{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T13:43:19Z","timestamp":1775655799671,"version":"3.50.1"},"reference-count":51,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["2020275"],"award-info":[{"award-number":["2020275"]}]},{"DOI":"10.13039\/100000015","name":"U.S. Department of Energy","doi-asserted-by":"crossref","award":["89233218CNA000001"],"award-info":[{"award-number":["89233218CNA000001"]}],"id":[{"id":"10.13039\/100000015","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"\n We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of\n \n &#x03B7;<\/mml:mi>\n <\/mml:math>\n particles and\n \n N<\/mml:mi>\n <\/mml:math>\n single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using\n \n O<\/mml:mi>\n (<\/mml:mo>\n \n &#x03B7;<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msup>\n \n N<\/mml:mi>\n <\/mml:msqrt>\n )<\/mml:mo>\n <\/mml:math>\n \n T<\/mml:mi>\n <\/mml:math>\n -gates, outperforming alternative algorithms when\n \n &#x03B7;<\/mml:mi>\n &#x2272;<\/mml:mo>\n \n N<\/mml:mi>\n <\/mml:msqrt>\n <\/mml:math>\n . To achieve such scaling, we require\n \n O<\/mml:mi>\n (<\/mml:mo>\n \n N<\/mml:mi>\n <\/mml:msqrt>\n )<\/mml:mo>\n <\/mml:math>\n dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford\n \n +<\/mml:mo>\n T<\/mml:mi>\n <\/mml:math>\n gates and study the impact of noise on the prepared state.\n <\/jats:p>","DOI":"10.22331\/q-2026-04-08-2056","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T12:43:57Z","timestamp":1775652237000},"page":"2056","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping"],"prefix":"10.22331","volume":"10","author":[{"given":"E.","family":"Rule","sequence":"first","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA"},{"name":"Department of Physics, University of California, Berkeley, CA 94720, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I. A.","family":"Chernyshev","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"Stetcu","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Carlson","sequence":"additional","affiliation":[{"name":"Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Weiss","sequence":"additional","affiliation":[{"name":"Department of Physics, Washington University in St. Louis, St. Louis, Missouri 63130, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Kenneth W Ford and John A Wheeler. ``Semiclassical description of scattering''. Annals of Physics 7, 259\u2013286 (1959).","DOI":"10.1016\/0003-4916(59)90026-0"},{"key":"1","doi-asserted-by":"publisher","unstructured":"M. Brack and R. Bhaduri. ``Semiclassical physics''. Frontiers in Physics. Avalon Publishing. (2003). url: https:\/\/doi.org\/10.1201\/9780429502828.","DOI":"10.1201\/9780429502828"},{"key":"2","unstructured":"D.M. Brink. ``Semi-classical methods for nucleus-nucleus scattering''. Cambridge University Press. (2025)."},{"key":"3","doi-asserted-by":"publisher","unstructured":"Ad\u00e9le D. Laurent and Denis Jacquemin. ``TD\u2011DFT benchmarks: A review''. International Journal of Quantum Chemistry 113, 2019\u20132039 (2013).","DOI":"10.1002\/qua.24438"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Aurel Bulgac, Piotr Magierski, Kenneth J. Roche, and Ionel Stetcu. ``Induced Fission of $^{240}\\mathrm{Pu}$ within a Real-Time Microscopic Framework''. Phys. Rev. Lett. 116, 122504 (2016).","DOI":"10.1103\/PhysRevLett.116.122504"},{"key":"5","doi-asserted-by":"publisher","unstructured":"D Chemla and Jagdeep Shah. ``Many-body and correlation effects in semiconductors''. Nature 411, 549\u201357 (2001).","DOI":"10.1038\/35079000"},{"key":"6","doi-asserted-by":"publisher","unstructured":"A. D. Klemm and R. G. Storer. ``The structure of quantum fluids: helium and neon''. Australian Journal of Physics 26, 43 (1973).","DOI":"10.1071\/PH730043"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Maria Piarulli and Ingo Tews. ``Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory''. Front. in Phys. 7, 245 (2020). arXiv:2002.00032.","DOI":"10.3389\/fphy.2019.00245"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Daniel S. Abrams and Seth Lloyd. ``Simulation of Many-Body Fermi Systems on a Universal Quantum Computer''. Phys. Rev. Lett. 79, 2586\u20132589 (1997).","DOI":"10.1103\/PhysRevLett.79.2586"},{"key":"9","doi-asserted-by":"publisher","unstructured":"G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme. ``Quantum algorithms for fermionic simulations''. Phys. Rev. A 64, 022319 (2001).","DOI":"10.1103\/PhysRevA.64.022319"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Al\u00e1n Aspuru-Guzik, Anthony D. Dutoi, Peter J. Love, and Martin Head-Gordon. ``Simulated Quantum Computation of Molecular Energies''. Science 309, 1704\u20131707 (2005). arXiv:quant-ph\/0604193.","DOI":"10.1126\/science.1113479"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Seth Lloyd. ``Universal Quantum Simulators''. Science 273, 1073 (1996).","DOI":"10.1126\/science.273.5278.1073"},{"key":"12","doi-asserted-by":"publisher","unstructured":"C. Zalka. ``Simulating quantum systems on a quantum computer''. Proceedings of the Royal Society of London Series A 454, 313 (1998).","DOI":"10.1098\/rspa.1998.0162"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Michael A. Nielsen and Isaac L. Chuang. ``Quantum computation and quantum information: 10th anniversary edition''. Cambridge University Press. (2010).","DOI":"10.1017\/CBO9780511976667"},{"key":"14","doi-asserted-by":"publisher","unstructured":"I. Stetcu, A. Baroni, and J. Carlson. ``Projection algorithm for state preparation on quantum computers''. Phys. Rev. C 108, L031306 (2023).","DOI":"10.1103\/PhysRevC.108.L031306"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Yu Shee, Pei-Kai Tsai, Cheng-Lin Hong, Hao-Chung Cheng, and Hsi-Sheng Goan. ``Qubit-efficient encoding scheme for quantum simulations of electronic structure''. Phys. Rev. Res. 4, 023154 (2022).","DOI":"10.1103\/PhysRevResearch.4.023154"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Ryan Babbush, Nathan Wiebe, Jarrod McClean, James McClain, Hartmut Neven, and Garnet Kin-Lic Chan. ``Low-depth quantum simulation of materials''. Phys. Rev. X 8, 011044 (2018).","DOI":"10.1103\/PhysRevX.8.011044"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Ang Li, Alessandro Baroni, Ionel Stetcu, and Travis S. Humble. ``Deep quantum circuit simulations of low-energy nuclear states''. The European Physical Journal A 60, 106 (2024).","DOI":"10.1140\/epja\/s10050-024-01286-7"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Dominic W. Berry, M\u00e1ria Kieferov\u00e1, Artur Scherer, Yuval R. Sanders, Guang Hao Low, Nathan Wiebe, Craig Gidney, and Ryan Babbush. ``Improved techniques for preparing eigenstates of fermionic hamiltonians''. npj Quantum Information 4 (2018).","DOI":"10.1038\/s41534-018-0071-5"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Alain Delgado, Pablo A. M. Casares, Roberto dos Reis, Modjtaba Shokrian Zini, Roberto Campos, Norge Cruz-Hern\u00e1ndez, Arne-Christian Voigt, Angus Lowe, Soran Jahangiri, M. A. Martin-Delgado, Jonathan E. Mueller, and Juan Miguel Arrazola. ``Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer''. Phys. Rev. A 106, 032428 (2022).","DOI":"10.1103\/PhysRevA.106.032428"},{"key":"20","doi-asserted-by":"publisher","unstructured":"Ryan Babbush, William J. Huggins, Dominic W. Berry, Shu Fay Ung, Andrew Zhao, David R. Reichman, Hartmut Neven, Andrew D. Baczewski, and Joonho Lee. ``Quantum simulation of exact electron dynamics can be more efficient than classical mean-field methods''. Nature Commun. 14, 4058 (2023).","DOI":"10.1038\/s41467-023-39024-0"},{"key":"21","doi-asserted-by":"publisher","unstructured":"William J. Huggins, Oskar Leimkuhler, Torin F. Stetina, and K. Birgitta Whaley. ``Efficient state preparation for the quantum simulation of molecules in first quantization''. PRX Quantum 6, 020319 (2025).","DOI":"10.1103\/PRXQuantum.6.020319"},{"key":"22","doi-asserted-by":"publisher","unstructured":"M. Ajtai, J. Koml\u00f3s, and E. Szemer\u00e9di. ``An 0(n log n) sorting network''. In Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing. Page 1\u20139. STOC '83New York, NY, USA (1983). Association for Computing Machinery.","DOI":"10.1145\/800061.808726"},{"key":"23","doi-asserted-by":"publisher","unstructured":"M. S. Paterson. ``Improved sorting networks with O(logN) depth''. Algorithmica 5, 75\u201392 (1990).","DOI":"10.1007\/BF01840378"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Michael T. Goodrich. ``Zig-zag sort: a simple deterministic data-oblivious sorting algorithm running in o(n log n) time''. In Proceedings of the Forty-Sixth Annual ACM Symposium on Theory of Computing. Page 684\u2013693. STOC '14New York, NY, USA (2014). Association for Computing Machinery.","DOI":"10.1145\/2591796.2591830"},{"key":"25","doi-asserted-by":"publisher","unstructured":"K. E. Batcher. ``Sorting networks and their applications''. In Proceedings of the April 30\u2013May 2, 1968, Spring Joint Computer Conference. Page 307\u2013314. AFIPS '68 (Spring)New York, NY, USA (1968). Association for Computing Machinery.","DOI":"10.1145\/1468075.1468121"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Peter Selinger. ``Quantum circuits of $t$-depth one''. Phys. Rev. A 87, 042302 (2013).","DOI":"10.1103\/PhysRevA.87.042302"},{"key":"27","doi-asserted-by":"publisher","unstructured":"Cody Jones. ``Low-overhead constructions for the fault-tolerant toffoli gate''. Phys. Rev. A 87, 022328 (2013).","DOI":"10.1103\/PhysRevA.87.022328"},{"key":"28","doi-asserted-by":"publisher","unstructured":"Michael Beverland, Earl Campbell, Mark Howard, and Vadym Kliuchnikov. ``Lower bounds on the non-clifford resources for quantum computations''. Quantum Science and Technology 5, 035009 (2020).","DOI":"10.1088\/2058-9565\/ab8963"},{"key":"29","unstructured":"David Gosset, Robin Kothari, and Chenyi Zhang. ``Multi-qubit Toffoli with exponentially fewer T gates'' (2025). arXiv:2510.07223."},{"key":"30","doi-asserted-by":"publisher","unstructured":"Neil J. Ross and Peter Selinger. ``Optimal ancilla-free Clifford+T approximation of z-rotations''. Quantum Info. Comput. 16, 901\u2013953 (2016).","DOI":"10.26421\/QIC16.11-12-1"},{"key":"31","doi-asserted-by":"publisher","unstructured":"Guang Hao Low, Vadym Kliuchnikov, and Luke Schaeffer. ``Trading T gates for dirty qubits in state preparation and unitary synthesis''. Quantum 8, 1375 (2024).","DOI":"10.22331\/q-2024-06-17-1375"},{"key":"32","unstructured":"David Gosset, Robin Kothari, and Kewen Wu. ``Quantum state preparation with optimal T-count'' (2024). arXiv:2411.04790."},{"key":"33","doi-asserted-by":"publisher","unstructured":"Tatsuya Tomaru, Hideo Takahashi, Toshiyuki Hirano, Saisei Tahara, and Fumitoshi Sato. ``Chemical reaction simulator on quantum computers by first quantization\u2014basic treatment: Theoretical''. AIP Advances 14, 125306 (2024).","DOI":"10.1063\/5.0239980"},{"key":"34","unstructured":"Ionel Stetcu. ``Antisymmetrization of composite fermionic states for quantum simulations of nuclear reactions in first-quantization mapping'' (2025). arXiv:2512.16138."},{"key":"35","unstructured":"Hyeongrak Choi, Frederic T. Chong, Dirk Englund, and Yongshan Ding. ``Fault tolerant non-clifford state preparation for arbitrary rotations'' (2023). arXiv:2303.17380."},{"key":"36","unstructured":"Karl Mayer et al. ``Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer'' (2024). arXiv:2404.08616."},{"key":"37","doi-asserted-by":"publisher","unstructured":"Surabhi Luthra, Alexandra E. Moylett, Dan E. Browne, and Earl T. Campbell. ``Unlocking early fault-tolerant quantum computing with mitigated magic dilution''. Quantum Sci. Technol. 10, 045066 (2025).","DOI":"10.1088\/2058-9565\/ae0aef"},{"key":"38","doi-asserted-by":"publisher","unstructured":"Zhi-Cheng He and Zheng-Yuan Xue. ``High-fidelity initialization of a logical qubit with multiple injections''. Phys. Rev. A 111, 052419 (2025).","DOI":"10.1103\/PhysRevA.111.052419"},{"key":"39","doi-asserted-by":"publisher","unstructured":"Sayam Sethi and Jonathan Mark Baker. ``Rescq: Realtime scheduling for continuous angle quantum error correction architectures''. In Proceedings of the 30th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 2. Page 1028\u20131043. ASPLOS '25New York, NY, USA (2025). Association for Computing Machinery.","DOI":"10.1145\/3676641.3716018"},{"key":"40","unstructured":"Ali Javadi-Abhari et al. ``Quantum computing with Qiskit'' (2024). arXiv:2405.08810."},{"key":"41","unstructured":"A. Paetznick et al. ``Demonstration of logical qubits and repeated error correction with better-than-physical error rates'' (2024). arXiv:2404.02280."},{"key":"42","doi-asserted-by":"publisher","unstructured":"Dolev Bluvstein, Simon J Evered, Alexandra A Geim, Sophie H Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, et al. ``Logical quantum processor based on reconfigurable atom arrays''. Nature 626, 58\u201365 (2024).","DOI":"10.1038\/s41586-023-06927-3"},{"key":"43","doi-asserted-by":"publisher","unstructured":"Laird Egan, Dripto M. Debroy, Crystal Noel, Andrew Risinger, Daiwei Zhu, Debopriyo Biswas, Michael Newman, Muyuan Li, Kenneth R. Brown, Marko Cetina, and Christopher Monroe. ``Fault-tolerant control of an error-corrected qubit''. Nature 598, 281\u2013286 (2021).","DOI":"10.1038\/s41586-021-03928-y"},{"key":"44","doi-asserted-by":"publisher","unstructured":"Lucas Daguerre, Robin Blume-Kohout, Natalie C. Brown, David Hayes, and Isaac H. Kim. ``Experimental Demonstration of High-Fidelity Logical Magic States from Code Switching''. Phys. Rev. X 15, 041008 (2025).","DOI":"10.1103\/dck4-x9c2"},{"key":"45","doi-asserted-by":"publisher","unstructured":"Pedro Sales Rodriguez et al. ``Experimental demonstration of logical magic state distillation''. Nature 645, 620\u2013625 (2025).","DOI":"10.1038\/s41586-025-09367-3"},{"key":"46","doi-asserted-by":"publisher","unstructured":"Richard Jozsa. ``Fidelity for mixed quantum states''. Journal of Modern Optics 41, 2315\u20132323 (1994).","DOI":"10.1080\/09500349414552171"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Ronen Weiss, Alessandro Baroni, Joseph Carlson, and Ionel Stetcu. ``Solving reaction dynamics with quantum computing algorithms''. Phys. Rev. C 111, 064004 (2025).","DOI":"10.1103\/vs78-kwgz"},{"key":"48","doi-asserted-by":"publisher","unstructured":"W. Dur, G. Vidal, and J. I. Cirac. ``Three qubits can be entangled in two inequivalent ways''. Phys. Rev. A 62, 062314 (2000).","DOI":"10.1103\/PhysRevA.62.062314"},{"key":"49","doi-asserted-by":"publisher","unstructured":"Diogo Cruz, Romain Fournier, Fabien Gremion, Alix Jeannerot, Kenichi Komagata, Tara Tosic, Jarla Thiesbrummel, Chun Lam Chan, Nicolas Macris, Marc-Andr\u00e9 Dupertuis, and Cl\u00e9ment Javerzac-Galy. ``Efficient quantum algorithms for ghz and w states, and implementation on the ibm quantum computer''. Advanced Quantum Technologies 2, 1900015 (2019).","DOI":"10.1002\/qute.201900015"},{"key":"50","doi-asserted-by":"publisher","unstructured":"Matthew Amy, Dmitri Maslov, Michele Mosca, and Martin Roetteler. ``A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits''. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 32, 818\u2013830 (2013).","DOI":"10.1109\/TCAD.2013.2244643"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-04-08-2056\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T12:43:59Z","timestamp":1775652239000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2026-04-08-2056\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,8]]},"references-count":51,"URL":"https:\/\/doi.org\/10.22331\/q-2026-04-08-2056","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,8]]},"article-number":"2056"}}