The Fermionic Quantum Emulator

Nicholas C. Rubin1, Klaas Gunst2, Alec White2, Leon Freitag2, Kyle Throssell2, Garnet Kin-Lic Chan3, Ryan Babbush1, and Toru Shiozaki2

1Google Quantum AI, Mountain View, CA, 94043
2Quantum Simulation Technologies, Inc., Cambridge, MA 02139
3Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena CA 91125

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


The fermionic quantum emulator (FQE) is a collection of protocols for emulating quantum dynamics of fermions efficiently taking advantage of common symmetries present in chemical, materials, and condensed-matter systems. The library is fully integrated with the OpenFermion software package and serves as the simulation backend. The FQE reduces memory footprint by exploiting number and spin symmetry along with custom evolution routines for sparse and dense Hamiltonians, allowing us to study significantly larger quantum circuits at modest computational cost when compared against qubit state vector simulators. This release paper outlines the technical details of the simulation methods and key advantages.

► BibTeX data

► References

[1] Daniel S Abrams and Seth Lloyd. Simulation of Many-Body Fermi Systems on a Universal Quantum Computer. Phys. Rev. Lett., 79 (13): 4, 1997. https:/​/​​10.1103/​PhysRevLett.79.2586.

[2] E. Anderson, Z. Bai, C. Bischof, S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LAPACK Users' Guide. Society for Industrial and Applied Mathematics, Philadelphia, PA, third edition, 1999. ISBN 0-89871-447-8 (paperback). URL https:/​/​​lapack/​lug/​.

[3] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C. Bardin, Rami Barends, Sergio Boixo, Michael Broughton, Bob B. Buckley, David A. Buell, Brian Burkett, Nicholas Bushnell, Yu Chen, Zijun Chen, Benjamin Chiaro, Roberto Collins, William Courtney, Sean Demura, Andrew Dunsworth, Edward Farhi, Austin Fowler, Brooks Foxen, Craig Gidney, Marissa Giustina, Rob Graff, Steve Habegger, Matthew P. Harrigan, Alan Ho, Sabrina Hong, Trent Huang, William J. Huggins, Lev Ioffe, Sergei V. Isakov, Evan Jeffrey, Zhang Jiang, Cody Jones, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Seon Kim, Paul V. Klimov, Alexander Korotkov, Fedor Kostritsa, David Landhuis, Pavel Laptev, Mike Lindmark, Erik Lucero, Orion Martin, John M. Martinis, Jarrod R. McClean, Matt McEwen, Anthony Megrant, Xiao Mi, Masoud Mohseni, Wojciech Mruczkiewicz, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Hartmut Neven, Murphy Yuezhen Niu, Thomas E. O’Brien, Eric Ostby, Andre Petukhov, Harald Putterman, Chris Quintana, Pedram Roushan, Nicholas C. Rubin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Doug Strain, Kevin J. Sung, Marco Szalay, Tyler Y. Takeshita, Amit Vainsencher, Theodore White, Nathan Wiebe, Z. Jamie Yao, Ping Yeh, and Adam Zalcman. Hartree-fock on a superconducting qubit quantum computer. Science, 369 (6507): 1084–1089, 2020. ISSN 0036-8075. 10.1126/​science.abb9811. URL https:/​/​​content/​369/​6507/​1084.

[4] Alan Aspuru-Guzik, Anthony D Dutoi, Peter J Love, and Martin Head-Gordon. Simulated Quantum Computation of Molecular Energies. Science, 309 (5741): 1704, 2005. 10.1126/​science.1113479.

[5] Gregory J. Atchity and Klaus Ruedenberg. Orbital transformations and configurational transformations of electronic wavefunctions. J. Chem. Phys., 111 (7): 2910–2920, 1999. 10.1063/​1.479573. URL https:/​/​​10.1063/​1.479573.

[6] Sergio Boixo, Sergei V Isakov, Vadim N Smelyanskiy, and Hartmut Neven. Simulation of low-depth quantum circuits as complex undirected graphical models. arXiv preprint arXiv:1712.05384, 2017. URL https:/​/​​abs/​1712.05384.

[7] Sergey Bravyi, Dan Browne, Padraic Calpin, Earl Campbell, David Gosset, and Mark Howard. Simulation of quantum circuits by low-rank stabilizer decompositions. Quantum, 3: 181, 2019. URL https:/​/​​10.22331/​q-2019-09-02-181.

[8] Jia Chen, Hai-Ping Cheng, and James K. Freericks. Quantum-inspired algorithm for the factorized form of unitary coupled cluster theory. J. Chem. Theory Comput., 17 (2): 841–847, 2021. 10.1021/​acs.jctc.0c01052. URL https:/​/​​10.1021/​acs.jctc.0c01052.

[9] Cirq Developers. Cirq, March 2021. URL https:/​/​​10.5281/​zenodo.4586899. See full list of authors on Github: https:/​/​github .com/​quantumlib/​Cirq/​graphs/​contributors.

[10] William R Clements, Peter C Humphreys, Benjamin J Metcalf, W Steven Kolthammer, and Ian A Walmsley. Optimal design for universal multiport interferometers. Optica, 3 (12): 1460–1465, 2016. 10.1364/​OPTICA.3.001460. URL https:/​/​​optica/​fulltext.cfm?uri=optica-3-12-1460.

[11] Francesco A. Evangelista, Garnet Kin-Lic Chan, and Gustavo E. Scuseria. Exact parameterization of fermionic wave functions via unitary coupled cluster theory. J. Chem. Phys., 151 (24): 244112, 2019. 10.1063/​1.5133059. URL https:/​/​​10.1063/​1.5133059.

[12] Richard P Feynman. Simulating physics with computers. Int. J. Theor. Phys., 21 (6-7): 467–488, 1982. ISSN 00207748. 10.1007/​BF02650179.

[13] Maria-Andreea Filip and Alex J. W. Thom. A stochastic approach to unitary coupled cluster. J. Chem. Phys., 153 (21): 214106, 2020. 10.1063/​5.0026141. URL https:/​/​​10.1063/​5.0026141.

[14] Johnnie Gray and Stefanos Kourtis. Hyper-optimized tensor network contraction. Quantum, 5: 410, 2021. URL https:/​/​​10.22331/​q-2021-03-15-410.

[15] Robert J. Harrison and Sohrab Zarrabian. An efficient implementation of the full-ci method using an (n–2)-electron projection space. Chem. Phys. Lett., 158 (5): 393–398, 1989. ISSN 0009-2614. https:/​/​​10.1016/​0009-2614(89)87358-0. URL https:/​/​​science/​article/​pii/​0009261489873580.

[16] Cupjin Huang, Fang Zhang, Michael Newman, Junjie Cai, Xun Gao, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, et al. Classical simulation of quantum supremacy circuits. arXiv preprint arXiv:2005.06787, 2020. URL https:/​/​​abs/​2005.06787.

[17] Yifei Huang and Peter Love. Approximate stabilizer rank and improved weak simulation of clifford-dominated circuits for qudits. Phys. Rev. A, 99: 052307, May 2019. 10.1103/​PhysRevA.99.052307. URL https:/​/​​doi/​10.1103/​PhysRevA.99.052307.

[18] Yifei Huang and Peter Love. Feynman-path-type simulation using stabilizer projector decomposition of unitaries. Phys. Rev. A, 103: 022428, Feb 2021. 10.1103/​PhysRevA.103.022428. URL https:/​/​​doi/​10.1103/​PhysRevA.103.022428.

[19] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M Chow, and Jay M Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549 (7671): 242–246, 2017. https:/​/​​10.1038/​nature23879. URL https:/​/​​articles/​nature23879.

[20] Peter J. Knowles and Nicholas C. Handy. A determinant based full configuration interaction program. Comput. Phys. Comm., 54 (1): 75–83, 1989. ISSN 0010-4655. https:/​/​​10.1016/​0010-4655(89)90033-7. URL https:/​/​​science/​article/​pii/​0010465589900337.

[21] P.J. Knowles and N.C. Handy. A new determinant-based full configuration interaction method. Chem. Phys. Lett., 111 (4): 315–321, 1984. ISSN 0009-2614. https:/​/​​10.1016/​0009-2614(84)85513-X. URL https:/​/​​science/​article/​pii/​000926148485513X.

[22] R Kosloff. Propagation methods for quantum molecular dynamics. Annu. Rev. Phys. Chem., 45 (1): 145–178, 1994. 10.1146/​annurev.pc.45.100194.001045. URL https:/​/​​10.1146/​annurev.pc.45.100194.001045.

[23] Joonho Lee, William J Huggins, Martin Head-Gordon, and K Birgitta Whaley. Generalized unitary coupled cluster wave functions for quantum computation. J. Chem. Theory Comput., 15 (1): 311–324, 2018. https:/​/​​10.1021/​acs.jctc.8b01004. URL https:/​/​​doi/​10.1021/​acs.jctc.8b01004.

[24] Xiu-Zhe Luo, Jin-Guo Liu, Pan Zhang, and Lei Wang. Yao. jl: Extensible, efficient framework for quantum algorithm design. Quantum, 4: 341, 2020. https:/​/​​10.22331/​q-2020-10-11-341. URL https:/​/​​papers/​q-2020-10-11-341/​.

[25] Per Åke Malmqvist. Calculation of transition density matrices by nonunitary orbital transformations. Int. J. Quantum Chem., 30 (4): 479–494, 1986. https:/​/​​10.1002/​qua.560300404. URL https:/​/​​doi/​abs/​10.1002/​qua.560300404.

[26] Igor L Markov and Yaoyun Shi. Simulating Quantum Computation by Contracting Tensor Networks. SIAM J. Comput., 38 (3): 963–981, 2008. ISSN 0097-5397. 10.1137/​050644756. URL http:/​/​​doi/​abs/​10.1137/​050644756.

[27] Jarrod R McClean, Nicholas C Rubin, Kevin J Sung, Ian D Kivlichan, Xavier Bonet-Monroig, Yudong Cao, Chengyu Dai, E Schuyler Fried, Craig Gidney, Brendan Gimby, et al. Openfermion: the electronic structure package for quantum computers. Quantum Science and Technology, 5 (3): 034014, 2020. 10.1088/​2058-9565/​ab8ebc. URL https:/​/​​10.1088/​2058-9565/​ab8ebc.

[28] A. Mitrushchenkov and H.-J. Werner. Calculation of transition moments between internally contracted mrci wave functions with non-orthogonal orbitals. Mol. Phys., 105 (9): 1239–1249, 2007. 10.1080/​00268970701326978. URL https:/​/​​10.1080/​0026897070132697.

[29] Mario Motta, Erika Ye, Jarrod R McClean, Zhendong Li, Austin J Minnich, Ryan Babbush, and Garnet Kin-Lic Chan. Low rank representations for quantum simulation of electronic structure. arXiv preprint arXiv:1808.02625, 2018. URL https:/​/​​abs/​1808.02625.

[30] Jeppe Olsen, Björn O. Roos, Poul Jørgensen, and Hans J. "Aa". Jensen. Determinant based configuration interaction algorithms for complete and restricted configuration interaction spaces. J. Chem. Phys., 89 (4): 2185–2192, 1988. 10.1063/​1.455063. URL https:/​/​​10.1063/​1.455063.

[31] G Ortiz, J Gubernatis, E Knill, and R Laflamme. Quantum algorithms for fermionic simulations. Phys. Rev. A, 64 (2): 22319, 2001. ISSN 1050-2947. 10.1103/​PhysRevA.64.022319. URL http:/​/​​doi/​10.1103/​PhysRevA.64.022319.

[32] Quantum AI team and collaborators. qsim, September 2020. URL https:/​/​​10.5281/​zenodo.4023103.

[33] Nicholas C. Rubin, Toru Shiozaki, Kyle Throssell, Garnet K.-L. Chan, and Ryan Babbush. The Fermionic Quantum Emulator: https:/​/​​quantumlib/​openfermion-fqe, Aug 2020. URL https:/​/​​quantumlib/​OpenFermion-FQE.

[34] C. David Sherrill and Henry F. Schaefer. The Configuration Interaction Method: Advances in Highly Correlated Approaches. Advances in Quantum Chemistry, 34 (C): 143–269, 1999. ISSN 00653276. 10.1016/​S0065-3276(08)60532-8.

[35] Toru Shiozaki. Bagel: Brilliantly advanced general electronic-structure library. Wiley Interdiscip. Rev. Comput. Mol. Sci., 8 (1): e1331, 2018. https:/​/​​10.1002/​wcms.1331. URL https:/​/​​doi/​abs/​10.1002/​wcms.1331.

[36] Per E.M. Siegbahn. A new direct ci method for large ci expansions in a small orbital space. Chem. Phys. Lett., 109 (5): 417–423, 1984. ISSN 0009-2614. https:/​/​​10.1016/​0009-2614(84)80336-X. URL https:/​/​​science/​article/​pii/​000926148480336X.

[37] Mikhail Smelyanskiy, Nicolas PD Sawaya, and Alán Aspuru-Guzik. qhipster: The quantum high performance software testing environment. arXiv preprint arXiv:1601.07195, 2016. URL https:/​/​​abs/​1601.07195.

[38] Daniel GA Smith, Lori A Burns, Andrew C Simmonett, Robert M Parrish, Matthew C Schieber, Raimondas Galvelis, Peter Kraus, Holger Kruse, Roberto Di Remigio, Asem Alenaizan, et al. Psi4 1.4: Open-source software for high-throughput quantum chemistry. J. Chem. Phys., 152 (18): 184108, 2020. https:/​/​​10.1063/​5.0006002. URL https:/​/​​doi/​10.1063/​5.0006002.

[39] Nicholas H Stair and Francesco A Evangelista. Qforte: an efficient state simulator and quantum algorithms library for molecular electronic structure. arXiv preprint arXiv:2108.04413, 2021. URL https:/​/​​abs/​2108.04413.

[40] Qiming Sun, Timothy C Berkelbach, Nick S Blunt, George H Booth, Sheng Guo, Zhendong Li, Junzi Liu, James D McClain, Elvira R Sayfutyarova, Sandeep Sharma, et al. Pyscf: the python-based simulations of chemistry framework. Wiley Interdiscip. Rev. Comput. Mol. Sci., 8 (1): e1340, 2018. https:/​/​​10.1063/​5.0006002. URL https:/​/​​doi/​abs/​10.1002/​wcms.1340.

[41] Yasunari Suzuki, Yoshiaki Kawase, Yuya Masumura, Yuria Hiraga, Masahiro Nakadai, Jiabao Chen, Ken M Nakanishi, Kosuke Mitarai, Ryosuke Imai, Shiro Tamiya, et al. Qulacs: a fast and versatile quantum circuit simulator for research purpose. arXiv preprint arXiv:2011.13524, 2020. URL https:/​/​​abs/​2011.13524. https:/​/​​10.22331/​q-2021-10-06-559.

[42] Barbara M. Terhal and David P. DiVincenzo. Classical simulation of noninteracting-fermion quantum circuits. Phys. Rev. A, 65: 032325, Mar 2002. 10.1103/​PhysRevA.65.032325. URL https:/​/​​doi/​10.1103/​PhysRevA.65.032325.

Cited by

[1] Lucas C. Céleri, Daniel Huerga, Francisco Albarrán-Arriagada, Enrique Solano, Mikel Garcia de Andoin, and Mikel Sanz, "Digital-Analog Quantum Simulation of Fermionic Models", Physical Review Applied 19 6, 064086 (2023).

[2] Fionn D. Malone, Ankit Mahajan, James S. Spencer, and Joonho Lee, "ipie: A Python-Based Auxiliary-Field Quantum Monte Carlo Program with Flexibility and Efficiency on CPUs and GPUs", Journal of Chemical Theory and Computation 19 1, 109 (2023).

[3] Weitang Li, Jonathan Allcock, Lixue Cheng, Shi-Xin Zhang, Yu-Qin Chen, Jonathan P. Mailoa, Zhigang Shuai, and Shengyu Zhang, "TenCirChem: An Efficient Quantum Computational Chemistry Package for the NISQ Era", Journal of Chemical Theory and Computation 19 13, 3966 (2023).

[4] Weitang Li, Yufei Ge, Shi-Xin Zhang, Yu-Qin Chen, and Shengyu Zhang, "Efficient and Robust Parameter Optimization of the Unitary Coupled-Cluster Ansatz", Journal of Chemical Theory and Computation 20 9, 3683 (2024).

[5] Nicholas C. Rubin, Dominic W. Berry, Alina Kononov, Fionn D. Malone, Tanuj Khattar, Alec White, Joonho Lee, Hartmut Neven, Ryan Babbush, and Andrew D. Baczewski, "Quantum computation of stopping power for inertial fusion target design", Proceedings of the National Academy of Sciences 121 23, e2317772121 (2024).

[6] Shaojun Guo, Jinzhao Sun, Haoran Qian, Ming Gong, Yukun Zhang, Fusheng Chen, Yangsen Ye, Yulin Wu, Sirui Cao, Kun Liu, Chen Zha, Chong Ying, Qingling Zhu, He-Liang Huang, Youwei Zhao, Shaowei Li, Shiyu Wang, Jiale Yu, Daojin Fan, Dachao Wu, Hong Su, Hui Deng, Hao Rong, Yuan Li, Kaili Zhang, Tung-Hsun Chung, Futian Liang, Jin Lin, Yu Xu, Lihua Sun, Cheng Guo, Na Li, Yong-Heng Huo, Cheng-Zhi Peng, Chao-Yang Lu, Xiao Yuan, Xiaobo Zhu, and Jian-Wei Pan, "Experimental quantum computational chemistry with optimized unitary coupled cluster ansatz", Nature Physics (2024).

[7] Justin Provazza, Klaas Gunst, Huanchen Zhai, Garnet K.-L. Chan, Toru Shiozaki, Nicholas C. Rubin, and Alec F. White, "Fast Emulation of Fermionic Circuits with Matrix Product States", Journal of Chemical Theory and Computation 20 9, 3719 (2024).

[8] Gaurav Gyawali and Michael J. Lawler, "Adaptive variational preparation of the Fermi-Hubbard eigenstates", Physical Review A 105 1, 012413 (2022).

[9] Nicholas H. Stair and Francesco A. Evangelista, "QForte: An Efficient State-Vector Emulator and Quantum Algorithms Library for Molecular Electronic Structure", Journal of Chemical Theory and Computation 18 3, 1555 (2022).

[10] Maximilian Scheurer, Gian-Luca R. Anselmetti, Oumarou Oumarou, Christian Gogolin, and Nicholas C. Rubin, "Tailored and Externally Corrected Coupled Cluster with Quantum Inputs", Journal of Chemical Theory and Computation acs.jctc.4c00037 (2024).

[11] Yusen Wu, Zigeng Huang, Jinzhao Sun, Xiao Yuan, Jingbo B Wang, and Dingshun Lv, "Orbital expansion variational quantum eigensolver", Quantum Science and Technology 8 4, 045030 (2023).

[12] Weitang Li, Zigeng Huang, Changsu Cao, Yifei Huang, Zhigang Shuai, Xiaoming Sun, Jinzhao Sun, Xiao Yuan, and Dingshun Lv, "Toward practical quantum embedding simulation of realistic chemical systems on near-term quantum computers", Chemical Science 13 31, 8953 (2022).

[13] Yi Fan, Changsu Cao, Xusheng Xu, Zhenyu Li, Dingshun Lv, and Man-Hong Yung, "Circuit-Depth Reduction of Unitary-Coupled-Cluster Ansatz by Energy Sorting", The Journal of Physical Chemistry Letters 14 43, 9596 (2023).

[14] Nicholas C. Rubin, Klaas Gunst, Alec White, Leon Freitag, Kyle Throssell, Garnet Kin-Lic Chan, Ryan Babbush, and Toru Shiozaki, "The Fermionic Quantum Emulator", Quantum 5, 568 (2021).

[15] Alexander M. Czajka, Zhong-Bo Kang, Yuxuan Tee, and Fanyi Zhao, "Studying chirality imbalance with quantum algorithms", arXiv:2210.03062, (2022).

[16] Nicholas H. Stair and Francesco A. Evangelista, "QForte: an efficient state simulator and quantum algorithms library for molecular electronic structure", arXiv:2108.04413, (2021).

[17] Qingchun Wang, Huan-Yu Liu, Qing-Song Li, Jianyu Zhao, Qiankun Gong, Ye Li, Yu-Chun Wu, and Guo-Ping Guo, "ChemiQ: A Chemistry Simulator for Quantum Computer", arXiv:2106.10162, (2021).

[18] Nicholas C. Rubin, Joonho Lee, and Ryan Babbush, "Compressing Many-Body Fermion Operators Under Unitary Constraints", arXiv:2109.05010, (2021).

The above citations are from Crossref's cited-by service (last updated successfully 2024-06-22 02:17:17) and SAO/NASA ADS (last updated successfully 2024-06-22 02:17:18). The list may be incomplete as not all publishers provide suitable and complete citation data.