{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T10:34:08Z","timestamp":1788258848440,"version":"build-2803163510"},"reference-count":40,"publisher":"American Chemical Society (ACS)","issue":"16","license":[{"start":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T00:00:00Z","timestamp":1786665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100020639","name":"Bayerische Staatsministerium f?r Wirtschaft, Landesentwicklung und Energie","doi-asserted-by":"publisher","award":["NA"],"award-info":[{"award-number":["NA"]}],"id":[{"id":"10.13039\/501100020639","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Auxiliary Field Quantum Monte Carlo (AFQMC) has emerged as a powerful framework for treating strongly correlated electronic systems, offering a favorable balance between computational cost and accuracy. In this paper, we present a novel AFQMC method that uses the isometric tensor hypercontraction (ITHC) technique to diagonalize the two-body Coulomb interaction of molecular electronic Hamiltonians by introducing additional fictitious Fermionic modes. While traditional low-rank approximations such as the Tensor Hypercontraction (THC) decomposition have been used in AFQMC in the past, their conventional role has been to provide compact representation of the two-electron interaction, thereby reducing the memory footprint. In comparison, our method not only reduces memory usage but also exhibits lower theoretical complexity and better practical performance for both propagation and local energy evaluation compared to the standard AFQMC method. We demonstrate the efficacy of this approach by computing the ground-state energies of a linear H10-chain and the benzene molecule. Our results show that the extended-basis AFQMC recovers many-body correlations with a precision comparable to that of high-level wave function methods such as Coupled Clusters (CC) or Density Matrix Renormalization Group (DMRG), while offering significantly improved scaling.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c00749","type":"journal-article","created":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T15:02:22Z","timestamp":1786719742000},"page":"8227-8238","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Auxiliary-Field\nQuantum Monte Carlo Using\nIsometric Tensor Hypercontraction"],"prefix":"10.1021","volume":"22","author":[{"given":"Maxine","family":"Luo","sequence":"first","affiliation":[{"name":"Max Planck Institute of Quantum Optics , Hans-Kopfermann-Stra\u00dfe 1 , ,","place":["Garching, Germany, 85748"]},{"name":"Munich Center for Quantum Science and Technology , Schellingstra\u00dfe 4 , ,","place":["Mu\u0308nchen, Germany, 80799"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-8330-4963","authenticated-orcid":true,"given":"Victor","family":"Chen","sequence":"additional","affiliation":[{"name":"Technical University of Munich , , Lichtenbergstra\u00dfe 4 , ,","place":["Garching, Germany, 85748"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-3972-4388","authenticated-orcid":true,"given":"Yu","family":"Wang","sequence":"additional","affiliation":[{"name":"Technical University of Munich, CIT , , Boltzmannstra\u00dfe 3 , ,","place":["Garching, Germany, 85748"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian B.","family":"Mendl","sequence":"additional","affiliation":[{"name":"Technical University of Munich, CIT , , Boltzmannstra\u00dfe 3 , ,","place":["Garching, Germany, 85748"]},{"name":"Technical University of Munich , , Lichtenbergstra\u00dfe 2a , ,","place":["Garching, Germany, 85748"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,14]]},"reference":[{"key":"2026083118575784100_cit1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRev.140.A1133","article-title":"Self-Consistent Equations Including Exchange and Correlation\nEffects","volume":"140","author":"Kohn","year":"1965","journal-title":"Phys. Rev."},{"key":"2026083118575784100_cit2","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1103\/RevModPhys.87.897","article-title":"Density\nfunctional theory: Its origins, rise to prominence, and future","volume":"87","author":"Jones","year":"2015","journal-title":"Rev. Mod. Phys."},{"key":"2026083118575784100_cit3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.7.031059","article-title":"Towards\nthe Solution\nof the Many-Electron Problem in Real Materials: Equation of State\nof the Hydrogen Chain with State-of-the-Art Many-Body Methods","volume":"7","author":"Motta","year":"2017","journal-title":"Phys. Rev. X"},{"key":"2026083118575784100_cit4","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1103\/RevModPhys.32.211","article-title":"Configuration\ninteraction in the\nhydrogen molecule \u2013 the ground state","volume":"32","author":"McLean","year":"1960","journal-title":"Rev. Mod. Phys."},{"key":"2026083118575784100_cit5","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1103\/RevModPhys.79.291","article-title":"Coupled-cluster theory in quantum\nchemistry","volume":"79","author":"Bartlett","year":"2007","journal-title":"Rev. Mod. Phys."},{"key":"2026083118575784100_cit6","doi-asserted-by":"publisher","first-page":"5633","DOI":"10.1021\/acs.chemrev.0c00901","article-title":"Quantum\nChemistry Calculations for\nMetabolomics","volume":"121","author":"Borges","year":"2021","journal-title":"Chem. Rev."},{"key":"2026083118575784100_cit7","doi-asserted-by":"publisher","DOI":"10.1088\/1361-648X\/aab9c3","article-title":"QMCPACK: an open source\nab initio quantum Monte Carlo package for\nthe electronic structure of atoms, molecules and solids","volume":"30","author":"Kim","year":"2018","journal-title":"J. Phys.: Condens. Matter"},{"key":"2026083118575784100_cit8","doi-asserted-by":"publisher","DOI":"10.1002\/wcms.1364","article-title":"Ab initio computations\nof molecular systems by the auxiliary- field\nquantum Monte Carlo method","volume":"8","author":"Motta","year":"2018","journal-title":"WIREs Comput. Mol.\nSci."},{"key":"2026083118575784100_cit9","doi-asserted-by":"publisher","first-page":"7024","DOI":"10.1021\/acs.jctc.2c00802","article-title":"Twenty\nYears of auxiliary-field quantum\nMonte Carlo in quantum chemistry: An overview and assessment on main\ngroup chemistry and bond-breaking","volume":"18","author":"Lee","year":"2022","journal-title":"J. Chem.\nTheory Comput."},{"key":"2026083118575784100_cit10","doi-asserted-by":"publisher","DOI":"10.1063\/5.0024835","article-title":"The performance of phaseless auxiliary-field\nquantum Monte Carlo on the ground state electronic energy of benzene","volume":"153","author":"Lee","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2026083118575784100_cit11","doi-asserted-by":"publisher","first-page":"1161","DOI":"10.1126\/science.aak9546","article-title":"Numerical evidence of fluctuating\nstripes in the normal state of high- Tc cuprate superconductors","volume":"358","author":"Huang","year":"2017","journal-title":"Science"},{"key":"2026083118575784100_cit12","doi-asserted-by":"publisher","DOI":"10.1126\/science.adh7691","article-title":"Coexistence of superconductivity\nwith partially filled stripes in the Hubbard model","volume":"384","author":"Xu","year":"2024","journal-title":"Science"},{"key":"2026083118575784100_cit13","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1021\/acs.jctc.8b00944","article-title":"Overcoming the memory bottleneck\nin auxiliary field quantum Monte Carlo simulations with interpolative\nseparable density fitting","volume":"15","author":"Malone","year":"2019","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118575784100_cit14","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.2.030305","article-title":"Even more\nefficient quantum computations\nof chemistry through tensor hyper- contraction","volume":"2","author":"Lee","year":"2021","journal-title":"PRX Quantum"},{"key":"2026083118575784100_cit15","doi-asserted-by":"publisher","DOI":"10.1103\/PRXQuantum.6.010355","article-title":"Efficient simulation\nof quantum chemistry problems\nin an enlarged basis set","volume":"6","author":"Luo","year":"2025","journal-title":"PRX Quantum"},{"key":"2026083118575784100_cit16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1021\/acs.jctc.2c00934","article-title":"ipie: A Python-based\nauxiliary-field quantum Monte Carlo program with flexibility and efficiency\non CPUs and GPUs","volume":"19","author":"Malone","year":"2023","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118575784100_cit17","doi-asserted-by":"publisher","DOI":"10.1063\/1.4732310","article-title":"Tensor\nhypercontraction density fitting.\nI. Quartic scaling second- and third-order M\u00f8ller-Plesset perturbation\ntheory","volume":"137","author":"Hohenstein","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2026083118575784100_cit18","doi-asserted-by":"publisher","DOI":"10.1063\/1.4768233","article-title":"Tensor hypercon-\ntraction. II. Least-squares renormalization","volume":"137","author":"Parrish","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2026083118575784100_cit19","doi-asserted-by":"publisher","first-page":"329","DOI":"10.1016\/j.jcp.2015.09.014","article-title":"Compression of the electron repulsion integral tensor in tensor hyper-\ncontraction format with cubic scaling cost","volume":"302","author":"Lu","year":"2015","journal-title":"J. Comput. Phys."},{"key":"2026083118575784100_cit20","doi-asserted-by":"publisher","first-page":"1311","DOI":"10.1021\/acs.jctc.7b01113","article-title":"Interpolative separable\ndensity fitting through centroidal\nVoronoi tessellation with applications to hybrid functional electronic\nstructure calculations","volume":"14","author":"Dong","year":"2018","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118575784100_cit21","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1021\/acs.jctc.9b00820","article-title":"Systematically\nImprovable Tensor Hypercontraction:\nInterpolative Separable Density-Fitting for Molecules Applied to Exact\nExchange, Second- and Third-Order M\u00f8ller-Plesset Perturbation\nTheory","volume":"16","author":"Lee","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118575784100_cit22","doi-asserted-by":"publisher","first-page":"1382","DOI":"10.1021\/acs.jctc.9b01205","article-title":"Improved\nGrid Optimization and Fitting in Least Squares Tensor Hypercontraction","volume":"16","author":"Matthews","year":"2020","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118575784100_cit23","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/S0166-1280(96)04821-X","article-title":"Review\nof quantum Monte Carlo methods and their applications","volume":"394","author":"Acioli","year":"1997","journal-title":"J. Mol. Struct. Theochem."},{"key":"2026083118575784100_cit24","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1090\/S0002-9939-1959-0108732-6","article-title":"On the\nproduct of semi-groups of operators","volume":"10","author":"Trotter","year":"1959","journal-title":"Proc. Am.\nMath. Soc."},{"key":"2026083118575784100_cit25","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/41\/49\/493001","article-title":"Quantum Zeno dynamics: mathematical and physical aspects","volume":"41","author":"Facchi","year":"2008","journal-title":"J. Phys. A: Math. Theor."},{"key":"2026083118575784100_cit26","doi-asserted-by":"publisher","DOI":"10.22331\/q-2020-07-06-289","article-title":"Quantum Zeno\ndynamics from general quantum operations","volume":"4","author":"Burgarth","year":"2020","journal-title":"Quantum"},{"key":"2026083118575784100_cit27","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1103\/PhysRevLett.3.77","article-title":"Calculation\nof partition functions","volume":"3","author":"Hubbard","year":"1959","journal-title":"Phys. Rev. Lett."},{"key":"2026083118575784100_cit28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.90.136401","article-title":"Quantum Monte Carlo\nmethod using phase-free random\nwalks with Slater determinants","volume":"90","author":"Zhang","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"2026083118575784100_cit29","doi-asserted-by":"publisher","first-page":"337","DOI":"10.1146\/annurev-conmatphys-033117-054307","article-title":"Sign-Problem-Free Fermionic\nQuantum Monte Carlo: Developments and\nApplications","volume":"10","author":"Li","year":"2019","journal-title":"Annu. Rev. Conden. Matter P.hys"},{"key":"2026083118575784100_cit30","doi-asserted-by":"publisher","DOI":"10.1063\/5.0225596","article-title":"Improved modularity\nand new features in ipie: Toward even larger AFQMC calculations on\nCPUs and GPUs at zero and finite temperatures","volume":"161","author":"Jiang","year":"2024","journal-title":"J. Chem. Phys."},{"key":"2026083118575784100_cit31","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/0029-5582(60)90048-1","article-title":"Stability\nconditions and nuclear rotations in the Hartree-Fock theory","volume":"21","author":"Thouless","year":"1960","journal-title":"Nucl. Phys."},{"key":"2026083118575784100_cit32","doi-asserted-by":"crossref","unstructured":"Luo, M.; Chen, V.; Wang, Y.; Mendl, C. B. Efficient Auxiliary-Field Quantum Monte Carlo Using\nIsometric Tensor Hypercontraction. 2026,  10.5281\/zenodo.19368252.","DOI":"10.1021\/acs.jctc.6c00749"},{"key":"2026083118575784100_cit33","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1103\/PhysRev.81.385","article-title":"A Simplification\nof the Hartree-Fock Method","volume":"81","author":"Slater","year":"1951","journal-title":"Phys. Rev."},{"key":"2026083118575784100_cit34","volume-title":"Modern\nQuantum Chemistry:\nIntroduction to Advanced Electronic Structure Theory","author":"Szabo","year":"2012"},{"key":"2026083118575784100_cit35","unstructured":"Luo, M.\n          \n          2025\n          https:\/\/github.com\/carrot6869\/Isometric-THC, GitHub repository\n(accessed April 01, 2026)."},{"key":"2026083118575784100_cit36","first-page":"1","article-title":"CVXPY: A Python-embedded\nmodeling language for convex optimization","volume":"17","author":"Diamond","year":"2016","journal-title":"J.\nMach. Learn. Res."},{"key":"2026083118575784100_cit37","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1080\/23307706.2017.1397554","article-title":"A rewriting system\nfor convex optimization problems","volume":"5","author":"Agrawal","year":"2018","journal-title":"J. Control\nDecis."},{"key":"2026083118575784100_cit38","unstructured":"Hessel, M.; Budden, D.; Viola, F.; Rosca, M.; Sezener, E.; Hennigan, T.\n          Optax:\ncomposable gradient transformation\nand optimization, in JAX!. 2020https:\/\/github.com\/google-deepmind\/optax."},{"key":"2026083118575784100_cit39","doi-asserted-by":"publisher","DOI":"10.1063\/5.0068887","article-title":"Hybrid gausslet\/Gaussian\nbasis sets","volume":"155","author":"Qiu","year":"2021","journal-title":"J. Chem. Phys."},{"key":"2026083118575784100_cit40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevX.11.011020","article-title":"Theory of Trotter Error\nwith Commutator Scaling","volume":"11","author":"Childs","year":"2021","journal-title":"Phys. Rev. X"}],"container-title":["Journal of Chemical Theory\nand Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.acs.org\/doi\/pdf\/10.1021\/acs.jctc.6c00749","content-type":"application\/pdf","content-version":"vor","intended-application":"unspecified"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/16\/8227\/66545964\/acs.jctc.6c00749.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.acs.org\/jctcce\/article-pdf\/22\/16\/8227\/66545964\/acs.jctc.6c00749.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T22:58:04Z","timestamp":1788217084000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.acs.org\/jctcce\/article\/22\/16\/8227\/5255458\/Efficient-Auxiliary-Field-Quantum-Monte-Carlo"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,14]]},"references-count":40,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2026,8,14]]},"published-print":{"date-parts":[[2026,8,25]]}},"URL":"https:\/\/doi.org\/10.1021\/acs.jctc.6c00749","relation":{},"ISSN":["1549-9618","1549-9626"],"issn-type":[{"value":"1549-9618","type":"print"},{"value":"1549-9626","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,14]]}}}