Unitary Selective Coupled-Cluster Method

Dmitry A. Fedorov; Yuri Alexeev; Stephen K. Gray; Matthew Otten

doi:10.22331/q-2022-05-02-703

Unitary Selective Coupled-Cluster Method

Dmitry A. Fedorov^1,2, Yuri Alexeev¹, Stephen K. Gray³, and Matthew Otten⁴

¹Computational Science Division, Argonne National Laboratory, 9700 S. Cass Ave., Lemont, IL 60439, USA
²Oak Ridge Associated Universities, Oak Ridge, TN 37830
³Center for Nanoscale Materials, Argonne National Laboratory, 9700 S. Cass Ave, Lemont, IL 60439, USA
⁴HRL Laboratories, LLC, 3011 Malibu Canyon Road, Malibu, CA 90265

Published:	2022-05-02, volume 6, page 703
Eprint:	arXiv:2109.12652v5
Doi:	https://doi.org/10.22331/q-2022-05-02-703
Citation:	Quantum 6, 703 (2022).

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Abstract

Simulating molecules using the Variational Quantum Eigensolver method is one of the promising applications for NISQ-era quantum computers. Designing an efficient ansatz to represent the electronic wave function is crucial in such simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD) ansatz tends to have a large number of insignificant terms that do not lower the energy of the system. In this work, we present a unitary selective coupled-cluster method, a way to construct a unitary coupled-cluster ansatz iteratively using a selection procedure with excitations up to fourth order. This approach uses the electronic Hamiltonian matrix elements and the amplitudes for excitations already present in the ansatz to find the important excitations of higher order and to add them to the ansatz. The important feature of the method is that it systematically reduces the energy error with increasing ansatz size for a set of test molecules. {The main advantage of the proposed method is that the effort to increase the ansatz does not require any additional measurements on a quantum computer.}

► BibTeX data

@article{Fedorov2022unitaryselective,
  doi = {10.22331/q-2022-05-02-703},
  url = {https://doi.org/10.22331/q-2022-05-02-703},
  title = {Unitary {S}elective {C}oupled-{C}luster {M}ethod},
  author = {Fedorov, Dmitry A. and Alexeev, Yuri and Gray, Stephen K. and Otten, Matthew},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {703},
  month = may,
  year = {2022}
}

► References

[1] Daniel S. Abrams and Seth Lloyd. Simulation of many-body fermi systems on a universal quantum computer. Phys. Rev. Lett., 79: 2586–2589, Sep 1997. https://doi.org/10.1103/PhysRevLett.79.2586. URL https://link.aps.org/doi/10.1103/PhysRevLett.79.2586.
https://doi.org/10.1103/PhysRevLett.79.2586

[2] Daniel S. Abrams and Seth Lloyd. Quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors. Phys. Rev. Lett., 83: 5162–5165, Dec 1999. https://doi.org/10.1103/PhysRevLett.83.5162. URL https://link.aps.org/doi/10.1103/PhysRevLett.83.5162.
https://doi.org/10.1103/PhysRevLett.83.5162

[3] Abhinav Anand, Philipp Schleich, Sumner Alperin-Lea, Phillip W. K. Jensen, Sukin Sim, Manuel Díaz-Tinoco, Jakob S. Kottmann, Matthias Degroote, Artur F. Izmaylov, and Alán Aspuru-Guzik. A quantum computing view on unitary coupled cluster theory. Chem. Soc. Rev., 51: 1659–1684, 2022. https://doi.org/10.1039/D1CS00932J. URL http://dx.doi.org/10.1039/D1CS00932J.
https://doi.org/10.1039/D1CS00932J

[4] MD SAJID ANIS, Héctor Abraham, AduOffei, Rochisha Agarwal, Gabriele Agliardi, Merav Aharoni, Ismail Yunus Akhalwaya, Gadi Aleksandrowicz, Thomas Alexander, Matthew Amy, Sashwat Anagolum, Eli Arbel, Abraham Asfaw, Anish Athalye, Artur Avkhadiev, Carlos Azaustre, Abhik Banerjee, Santanu Banerjee, Will Bang, Aman Bansal, Panagiotis Barkoutsos, Ashish Barnawal, George Barron, George S. Barron, Luciano Bello, Yael Ben-Haim, Daniel Bevenius, Dhruv Bhatnagar, Arjun Bhobe, Paolo Bianchini, Lev S. Bishop, Carsten Blank, Sorin Bolos, Soham Bopardikar, Samuel Bosch, Sebastian Brandhofer, Brandon, Sergey Bravyi, Nick Bronn, Bryce-Fuller, David Bucher, Artemiy Burov, Fran Cabrera, Padraic Calpin, Lauren Capelluto, Jorge Carballo, Ginés Carrascal, Adam Carriker, Ivan Carvalho, Adrian Chen, Chun-Fu Chen, Edward Chen, Jielun (Chris) Chen, Richard Chen, Franck Chevallier, Rathish Cholarajan, Jerry M. Chow, Spencer Churchill, Christian Claus, Christian Clauss, Caleb Clothier, Romilly Cocking, Ryan Cocuzzo, Jordan Connor, Filipe Correa, Abigail J. Cross, Andrew W. Cross, Simon Cross, Juan Cruz-Benito, Chris Culver, Antonio D. Córcoles-Gonzales, Navaneeth D, Sean Dague, Tareq El Dandachi, Animesh N Dangwal, Jonathan Daniel, Marcus Daniels, Matthieu Dartiailh, Abdón Rodríguez Davila, Faisal Debouni, Anton Dekusar, Amol Deshmukh, Mohit Deshpande, Delton Ding, Jun Doi, Eli M. Dow, Eric Drechsler, Eugene Dumitrescu, Karel Dumon, Ivan Duran, Kareem EL-Safty, Eric Eastman, Grant Eberle, Amir Ebrahimi, Pieter Eendebak, Daniel Egger, Alberto Espiricueta, Mark Everitt, Davide Facoetti, Farida, Paco Martín Fernández, Samuele Ferracin, Davide Ferrari, Axel Hernández Ferrera, Romain Fouilland, Albert Frisch, Andreas Fuhrer, Bryce Fuller, MELVIN GEORGE, Julien Gacon, Borja Godoy Gago, Claudio Gambella, Jay M. Gambetta, Adhisha Gammanpila, Luis Garcia, Tanya Garg, Shelly Garion, Tim Gates, Leron Gil, Austin Gilliam, Aditya Giridharan, Juan Gomez-Mosquera, Gonzalo, Salvador de la Puente González, Jesse Gorzinski, Ian Gould, Donny Greenberg, Dmitry Grinko, Wen Guan, John A. Gunnels, Naman Gupta, Jakob M. Günther, Mikael Haglund, Isabel Haide, Ikko Hamamura, Omar Costa Hamido, Frank Harkins, Areeq Hasan, Vojtech Havlicek, Joe Hellmers, Łukasz Herok, Stefan Hillmich, Hiroshi Horii, Connor Howington, Shaohan Hu, Wei Hu, Junye Huang, Rolf Huisman, Haruki Imai, Takashi Imamichi, Kazuaki Ishizaki, Ishwor, Raban Iten, Toshinari Itoko, Ali Javadi, Ali Javadi-Abhari, Wahaj Javed, Madhav Jivrajani, Kiran Johns, Scott Johnstun, Jonathan-Shoemaker, JosDenmark, JoshDumo, John Judge, Tal Kachmann, Akshay Kale, Naoki Kanazawa, Jessica Kane, Kang-Bae, Annanay Kapila, Anton Karazeev, Paul Kassebaum, Josh Kelso, Scott Kelso, Vismai Khanderao, Spencer King, Yuri Kobayashi, Arseny Kovyrshin, Rajiv Krishnakumar, Vivek Krishnan, Kevin Krsulich, Prasad Kumkar, Gawel Kus, Ryan LaRose, Enrique Lacal, Raphaël Lambert, John Lapeyre, Joe Latone, Scott Lawrence, Christina Lee, Gushu Li, Jake Lishman, Dennis Liu, Peng Liu, Yunho Maeng, Saurav Maheshkar, Kahan Majmudar, Aleksei Malyshev, Mohamed El Mandouh, Joshua Manela, Manjula, Jakub Marecek, Manoel Marques, Kunal Marwaha, Dmitri Maslov, Paweł Maszota, Dolph Mathews, Atsushi Matsuo, Farai Mazhandu, Doug McClure, Maureen McElaney, Cameron McGarry, David McKay, Dan McPherson, Srujan Meesala, Dekel Meirom, Corey Mendell, Thomas Metcalfe, Martin Mevissen, Andrew Meyer, Antonio Mezzacapo, Rohit Midha, Zlatko Minev, Abby Mitchell, Nikolaj Moll, Alejandro Montanez, Gabriel Monteiro, Michael Duane Mooring, Renier Morales, Niall Moran, David Morcuende, Seif Mostafa, Mario Motta, Romain Moyard, Prakash Murali, Jan Müggenburg, David Nadlinger, Ken Nakanishi, Giacomo Nannicini, Paul Nation, Edwin Navarro, Yehuda Naveh, Scott Wyman Neagle, Patrick Neuweiler, Aziz Ngoueya, Johan Nicander, Nick-Singstock, Pradeep Niroula, Hassi Norlen, NuoWenLei, Lee James O'Riordan, Oluwatobi Ogunbayo, Pauline Ollitrault, Tamiya Onodera, Raul Otaolea, Steven Oud, Dan Padilha, Hanhee Paik, Soham Pal, Yuchen Pang, Ashish Panigrahi, Vincent R. Pascuzzi, Simone Perriello, Eric Peterson, Anna Phan, Francesco Piro, Marco Pistoia, Christophe Piveteau, Julia Plewa, Pierre Pocreau, Alejandro Pozas-Kerstjens, Rafał Pracht, Milos Prokop, Viktor Prutyanov, Sumit Puri, Daniel Puzzuoli, Jesús Pérez, Quintiii, Rafey Iqbal Rahman, Arun Raja, Roshan Rajeev, Nipun Ramagiri, Anirudh Rao, Rudy Raymond, Oliver Reardon-Smith, Rafael Martín-Cuevas Redondo, Max Reuter, Julia Rice, Matt Riedemann, Drew Risinger, Marcello La Rocca, Diego M. Rodríguez, RohithKarur, Ben Rosand, Max Rossmannek, Mingi Ryu, Tharrmashastha SAPV, Arijit Saha, Abdullah Ash-Saki, Martin Sandberg, Hirmay Sandesara, Ritvik Sapra, Hayk Sargsyan, Aniruddha Sarkar, Ninad Sathaye, Bruno Schmitt, Chris Schnabel, Zachary Schoenfeld, Travis L. Scholten, Eddie Schoute, Mark Schulterbrandt, Joachim Schwarm, James Seaward, Sergi, Ismael Faro Sertage, Kanav Setia, Freya Shah, Nathan Shammah, Rohan Sharma, Yunong Shi, Jonathan Shoemaker, Adenilton Silva, Andrea Simonetto, Divyanshu Singh, Parmeet Singh, Phattharaporn Singkanipa, Yukio Siraichi, Siri, Jesús Sistos, Iskandar Sitdikov, Seyon Sivarajah, Magnus Berg Sletfjerding, John A. Smolin, Mathias Soeken, Igor Olegovich Sokolov, Igor Sokolov, SooluThomas, Starfish, Dominik Steenken, Matt Stypulkoski, Adrien Suau, Shaojun Sun, Kevin J. Sung, Makoto Suwama, Oskar Słowik, Hitomi Takahashi, Tanvesh Takawale, Ivano Tavernelli, Charles Taylor, Pete Taylour, Soolu Thomas, Mathieu Tillet, Maddy Tod, Miroslav Tomasik, Enrique de la Torre, Juan Luis Sánchez Toural, Kenso Trabing, Matthew Treinish, Dimitar Trenev, TrishaPe, Felix Truger, Georgios Tsilimigkounakis, Davindra Tulsi, Wes Turner, Yotam Vaknin, Carmen Recio Valcarce, Francois Varchon, Adish Vartak, Almudena Carrera Vazquez, Prajjwal Vijaywargiya, Victor Villar, Bhargav Vishnu, Desiree Vogt-Lee, Christophe Vuillot, James Weaver, Johannes Weidenfeller, Rafal Wieczorek, Jonathan A. Wildstrom, Jessica Wilson, Erick Winston, WinterSoldier, Jack J. Woehr, Stefan Woerner, Ryan Woo, Christopher J. Wood, Ryan Wood, Steve Wood, James Wootton, Matt Wright, Bo Yang, Daniyar Yeralin, Ryota Yonekura, David Yonge-Mallo, Richard Young, Jessie Yu, Lebin Yu, Christopher Zachow, Laura Zdanski, Helena Zhang, Christa Zoufal, aeddins ibm, alexzhang13, b63, bartek bartlomiej, bcamorrison, brandhsn, catornow, charmerDark, deeplokhande, dekel.meirom, dime10, ehchen, fanizzamarco, fs1132429, gadial, galeinston, georgezhou20, georgios ts, gruu, hhorii, hykavitha, itoko, jliu45, jscott2, klinvill, krutik2966, ma5x, michelle4654, msuwama, ntgiwsvp, ordmoj, sagar pahwa, pritamsinha2304, ryancocuzzo, saswati qiskit, septembrr, sethmerkel, shaashwat, sternparky, strickroman, tigerjack, tsura crisaldo, welien, willhbang, yang.luh, and Mantas Čepulkovskis. Qiskit: An open-source framework for quantum computing. 2021. https://doi.org/10.5281/zenodo.2573505. URL https://qiskit.org/.
https://doi.org/10.5281/zenodo.2573505
https://qiskit.org/

[5] Alán Aspuru-Guzik, Anthony D. Dutoi, Peter J. Love, and Martin Head-Gordon. Simulated quantum computation of molecular energies. Science, 309 (5741): 1704–1707, 2005. https://doi.org/10.1126/science.1113479. URL https://www.science.org/doi/abs/10.1126/science.1113479.
https://doi.org/10.1126/science.1113479

[6] Panagiotis Kl. Barkoutsos, Jerome F. Gonthier, Igor Sokolov, Nikolaj Moll, Gian Salis, Andreas Fuhrer, Marc Ganzhorn, Daniel J. Egger, Matthias Troyer, Antonio Mezzacapo, Stefan Filipp, and Ivano Tavernelli. Quantum algorithms for electronic structure calculations: Particle-hole Hamiltonian and optimized wave-function expansions. Physical Review A, 98 (2): 022322, 2018. ISSN 2469-9926. https://doi.org/10.1103/physreva.98.022322.
https://doi.org/10.1103/physreva.98.022322

[7] Rodney J. Bartlett and Monika Musiał. Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys., 79: 291–352, Feb 2007. https://doi.org/10.1103/RevModPhys.79.291. URL https://doi.org/10.1103/RevModPhys.79.291.
https://doi.org/10.1103/RevModPhys.79.291

[8] Rodney J. Bartlett and George D. Purvis. Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitations for the correlation problem. International Journal of Quantum Chemistry, 14 (5): 561–581, 1978. https://doi.org/10.1002/qua.560140504. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.560140504.
https://doi.org/10.1002/qua.560140504

[9] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alán Aspuru-Guzik. Noisy intermediate-scale quantum algorithms. Rev. Mod. Phys., 94: 015004, Feb 2022. https://doi.org/10.1103/RevModPhys.94.015004. URL https://link.aps.org/doi/10.1103/RevModPhys.94.015004.
https://doi.org/10.1103/RevModPhys.94.015004

[10] Changsu Cao, Jiaqi Hu, Wengang Zhang, Xusheng Xu, Dechin Chen, Fan Yu, Jun Li, Hanshi Hu, Dingshun Lv, and Man-Hong Yung. Towards a larger molecular simulation on the quantum computer: Up to 28 qubits systems accelerated by point group symmetry. arXiv preprint arXiv:2109.02110, 2021. https://doi.org/10.48550/arXiv.2109.02110. URL https://arxiv.org/abs/2109.02110.
https://doi.org/10.48550/arXiv.2109.02110
arXiv:2109.02110

[11] Yudong Cao, Jonathan Romero, Jonathan P. Olson, Matthias Degroote, Peter D. Johnson, Maria Kieferova, Ian D. Kivlichan, Tim Menke, Borja Peropadre, Nicolas P. D. Sawaya, Sukin Sim, Libor Veis, and Alan Aspuru-Guzik. Quantum chemistry in the age of quantum computing. Chem. Rev., 119 (19): 10856–10915, 2019. ISSN 0009-2665. https://doi.org/10.1021/acs.chemrev.8b00803.
https://doi.org/10.1021/acs.chemrev.8b00803

[12] M Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J Coles. Variational quantum algorithms. Nature Reviews Physics, 3 (9): 625–644, 2021a. ISSN 2522-5820. https://doi.org/10.1038/s42254-021-00348-9. URL https://doi.org/10.1038/s42254-021-00348-9.
https://doi.org/10.1038/s42254-021-00348-9

[13] M Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles. Cost function dependent barren plateaus in shallow parametrized quantum circuits. Nature Communications, 12 (1): 1791, 2021b. ISSN 2041-1723. https://doi.org/10.1038/s41467-021-21728-w. URL https://doi.org/10.1038/s41467-021-21728-w.
https://doi.org/10.1038/s41467-021-21728-w

[14] Alan D Chien, Adam A Holmes, Matthew Otten, Cyrus J Umrigar, Sandeep Sharma, and Paul M Zimmerman. Excited states of methylene, polyenes, and ozone from heat-bath configuration interaction. The Journal of Physical Chemistry A, 122 (10): 2714–2722, 2018. https://doi.org/10.1021/acs.jpca.8b01554. URL https://doi.org/10.1021/acs.jpca.8b01554.
https://doi.org/10.1021/acs.jpca.8b01554

[15] Daniel Claudino, Jerimiah Wright, Alexander J. McCaskey, and Travis S. Humble. Benchmarking adaptive variational quantum eigensolvers. Frontiers in Chemistry, 8: 1152, 2020. ISSN 2296-2646. https://doi.org/10.3389/fchem.2020.606863. URL https://www.frontiersin.org/article/10.3389/fchem.2020.606863.
https://doi.org/10.3389/fchem.2020.606863

[16] Bridgette Cooper and Peter J. Knowles. Benchmark studies of variational, unitary and extended coupled cluster methods. J. Chem. Phys., 133 (23): 234102, dec 2010. ISSN 0021-9606. https://doi.org/10.1063/1.3520564. URL http://aip.scitation.org/doi/10.1063/1.3520564.
https://doi.org/10.1063/1.3520564

[17] Vincent E Elfving, Benno W Broer, Mark Webber, Jacob Gavartin, Mathew D Halls, K Patrick Lorton, and A Bochevarov. How will quantum computers provide an industrially relevant computational advantage in quantum chemistry? arXiv preprint arXiv:2009.12472, 2020. https://doi.org/10.48550/arXiv.2009.12472. URL https://arxiv.org/abs/2009.12472.
https://doi.org/10.48550/arXiv.2009.12472
arXiv:2009.12472

[18] 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, dec 2019. ISSN 0021-9606. https://doi.org/10.1063/1.5133059. URL http://aip.scitation.org/doi/10.1063/1.5133059.
https://doi.org/10.1063/1.5133059

[19] Stefano Evangelisti, Jean-Pierre Daudey, and Jean-Paul Malrieu. Convergence of an improved CIPSI algorithm. Chemical Physics, 75 (1): 91–102, 1983. https://doi.org/10.1016/0301-0104(83)85011-3. URL https://doi.org/10.1016/0301-0104(83)85011-3.
https://doi.org/10.1016/0301-0104(83)85011-3

[20] Dmitry A Fedorov, Bo Peng, Niranjan Govind, and Yuri Alexeev. VQE method: a short survey and recent developments. Materials Theory, 6 (1): 2, 2022. ISSN 2509-8012. 10.1186/s41313-021-00032-6. URL https://doi.org/10.1186/s41313-021-00032-6.
https://doi.org/10.1186/s41313-021-00032-6

[21] M. Ganzhorn, D.J. Egger, P. Barkoutsos, P. Ollitrault, G. Salis, N. Moll, M. Roth, A. Fuhrer, P. Mueller, S. Woerner, I. Tavernelli, and S. Filipp. Gate-efficient simulation of molecular eigenstates on a quantum computer. Phys. Rev. Applied, 11: 044092, Apr 2019. https://doi.org/10.1103/PhysRevApplied.11.044092. URL https://link.aps.org/doi/10.1103/PhysRevApplied.11.044092.
https://doi.org/10.1103/PhysRevApplied.11.044092

[22] Bryan T. Gard, Linghua Zhu, George S. Barron, Nicholas J. Mayhall, Sophia E. Economou, and Edwin Barnes. Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm. npj Quantum Information, 6 (1): 10, 1 2020. https://doi.org/10.1038/s41534-019-0240-1.
https://doi.org/10.1038/s41534-019-0240-1

[23] Niladri Gomes, Anirban Mukherjee, Feng Zhang, Thomas Iadecola, Cai-Zhuang Wang, Kai-Ming Ho, Peter P. Orth, and Yong-Xin Yao. Adaptive variational quantum imaginary time evolution approach for ground state preparation. Advanced Quantum Technologies, 4 (12): 2100114, 2021. https://doi.org/10.1002/qute.202100114. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/qute.202100114.
https://doi.org/10.1002/qute.202100114

[24] Harper R. Grimsley, Sophia E. Economou, Edwin Barnes, and Nicholas J. Mayhall. An adaptive variational algorithm for exact molecular simulations on a quantum computer. Nature Communications, 10 (1): 3007, dec 2019. ISSN 2041-1723. https://doi.org/10.1038/s41467-019-10988-2. URL http://www.nature.com/articles/s41467-019-10988-2.
https://doi.org/10.1038/s41467-019-10988-2
http://www.nature.com/articles/s41467-019-10988-2

[25] Gaurav Harsha, Toru Shiozaki, and Gustavo E. Scuseria. On the difference between variational and unitary coupled cluster theories. J. Chem. Phys., 148 (4): 044107, jan 2018. ISSN 0021-9606. https://doi.org/10.1063/1.5011033. URL http://aip.scitation.org/doi/10.1063/1.5011033.
https://doi.org/10.1063/1.5011033

[26] Naomichi Hatano and Masuo Suzuki. Finding exponential product formulas of higher orders. Lecture Notes in Physics, page 37–68, Nov 2005. ISSN 1616-6361. https://doi.org/10.1007/11526216_2. URL http://dx.doi.org/10.1007/11526216_2.
https://doi.org/10.1007/11526216_2

[27] Martin Head-Gordon, John A. Pople, and Michael J. Frisch. MP2 energy evaluation by direct methods. Chemical Physics Letters, 153 (6): 503–506, dec 1988. ISSN 00092614. https://doi.org/10.1016/0009-2614(88)85250-3. URL https://linkinghub.elsevier.com/retrieve/pii/0009261488852503.
https://doi.org/10.1016/0009-2614(88)85250-3
https://linkinghub.elsevier.com/retrieve/pii/0009261488852503

[28] Adam A Holmes, Norm M Tubman, and CJ Umrigar. Heat-bath configuration interaction: An efficient selected configuration interaction algorithm inspired by heat-bath sampling. Journal of Chemical Theory and Computation, 12 (8): 3674–3680, 2016. https://doi.org/10.1021/acs.jctc.6b00407.
https://doi.org/10.1021/acs.jctc.6b00407

[29] Adam A Holmes, CJ Umrigar, and Sandeep Sharma. Excited states using semistochastic heat-bath configuration interaction. The Journal of Chemical Physics, 147 (16): 164111, 2017. https://doi.org/10.1063/1.4998614.
https://doi.org/10.1063/1.4998614

[30] P. Jordan and E. Wigner. Über das Paulische Äquivalenzverbot. Z. Phys., 47 (9-10): 631–651, sep 1928. ISSN 1434-6001. 10.1007/BF01331938. URL http://link.springer.com/10.1007/BF01331938.
https://doi.org/10.1007/BF01331938

[31] 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. ISSN 0028-0836. https://doi.org/10.1038/nature23879.
https://doi.org/10.1038/nature23879

[32] Abhinav Kandala, Kristan Temme, Antonio D. Córcoles, Antonio Mezzacapo, Jerry M. Chow, and Jay M. Gambetta. Error mitigation extends the computational reach of a noisy quantum processor. Nature, 567 (7749): 491–495, 2019. ISSN 0028-0836. https://doi.org/10.1038/s41586-019-1040-7.
https://doi.org/10.1038/s41586-019-1040-7

[33] A Yu Kitaev. Quantum measurements and the Abelian Stabilizer Problem. arXiv preprint arXiv:9511026, 1995. https://doi.org/10.48550/arXiv.quant-ph/9511026. URL https://arxiv.org/abs/quant-ph/9511026.
https://doi.org/10.48550/arXiv.quant-ph/9511026
arXiv:9511026

[34] Peter J Knowles and Nicholas C Handy. A new determinant-based full configuration interaction method. Chemical Physics Letters, 111 (4-5): 315–321, 1984. https://doi.org/10.1016/0009-2614(84)85513-X.
https://doi.org/10.1016/0009-2614(84)85513-X

[35] Jakob S. Kottmann, Abhinav Anand, and Alán Aspuru-Guzik. A feasible approach for automatically differentiable unitary coupled-cluster on quantum computers. Chem. Sci., 12: 3497–3508, 2021. https://doi.org/10.1039/D0SC06627C. URL http://dx.doi.org/10.1039/D0SC06627C.
https://doi.org/10.1039/D0SC06627C

[36] Robert A. Lang, Ilya G. Ryabinkin, and Artur F. Izmaylov. Unitary transformation of the electronic hamiltonian with an exact quadratic truncation of the Baker–Campbell–Hausdorff expansion. arXiv preprint arXiv:2002.05701, 2020. https://doi.org/10.48550/arXiv.2002.05701. URL https://arxiv.org/abs/2002.05701.
https://doi.org/10.48550/arXiv.2002.05701
arXiv:2002.05701

[37] 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. ISSN 1549-9618. https://doi.org/10.1021/acs.jctc.8b01004.
https://doi.org/10.1021/acs.jctc.8b01004

[38] Junhao Li, Matthew Otten, Adam A Holmes, Sandeep Sharma, and Cyrus J Umrigar. Fast semistochastic heat-bath configuration interaction. The Journal of Chemical Physics, 149 (21): 214110, 2018. https://doi.org/10.1063/1.5055390.
https://doi.org/10.1063/1.5055390

[39] Junhao Li, Yuan Yao, Adam A Holmes, Matthew Otten, Qiming Sun, Sandeep Sharma, and CJ Umrigar. Accurate many-body electronic structure near the basis set limit: Application to the chromium dimer. Physical Review Research, 2 (1): 012015, 2020. https://doi.org/10.1103/PhysRevResearch.2.012015.
https://doi.org/10.1103/PhysRevResearch.2.012015

[40] Dmitry I Lyakh and Rodney J Bartlett. An adaptive coupled-cluster theory: @CC approach. The Journal of Chemical Physics, 133 (24): 244112, 2010. ISSN 0021-9606. https://doi.org/10.1063/1.3515476.
https://doi.org/10.1063/1.3515476

[41] David A. Mazziotti. Exactness of wave functions from two-body exponential transformations in many-body quantum theory. Phys. Rev. A, 69: 012507, Jan 2004. https://doi.org/10.1103/PhysRevA.69.012507. URL https://link.aps.org/doi/10.1103/PhysRevA.69.012507.
https://doi.org/10.1103/PhysRevA.69.012507

[42] David A. Mazziotti. Anti-Hermitian contracted Schrödinger equation: Direct determination of the two-electron reduced density matrices of many-electron molecules. Phys. Rev. Lett., 97: 143002, Oct 2006. https://doi.org/10.1103/PhysRevLett.97.143002. URL https://link.aps.org/doi/10.1103/PhysRevLett.97.143002.
https://doi.org/10.1103/PhysRevLett.97.143002

[43] David A. Mazziotti. Anti-Hermitian part of the contracted Schrödinger equation for the direct calculation of two-electron reduced density matrices. Phys. Rev. A, 75: 022505, Feb 2007. https://doi.org/10.1103/PhysRevA.75.022505. URL https://link.aps.org/doi/10.1103/PhysRevA.75.022505.
https://doi.org/10.1103/PhysRevA.75.022505

[44] David A. Mazziotti. Exact two-body expansion of the many-particle wave function. Phys. Rev. A, 102: 030802, Sep 2020. https://doi.org/10.1103/PhysRevA.102.030802. URL https://link.aps.org/doi/10.1103/PhysRevA.102.030802.
https://doi.org/10.1103/PhysRevA.102.030802

[45] Sam McArdle and Suguru Endo. Quantum computational chemistry. Rev. Mod. Phys., 92 (1): 015003, 2020. ISSN 0034-6861. https://doi.org/10.1103/revmodphys.92.015003.
https://doi.org/10.1103/revmodphys.92.015003

[46] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alán Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New J. Phys., 18 (2): 023023, feb 2016. https://doi.org/10.1088/1367-2630/18/2/023023. URL https://doi.org/10.1088/1367-2630/18/2/023023.
https://doi.org/10.1088/1367-2630/18/2/023023

[47] Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes. Nature Communications, 9 (1): 4812, 2018. https://doi.org/10.1038/s41467-018-07090-4.
https://doi.org/10.1038/s41467-018-07090-4

[48] Chr. Møller and M. S. Plesset. Note on an approximation treatment for many-electron systems. Physical Review, 46 (7): 618–622, oct 1934. ISSN 0031-899X. https://doi.org/10.1103/PhysRev.46.618. URL https://link.aps.org/doi/10.1103/PhysRev.46.618.
https://doi.org/10.1103/PhysRev.46.618

[49] Debashis Mukherjee and Werner Kutzelnigg. Irreducible Brillouin conditions and contracted Schrödinger equations for n-electron systems, I: the equations satisfied by the density cumulants. J. Chem. Phys., 114 (5): 2047–2061, feb 2001. ISSN 0021-9606. https://doi.org/10.1063/1.1337058. URL http://aip.scitation.org/doi/10.1063/1.1337058.
https://doi.org/10.1063/1.1337058

[50] P. J. J. O'Malley, R. Babbush, I. D. Kivlichan, J. Romero, J. R. McClean, R. Barends, J. Kelly, P. Roushan, A. Tranter, N. Ding, B. Campbell, Y. Chen, Z. Chen, B. Chiaro, A. Dunsworth, A. G. Fowler, E. Jeffrey, E. Lucero, A. Megrant, J. Y. Mutus, M. Neeley, C. Neill, C. Quintana, D. Sank, A. Vainsencher, J. Wenner, T. C. White, P. V. Coveney, P. J. Love, H. Neven, A. Aspuru-Guzik, and J. M. Martinis. Scalable quantum simulation of molecular energies. Phys. Rev. X, 6: 031007, Jul 2016. https://doi.org/10.1103/PhysRevX.6.031007. URL https://link.aps.org/doi/10.1103/PhysRevX.6.031007.
https://doi.org/10.1103/PhysRevX.6.031007

[51] Sourav Pal. Use of a unitary wavefunction in the calculation of static electronic properties. Theo. Chim. Acta, 66 (3): 207–215, 1984. ISSN 1432-2234. https://doi.org/10.1007/BF00549670. URL https://doi.org/10.1007/BF00549670.
https://doi.org/10.1007/BF00549670

[52] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O’Brien. A variational eigenvalue solver on a photonic quantum processor. Nature Communications, 5 (1): 4213, 2014. https://doi.org/10.1038/ncomms5213.
https://doi.org/10.1038/ncomms5213

[53] John Preskill. Quantum computing in the NISQ era and beyond. Quantum, 2: 79, 2018. https://doi.org/10.22331/q-2018-08-06-79.
https://doi.org/10.22331/q-2018-08-06-79

[54] George D. Purvis and Rodney J. Bartlett. A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples. The Journal of Chemical Physics, 76 (4): 1910–1918, feb 1982. ISSN 0021-9606. https://doi.org/10.1063/1.443164. URL http://aip.scitation.org/doi/10.1063/1.443164.
https://doi.org/10.1063/1.443164

[55] Jonathan Romero, Ryan Babbush, Jarrod R McClean, Cornelius Hempel, Peter J Love, and Alán Aspuru-Guzik. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz. Quantum Science and Technology, 4 (1): 014008, 2018. https://doi.org/10.1088/2058-9565/aad3e4.
https://doi.org/10.1088/2058-9565/aad3e4

[56] Ilya G Ryabinkin, Tzu-Ching Yen, Scott N Genin, and Artur F Izmaylov. Qubit coupled cluster method: A systematic approach to quantum chemistry on a quantum computer. Journal of Chemical Theory and Computation, 14 (12): 6317–6326, 2018. ISSN 1549-9618. https://doi.org/10.1021/acs.jctc.8b00932.
https://doi.org/10.1021/acs.jctc.8b00932

[57] Ilya G Ryabinkin, Robert A Lang, Scott N Genin, and Artur F Izmaylov. Iterative qubit coupled cluster approach with efficient screening of generators. Journal of Chemical Theory and Computation, 16 (2): 1055–1063, 2020. ISSN 1549-9618. https://doi.org/10.1021/acs.jctc.9b01084.
https://doi.org/10.1021/acs.jctc.9b01084

[58] V. O. Shkolnikov, Nicholas J. Mayhall, Sophia E. Economou, and Edwin Barnes. Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers. arXiv preprint at arXiv:2109.05340, 2021. https://doi.org/10.48550/arXiv.2109.05340. URL https://arxiv.org/abs/2109.05340.
https://doi.org/10.48550/arXiv.2109.05340
arXiv:2109.05340

[59] Sukin Sim, Jonathan Romero, Jérôme F Gonthier, and Alexander A Kunitsa. Adaptive pruning-based optimization of parameterized quantum circuits. Quantum Science and Technology, 6 (2): 025019, mar 2021. https://doi.org/10.1088/2058-9565/abe107. URL https://doi.org/10.1088/2058-9565/abe107.
https://doi.org/10.1088/2058-9565/abe107

[60] 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, Sebastian Wouters, and Garnet Kin‐Lic Chan. PySCF: the Python‐based simulations of chemistry framework. WIREs Computational Molecular Science, 8 (1), jan 2018. ISSN 1759-0876. https://doi.org/10.1002/wcms.1340. URL https://onlinelibrary.wiley.com/doi/10.1002/wcms.1340.
https://doi.org/10.1002/wcms.1340

[61] Ho Lun Tang, V.O. Shkolnikov, George S. Barron, Harper R. Grimsley, Nicholas J. Mayhall, Edwin Barnes, and Sophia E. Economou. Qubit-ADAPT-VQE: an adaptive algorithm for constructing hardware-efficient ansätze on a quantum processor. PRX Quantum, 2 (2): 020310, 2021. https://doi.org/10.1103/prxquantum.2.020310.
https://doi.org/10.1103/prxquantum.2.020310

[62] Andrew G. Taube and Rodney J. Bartlett. New perspectives on unitary coupled-cluster theory. Int. J. Quantum Chem., 106 (15): 3393–3401, 2006. ISSN 0020-7608. https://doi.org/10.1002/qua.21198. URL https://onlinelibrary.wiley.com/doi/10.1002/qua.21198.
https://doi.org/10.1002/qua.21198

[63] Jules Tilly, Hongxiang Chen, Shuxiang Cao, Dario Picozzi, Kanav Setia, Ying Li, Edward Grant, Leonard Wossnig, Ivan Rungger, George H. Booth, and Jonathan Tennyson. The variational quantum eigensolver: a review of methods and best practices. arXiv preprint arXiv:2111.05176, 2021. https://doi.org/10.48550/arXiv.2111.05176. URL https://arxiv.org/abs/2111.05176.
https://doi.org/10.48550/arXiv.2111.05176
arXiv:2111.05176

[64] Norm M Tubman, Joonho Lee, Tyler Y Takeshita, Martin Head-Gordon, and K Birgitta Whaley. A deterministic alternative to the full configuration interaction quantum Monte Carlo method. The Journal of Chemical Physics, 145 (4): 044112, 2016. https://doi.org/10.1063/1.4955109.
https://doi.org/10.1063/1.4955109

[65] Samson Wang, Enrico Fontana, M Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles. Noise-induced barren plateaus in variational quantum algorithms. Nature Communications, 12 (1): 6961, 2021. ISSN 2041-1723. https://doi.org/10.1038/s41467-021-27045-6. URL https://doi.org/10.1038/s41467-021-27045-6.
https://doi.org/10.1038/s41467-021-27045-6

[66] Enhua Xu, Motoyuki Uejima, and Seiichiro Lenka Ten-no. Full coupled-cluster reduction for accurate description of strong electron correlation. Phys. Rev. Lett., 121: 113001, Sep 2018. https://doi.org/10.1103/PhysRevLett.121.113001. URL https://link.aps.org/doi/10.1103/PhysRevLett.121.113001.
https://doi.org/10.1103/PhysRevLett.121.113001

[67] Yordan S. Yordanov, David R. M. Arvidsson-Shukur, and Crispin H. W. Barnes. Efficient quantum circuits for quantum computational chemistry. Physical Review A, 102 (6), 2020. ISSN 2469-9926. https://doi.org/10.1103/physreva.102.062612.
https://doi.org/10.1103/physreva.102.062612

[68] Yordan S Yordanov, V Armaos, Crispin H W Barnes, and David R M Arvidsson-Shukur. Qubit-excitation-based adaptive variational quantum eigensolver. Communications Physics, 4 (1): 228, 2021. ISSN 2399-3650. https://doi.org/10.1038/s42005-021-00730-0. URL https://doi.org/10.1038/s42005-021-00730-0.
https://doi.org/10.1038/s42005-021-00730-0

[69] Zi-Jian Zhang, Thi Ha Kyaw, Jakob S Kottmann, Matthias Degroote, and Alán Aspuru-Guzik. Mutual information-assisted adaptive variational quantum eigensolver. Quantum Science and Technology, 6 (3): 035001, jul 2021. https://doi.org/10.1088/2058-9565/abdca4. URL https://doi.org/10.1088/2058-9565/abdca4.
https://doi.org/10.1088/2058-9565/abdca4

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