{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T19:27:41Z","timestamp":1773775661494,"version":"3.50.1"},"reference-count":28,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T00:00:00Z","timestamp":1557100800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>We examine the problem of determining if a 2-local Hamiltonian is stoquastic by local basis changes. We analyze this problem for two-qubit Hamiltonians, presenting some basic tools and giving a concrete example where using unitaries beyond Clifford rotations is required in order to decide stoquasticity. We report on simple results for <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math>-qubit Hamiltonians with identical 2-local terms on bipartite graphs. Our most significant result is that we give an efficient algorithm to determine whether an arbitrary <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>n<\/mml:mi><\/mml:math>-qubit XYZ Heisenberg Hamiltonian is stoquastic by local basis changes.<\/jats:p>","DOI":"10.22331\/q-2019-05-06-139","type":"journal-article","created":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T16:51:17Z","timestamp":1557247877000},"page":"139","source":"Crossref","is-referenced-by-count":23,"title":["Two-local qubit Hamiltonians: when are they stoquastic?"],"prefix":"10.22331","volume":"3","author":[{"given":"Joel","family":"Klassen","sequence":"first","affiliation":[{"name":"QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands"}]},{"given":"Barbara M.","family":"Terhal","sequence":"additional","affiliation":[{"name":"QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, The Netherlands"},{"name":"Institute for Theoretical Nanoelectronics, Forschungszentrum Juelich, D-52425 Juelich, Germany"}]}],"member":"9598","published-online":{"date-parts":[[2019,5,6]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"S. Bravyi, D. P. DiVincenzo, R. I. Oliveira, and B. M. Terhal, ``The Complexity of Stoquastic Local Hamiltonian Problems,'' Quantum Information and Computation 8 no. 5, (2008) 0361-0385 , arXiv:0606140 [quant-ph].","DOI":"10.26421\/QIC8.5"},{"key":"1","doi-asserted-by":"publisher","unstructured":"N. J. Cerf and O. C. Martin, ``Projection Monte Carlo methods : an algorithmic analysis,'' International Journal of Modern Physics C 6 no. 5, (1995) 693-723.","DOI":"10.1142\/S0129183195000587"},{"key":"2","doi-asserted-by":"publisher","unstructured":"S. Sorella and L. Capriotti, ``Green function Monte Carlo with stochastic reconfiguration: An effective remedy for the sign problem,'' Physical Review B - Condensed Matter and Materials Physics 61 no. 4, (2000) 2599-2612, arXiv:9902211 [cond-mat].","DOI":"10.1103\/PhysRevB.61.2599"},{"key":"3","doi-asserted-by":"publisher","unstructured":"S. Bravyi, ``Monte Carlo Simulation of Stoquastic Hamiltonians,'' Quantum Information and Computation 15 no. 13\/14, (2015) 1122-1140, arXiv:1402.2295.","DOI":"10.26421\/QIC15.13-14"},{"key":"4","unstructured":"S. Wessel, ``Monte Carlo Simulations of Quantum Spin Models Institute for Theoretical Solid State Physics,'' in Autumn School on Correlated Electrons. 2013. https:\/\/www.cond-mat.de\/events\/correl13\/manuscripts\/."},{"key":"5","unstructured":"E. Crosson, Classical and Quantum Computation in Ground States and Beyond. PhD thesis, University of Washington, 2015. http:\/\/hdl.handle.net\/1773\/34128."},{"key":"6","doi-asserted-by":"publisher","unstructured":"S. Bravyi and D. Gosset, ``Polynomial-Time Classical Simulation of Quantum Ferromagnets,'' Physical Review Letters 119 no. 10, (2017) , arXiv:1612.05602.","DOI":"10.1103\/PhysRevLett.119.100503"},{"key":"7","doi-asserted-by":"publisher","unstructured":"T. Albash and D. A. Lidar, ``Adiabatic quantum computation,'' Reviews of Modern Physics 90 no. 1, (2018) 015002, arXiv:1611.04471 [quant-ph].","DOI":"10.1103\/RevModPhys.90.015002"},{"key":"8","doi-asserted-by":"publisher","unstructured":"S. Bravyi and B. Terhal, ``Complexity of stoquastic frustration-free Hamiltonians,'' SIAM J. Comput. 39 no. 4, (2009) 1642, arXiv:0806.1746.","DOI":"10.1137\/08072689X"},{"key":"9","doi-asserted-by":"publisher","unstructured":"M. B. Hastings and M. H. Freedman, ``Obstructions To Classically Simulating The Quantum Adiabatic Algorithm,'' Quantum Information and Computation 13 no.11\/12, (2013) 1038-1076 arXiv:1302.5733.","DOI":"10.26421\/QIC13.11-12"},{"key":"10","doi-asserted-by":"publisher","unstructured":"J. Bringewatt, W. Dorland, S. P. Jordan, and A. Mink, ``Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians,'' Phys. Rev. A 97 no. 2, (Feb., 2018) 022323, arXiv:1709.03971 [quant-ph].","DOI":"10.1103\/PhysRevA.97.022323"},{"key":"11","doi-asserted-by":"publisher","unstructured":"D. Kafri, C. Quintana, Y. Chen, A. Shabani, J. M. Martinis, and H. Neven, ``Tunable inductive coupling of superconducting qubits in the strongly nonlinear regime,'' Physical Review A 95 no. 5, (May, 2017) 052333, arXiv:1606.08382.","DOI":"10.1103\/PhysRevA.95.052333"},{"key":"12","doi-asserted-by":"publisher","unstructured":"L. Hormozi, E. W. Brown, G. Carleo, and M. Troyer, ``Nonstoquastic Hamiltonians and quantum annealing of an Ising spin glass,'' Phys. Rev. B 95 no. 18, (May, 2017) 184416, arXiv:1609.06558 [quant-ph].","DOI":"10.1103\/PhysRevB.95.184416"},{"key":"13","unstructured":"G. Samach, ``Tunable XX-Coupling Between High Coherence Flux Qubits,'' in APS March Meeting 2018. 2018. https:\/\/meetings.aps.org\/Meeting\/MAR18\/Session\/L33.13."},{"key":"14","doi-asserted-by":"publisher","unstructured":"V. I. Iglovikov, E. Khatami, and R. T. Scalettar, ``Geometry dependence of the sign problem in quantum Monte Carlo simulations,'' Phys. Rev. B 92 (Jul, 2015) 045110. https:\/\/link.aps.org\/doi\/10.1103\/PhysRevB.92.045110.","DOI":"10.1103\/PhysRevB.92.045110"},{"key":"15","doi-asserted-by":"publisher","unstructured":"C. Wu and S.-C. Zhang, ``Sufficient condition for absence of the sign problem in the fermionic quantum monte carlo algorithm,'' Phys. Rev. B 71 (Apr, 2005) 155115.","DOI":"10.1103\/PhysRevB.71.155115"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Z.-X. Li and H. Yao, ``Sign-Problem-Free Fermionic Quantum Monte Carlo: Developments and Applications,'' arXiv e-prints (May, 2018) arXiv:1805.08219, arXiv:1805.08219 [cond-mat.str-el].","DOI":"10.1146\/annurev-conmatphys-033117-054307"},{"key":"17","doi-asserted-by":"publisher","unstructured":"R. F. Bishop and D. J. J. Farnell, ``Marshall-Peierls sign rules, the quantum monte carlo method, and frustration,'' International Journal of Modern Physics B 15 no. 10n11, (2001) 1736-1739.","DOI":"10.1142\/9789812792754_0052"},{"key":"18","doi-asserted-by":"publisher","unstructured":"M. Marvian, D. A. Lidar, and I. Hen, ``On the Computational Complexity of Curing non-stoquastic Hamiltonians,'' Nature Communications 10 no. 1, (2019) 1571 , arXiv:1802.03408.","DOI":"10.1038\/s41467-019-09501-6"},{"key":"19","unstructured":"B. M. Terhal, ``The Power and Use of Stoquastic Hamiltonians,'' in Adiabatic Quantum Computing Conference. 2017. https:\/\/www.youtube.com\/watch?v=4dK30QExF4M."},{"key":"20","doi-asserted-by":"publisher","unstructured":"T. Cubitt, A. Montanaro, and S. Piddock, ``Universal Quantum Hamiltonians,'' National Academy of Sciences 115 no. 38 (2018) 9497-9502 , arXiv:1701.05182.","DOI":"10.1073\/pnas.1804949115"},{"key":"21","doi-asserted-by":"publisher","unstructured":"S. Bravyi and M. 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