doi-asserted-by":"crossref","unstructured":"Babai, L., Szemer\u00e9di, E.: On the complexity of matrix group problems I. In: Proceedings on IEEE FOCS, pp. 229\u2013240 (1984)","DOI":"10.1109\/SFCS.1984.715919"},{"issue":"5","key":"2959_CR11","doi-asserted-by":"publisher","first-page":"1510","DOI":"10.1137\/S0097539796300933","volume":"26","author":"C Bennett","year":"1997","unstructured":"Bennett, C., Bernstein, E., Brassard, G., Vazirani, U.: Strengths and weaknesses of quantum computing. SIAM J. Comput. 26(5), 1510\u20131523 (1997)","journal-title":"SIAM J. Comput."},{"key":"2959_CR12","first-page":"361","volume":"14","author":"AD Bookatz","year":"2014","unstructured":"Bookatz, A.D.: QMA-complete problems. Quantum Inf. Comput. 14, 361\u2013383 (2014)","journal-title":"Quantum Inf. Comput."},{"key":"2959_CR13","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1090\/conm\/536\/10552","volume":"536","author":"S Bravyi","year":"2011","unstructured":"Bravyi, S.: Efficient algorithm for a quantum analogue of 2-SAT. Contemp. Math. 536, 33\u201348 (2011)","journal-title":"Contemp. Math."},{"issue":"3","key":"2959_CR14","first-page":"187","volume":"5","author":"S Bravyi","year":"2005","unstructured":"Bravyi, S., Vyalyi, M.: Commutative version of the local Hamiltonian problem and common eigenspace problem. Quantum Inf. Comput. 5(3), 187\u2013215 (2005)","journal-title":"Quantum Inf. Comput."},{"issue":"16","key":"2959_CR15","doi-asserted-by":"publisher","first-page":"167902","DOI":"10.1103\/PhysRevLett.87.167902","volume":"87","author":"H Buhrman","year":"2001","unstructured":"Buhrman, H., Cleve, R., Watrous, J., De Wolf, R.: Quantum fingerprinting. Phys. Rev. Lett. 87(16), 167902 (2001)","journal-title":"Phys. Rev. Lett."},{"key":"2959_CR16","unstructured":"Cubitt, T.S., Schwarz, M.: A constructive commutative quantum Lov\u00e1sz Local Lemma, and beyond. arXiv: 1112.1413 (2011)"},{"issue":"3","key":"2959_CR17","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1145\/1516512.1516516","volume":"56","author":"X Chen","year":"2009","unstructured":"Chen, X., Deng, X., Teng, S.H.: Settling the complexity of computing two-player Nash equilibria. J. ACM (JACM) 56(3), 14 (2009)","journal-title":"J. ACM (JACM)"},{"key":"2959_CR18","doi-asserted-by":"crossref","unstructured":"Berry, D.W., Childs, A.M., Cleve, R., Kothari, R., Somma, R.D.: Exponential improvement in precision for simulating sparse Hamiltonians. In: Forum of Mathematics, Sigma, vol. 5. Cambridge University Press (2017)","DOI":"10.1017\/fms.2017.2"},{"issue":"1969","key":"2959_CR19","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1098\/rspa.1998.0164","volume":"454","author":"R Cleve","year":"1998","unstructured":"Cleve, R., Ekert, A., Macchiavello, C., Mosca, M.: Quantum algorithms revisited. Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci. 454(1969), 339\u2013354 (1998)","journal-title":"Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci."},{"issue":"1","key":"2959_CR20","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1137\/070699652","volume":"39","author":"C Daskalakis","year":"2009","unstructured":"Daskalakis, C., Goldberg, P.W., Papadimitriou, C.H.: The complexity of computing a Nash equilibrium. SIAM J. Comput. 39(1), 195\u2013259 (2009)","journal-title":"SIAM J. Comput."},{"key":"2959_CR21","doi-asserted-by":"crossref","unstructured":"Farhi, E., Gosset, D., Hassidim, A., Lutomirski, A., Shor, P.: Quantum money from knots. In Proceedings of the 3rd Innovations in Theoretical Computer Science Conference, pp. 276\u2013289. ACM (2012)","DOI":"10.1145\/2090236.2090260"},{"key":"2959_CR22","unstructured":"Gily\u00e9n, A., Sattath, O.: On preparing ground states of gapped Hamiltonians: an efficient quantum Lov\u00e1sz Local Lemma. In: 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pp. 439\u2013450. IEEE, 2017. arXiv preprint arXiv:1611.08571 (2016)"},{"key":"2959_CR23","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1016\/j.jcss.2017.12.003","volume":"94","author":"PW Goldberg","year":"2018","unstructured":"Goldberg, P.W., Papadimitriou, C.: Towards a unified complexity theory of total functions. J. Comput. Syst. Sci. 94, 167\u2013192 (2018)","journal-title":"J. Comput. Syst. Sci."},{"issue":"3","key":"2959_CR24","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1137\/140957056","volume":"45","author":"D Gosset","year":"2016","unstructured":"Gosset, D., Nagaj, D.: Quantum 3-SAT is QMA $$_1$$-complete. SIAM J. Comput. 45(3), 1080\u20131128 (2016)","journal-title":"SIAM J. Comput."},{"key":"2959_CR25","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search? In: Proceedings of 28th Annual ACM Symposium on Theory of Computing, May, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"key":"2959_CR26","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1103\/PhysRevLett.79.325","volume":"79","author":"LK Grover","year":"1997","unstructured":"Grover, L.K.: Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325\u2013328 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"2959_CR27","doi-asserted-by":"crossref","unstructured":"He, K., Li, Q., Sun, X., Zhang, J.: Quantum Lov\u00e1sz local lemma: Shearer\u2019s bound is tight. In: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing, pp. 461\u2013472 (2019)","DOI":"10.1145\/3313276.3316392"},{"key":"2959_CR28","doi-asserted-by":"crossref","unstructured":"Janzing, D., Wocjan, P., Beth, T.: Cooling and low energy state preparation for 3-local Hamiltonians are FQMA-complete. arXiv:quant-ph\/0303186 (2003)","DOI":"10.26421\/QIC3.6-7"},{"issue":"1","key":"2959_CR29","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1016\/0022-0000(88)90046-3","volume":"37","author":"DS Johnson","year":"1988","unstructured":"Johnson, D.S., Papadimitriou, C.H., Yannakakis, M.: How easy is local search? J. Comput. Syst. Sci. 37(1), 79\u2013100 (1988)","journal-title":"J. Comput. Syst. Sci."},{"key":"2959_CR30","doi-asserted-by":"publisher","first-page":"103","DOI":"10.24033\/bsmf.90","volume":"3","author":"C Jordan","year":"1875","unstructured":"Jordan, C.: Essai sur la g\u00e9om\u00e9trie \u00e0 $$n$$ dimensions. Bulletin de la Soci\u00e9t\u00e9 math\u00e9matique de France 3, 103\u2013174 (1875)","journal-title":"Bulletin de la Soci\u00e9t\u00e9 math\u00e9matique de France"},{"issue":"3","key":"2959_CR31","first-page":"258","volume":"3","author":"J Kempe","year":"2003","unstructured":"Kempe, J., Regev, O.: 3-Local Hamiltonian is QMA-complete. Quantum Inf. Comput. 3(3), 258\u2013264 (2003)","journal-title":"Quantum Inf. Comput."},{"key":"2959_CR32","unstructured":"Kitaev, A.Y.: Quantum measurements and the Abelian stabilizer problem. arXiv preprint, arXiv:quant-ph\/9511026 (1995)"},{"issue":"5","key":"2959_CR33","doi-asserted-by":"publisher","first-page":"1070","DOI":"10.1137\/S0097539704445226","volume":"35","author":"J Kempe","year":"2006","unstructured":"Kempe, J., Kitaev, A., Regev, O.: The complexity of the local Hamiltonian problem. SIAM J. Comput. 35(5), 1070\u20131097 (2006)","journal-title":"SIAM J. Comput."},{"key":"2959_CR34","volume-title":"Classical and Quantum Computation. Graduate Studies in Mathematics","author":"AY Kitaev","year":"2002","unstructured":"Kitaev, A.Y., Shen, A.H., Vyalyi, M.N.: Classical and Quantum Computation. Graduate Studies in Mathematics, vol. 47. AMS, Providence, RI (2002)"},{"key":"2959_CR35","unstructured":"Krentel, M.W.: Structure in locally optimal solutions. In: 30th Annual Symposium on Foundations of Computer Science, 1989, pp. 216\u2013221 (October). IEEE (1989)"},{"issue":"2","key":"2959_CR36","doi-asserted-by":"publisher","first-page":"122152","DOI":"10.1007\/s00037-005-0194-x","volume":"14","author":"C Marriott","year":"2005","unstructured":"Marriott, C., Watrous, J.: Quantum Arthur\u2013Merlin games. Comput. Complex. 14(2), 122152 (2005)","journal-title":"Comput. Complex."},{"key":"2959_CR37","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0304-3975(91)90200-L","volume":"81","author":"N Megiddo","year":"1991","unstructured":"Megiddo, N., Papadimitriou, C.H.: On total functions, existence theorems and computational complexity. Theor. Comput. Sci. 81, 317\u2013324 (1991)","journal-title":"Theor. Comput. Sci."},{"key":"2959_CR38","doi-asserted-by":"crossref","unstructured":"Moser, R.A.: A constructive proof of the Lov\u00e1sz Local Lemma. In: STOC, pp. 343\u2013350. arXiv:0810.4812 (2009)","DOI":"10.1145\/1536414.1536462"},{"issue":"2","key":"2959_CR39","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1145\/1667053.1667060","volume":"57","author":"RA Moser","year":"2010","unstructured":"Moser, R.A., Tardos, G.: A constructive proof of the general Lov\u00e1sz local lemma. J. ACM 57(2), 11 (2010)","journal-title":"J. ACM"},{"issue":"11","key":"2959_CR40","first-page":"1053","volume":"9","author":"D Nagaj","year":"2009","unstructured":"Nagaj, D., Wocjan, P., Zhang, Y.: Fast amplification of QMA. Quantum Inf. Comput. 9(11), 1053\u20131068 (2009)","journal-title":"Quantum Inf. Comput."},{"issue":"3","key":"2959_CR41","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1016\/S0022-0000(05)80063-7","volume":"48","author":"CH Papadimitriou","year":"1994","unstructured":"Papadimitriou, C.H.: On the complexity of the parity argument and other inefficient proofs of existence. J. Comput. Syst. Sci. 48(3), 498\u2013532 (1994)","journal-title":"J. Comput. Syst. Sci."},{"key":"2959_CR42","doi-asserted-by":"crossref","unstructured":"Papadimitriou, C.H., Schaeffer, A.A., Yannakakis, M.: On the complexity of local search. In: Proceedings of the Twenty-Second Annual ACM Symposium on Theory of Computing, pp. 438\u2013445. ACM (1990, April)","DOI":"10.1145\/100216.100274"},{"key":"2959_CR43","volume-title":"Witness-Preserving QMA Amplification, Quantum Computation Lecture Notes, Spring 2006","author":"O Regev","year":"2006","unstructured":"Regev, O.: Witness-Preserving QMA Amplification, Quantum Computation Lecture Notes, Spring 2006. Tel Aviv University, Tel Aviv-Yafo (2006)"},{"issue":"12","key":"2959_CR44","first-page":"987","volume":"15","author":"O Sattath","year":"2015","unstructured":"Sattath, O., Arad, I.: A Constructive quantum Lov\u00e1sz Local Lemma for commuting projectors. Quantum Inf. Comput. 15(12), 987\u2013996 (2015)","journal-title":"Quantum Inf. Comput."},{"issue":"23","key":"2959_CR45","doi-asserted-by":"publisher","first-page":"6433","DOI":"10.1073\/pnas.1519833113","volume":"113","author":"O Sattath","year":"2016","unstructured":"Sattath, O., Morampudi, S.C., Laumann, C.R., Moessner, R.: When a local Hamiltonian must be frustration-free. Proc. Natl. Acad. Sci. 113(23), 6433\u20136437 (2016)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"2959_CR46","unstructured":"Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: 35th Annual Symposium on Foundations of Computer Science, 1994 Proceedings, pp. 124\u2013134. IEEE (1994)"},{"key":"2959_CR47","first-page":"901","volume":"11","author":"N Schuch","year":"2011","unstructured":"Schuch, N.: Complexity of commuting Hamiltonians on a square lattice of qubits. Quantum Inf. Comput. 11, 901 (2011)","journal-title":"Quantum Inf. Comput."},{"key":"2959_CR48","unstructured":"Schwarz, M., Cubitt, T.S., Verstraete, F.: An information-theoretic proof of the constructive commutative quantum Lov\u00e1sz Local Lemma. arXiv:1311.6474 (2013)"},{"key":"2959_CR49","unstructured":"Szegedy, M.: Quantum speed-up of Markov chain based algorithms. In: Proceedings of 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 32\u201341 (2004)"},{"key":"2959_CR50","unstructured":"Watrous, J.: Succinct quantum proofs for properties of finite groups. In: Proceedings on 41st Annual Symposium on Foundations of Computer Science, 2000, pp. 537\u2013546. IEEE (2000)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02959-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-020-02959-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-020-02959-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,19]],"date-time":"2021-04-19T06:12:59Z","timestamp":1618812779000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-020-02959-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":50,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["2959"],"URL":"https:\/\/doi.org\/10.1007\/s11128-020-02959-0","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"3 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 December 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"35"}}