Accelerating Quantum Computations of Chemistry Through Regularized Compressed Double Factorization
1Covestro Deutschland AG, Leverkusen 51373, Germany
2QC Ware Corporation, Palo Alto, CA 94301, USA
| Published: | 2024-06-13, volume 8, page 1371 |
| Eprint: | arXiv:2212.07957v3 |
| Doi: | https://doi.org/10.22331/q-2024-06-13-1371 |
| Citation: | Quantum 8, 1371 (2024). |
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Abstract
We propose the regularized compressed double factorization (RC-DF) method to classically compute compressed representations of molecular Hamiltonians that enable efficient simulation with noisy intermediate scale (NISQ) and error corrected quantum algorithms. We find that already for small systems with 12 to 20 qubits, the resulting NISQ measurement scheme reduces the number of measurement bases by roughly a factor of three and the shot count to reach chemical accuracy by a factor of three to six compared to truncated double factorization (DF) and we see order of magnitude improvements over Pauli grouping schemes. We demonstrate the scalability of our approach by performing RC-DF on the CpdI species of cytochrome P450 with 58 orbitals and find that using the resulting compressed Hamiltonian cuts the run time of qubitization and truncated DF based error corrected algorithms almost in half and even outperforms the lambda parameters achievable with tensor hypercontraction (THC) while at the same time reducing the CCSD(T) energy error heuristic by an order of magnitude.
Featured image: Comparison of the achievable CCSD(T) error heuristic and lambda values $\lambda^{\mathrm{Burg}}_{\mathrm{DF}}$ for the truncated DF method, X-DF and RC-DF, as well as $\lambda^{\mathrm{Lee}}_{\mathrm{THC}}$ for THC. The color scheme represents the number of leafs $n_t$ for double factorization schemes, or the THC rank $M$. The encircled THC data point was used for the resource estimates there. To compare different levels of convergence we vary the squared Frobenius norm at which we abort the RC-DF optimization (Conv.~Tol.) and use $\rho=10^{-3}$.
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[1] T. E. O'Brien, G. Anselmetti, F. Gkritsis, V. E. Elfving, S. Polla, W. J. Huggins, O. Oumarou, K. Kechedzhi, D. Abanin, R. Acharya, I. Aleiner, R. Allen, T. I. Andersen, K. Anderson, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Atalaya, D. Bacon, J. C. Bardin, A. Bengtsson, S. Boixo, G. Bortoli, A. Bourassa, J. Bovaird, L. Brill, M. Broughton, B. Buckley, D. A. Buell, T. Burger, B. Burkett, N. Bushnell, J. Campero, Y. Chen, Z. Chen, B. Chiaro, D. Chik, J. Cogan, R. Collins, P. Conner, W. Courtney, A. L. Crook, B. Curtin, D. M. Debroy, S. Demura, I. Drozdov, A. Dunsworth, C. Erickson, L. Faoro, E. Farhi, R. Fatemi, V. S. Ferreira, L. Flores Burgos, E. Forati, A. G. Fowler, B. Foxen, W. Giang, C. Gidney, D. Gilboa, M. Giustina, R. Gosula, A. Grajales Dau, J. A. Gross, S. Habegger, M. C. Hamilton, M. Hansen, M. P. Harrigan, S. D. Harrington, P. Heu, J. Hilton, M. R. Hoffmann, S. Hong, T. Huang, A. Huff, L. B. Ioffe, S. V. Isakov, J. Iveland, E. Jeffrey, Z. Jiang, C. Jones, P. Juhas, D. Kafri, J. Kelly, T. Khattar, M. Khezri, M. Kieferová, S. Kim, P. V. Klimov, A. R. Klots, R. Kothari, A. N. Korotkov, F. Kostritsa, J. M. Kreikebaum, D. Landhuis, P. Laptev, K. Lau, L. Laws, J. Lee, K. Lee, B. J. Lester, A. T. Lill, W. Liu, W. P. Livingston, A. Locharla, E. Lucero, F. D. Malone, S. Mandra, O. Martin, S. Martin, J. R. McClean, T. McCourt, M. McEwen, A. Megrant, X. Mi, A. Mieszala, K. C. Miao, M. Mohseni, S. Montazeri, A. Morvan, R. Movassagh, W. Mruczkiewicz, O. Naaman, M. Neeley, C. Neill, A. Nersisyan, H. Neven, M. Newman, J. H. Ng, A. Nguyen, M. Nguyen, M. Y. Niu, S. Omonije, A. Opremcak, A. Petukhov, R. Potter, L. P. Pryadko, C. Quintana, C. Rocque, P. Roushan, N. Saei, D. Sank, K. Sankaragomathi, K. J. Satzinger, H. F. Schurkus, C. Schuster, M. J. Shearn, A. Shorter, N. Shutty, V. Shvarts, J. Skruzny, V. Smelyanskiy, W. C. Smith, R. Somma, G. Sterling, D. Strain, M. Szalay, D. Thor, A. Torres, G. Vidal, B. Villalonga, C. Vollgraff Heidweiller, T. White, B. W. K. Woo, C. Xing, Z. J. Yao, P. Yeh, J. Yoo, G. Young, A. Zalcman, Y. Zhang, N. Zhu, N. Zobrist, C. Gogolin, R. Babbush, and N. C. Rubin. ``Purification-based quantum error mitigation of pair-correlated electron simulations''. Nat. Phys. 19, 1787–1792 (2023).
https://doi.org/10.1038/s41567-023-02240-y
[2] 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, 1–7 (2014).
https://doi.org/10.1038/ncomms5213
[3] Thomas E O’Brien, Stefano Polla, Nicholas C Rubin, William J Huggins, Sam McArdle, Sergio Boixo, Jarrod R McClean, and Ryan Babbush. ``Error mitigation via verified phase estimation''. PRX Quantum 2, 020317 (2021).
https://doi.org/10.1103/PRXQuantum.2.020317
[4] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O'Brien. ``Quantum error mitigation''. Rev. Mod. Phys. 95, 045005 (2023).
https://doi.org/10.1103/RevModPhys.95.045005
[5] William J Huggins, Jarrod R McClean, Nicholas C Rubin, Zhang Jiang, Nathan Wiebe, K Birgitta Whaley, and Ryan Babbush. ``Efficient and noise resilient measurements for quantum chemistry on near-term quantum computers''. npj Quantum Information 7, 1–9 (2021).
https://doi.org/10.1038/s41534-020-00341-7
[6] Vladyslav Verteletskyi, Tzu-Ching Yen, and Artur F Izmaylov. ``Measurement optimization in the variational quantum eigensolver using a minimum clique cover''. The Journal of chemical physics 152, 124114 (2020).
https://doi.org/10.1063/1.5141458
[7] Laurin E Fischer, Daniel Miller, Francesco Tacchino, Panagiotis Kl Barkoutsos, Daniel J Egger, and Ivano Tavernelli. ``Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space''. Physical Review Research 4, 033027 (2022).
https://doi.org/10.1103/PhysRevResearch.4.033027
[8] Daniel Miller, Laurin E. Fischer, Igor O. Sokolov, Panagiotis Kl. Barkoutsos, and Ivano Tavernelli. ``Hardware-tailored diagonalization circuits'' (2022). arXiv:2203.03646.
arXiv:2203.03646
[9] J. L. Whitten. ``Coulombic potential energy integrals and approximations''. The Journal of Chemical Physics 58, 4496–4501 (1973).
https://doi.org/10.1063/1.1679012
[10] Edward G Hohenstein, Robert M Parrish, and Todd J Martínez. ``Tensor hypercontraction density fitting. i. quartic scaling second-and third-order møller-plesset perturbation theory''. The Journal of chemical physics 137, 044103 (2012).
https://doi.org/10.1063/1.4732310
[11] Joshua J. Goings, Alec White, Joonho Lee, Christofer S. Tautermann, Matthias Degroote, Craig Gidney, Toru Shiozaki, Ryan Babbush, and Nicholas C. Rubin. ``Reliably assessing the electronic structure of cytochrome p450 on today's classical computers and tomorrow's quantum computers''. Proceedings of the National Academy of Sciences 119, e2203533119 (2022).
https://doi.org/10.1073/pnas.2203533119
[12] Dominic W Berry, Craig Gidney, Mario Motta, Jarrod R McClean, and Ryan Babbush. ``Qubitization of arbitrary basis quantum chemistry leveraging sparsity and low rank factorization''. Quantum 3, 208 (2019).
https://doi.org/10.22331/q-2019-12-02-208
[13] Edward G. Hohenstein, Oumarou Oumarou, Rachael Al-Saadon, Gian-Luca R. Anselmetti, Maximilian Scheurer, Christian Gogolin, and Robert M. Parrish. ``Efficient quantum analytic nuclear gradients with double factorization''. The Journal of Chemical Physics 158, 114119 (2023).
https://doi.org/10.1063/5.0137167
[14] Jeffrey Cohn, Mario Motta, and Robert M. Parrish. ``Quantum Filter Diagonalization with Compressed Double-Factorized Hamiltonians''. PRX Quantum 2, 040352 (2021).
https://doi.org/10.1103/PRXQuantum.2.040352
[15] Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, and Hartmut Neven. ``Encoding electronic spectra in quantum circuits with linear t complexity''. Phys. Rev. X 8, 041015 (2018).
https://doi.org/10.1103/PhysRevX.8.041015
[16] Vera von Burg, Guang Hao Low, Thomas Häner, Damian S. Steiger, Markus Reiher, Martin Roetteler, and Matthias Troyer. ``Quantum computing enhanced computational catalysis''. Phys. Rev. Res. 3, 033055 (2021).
https://doi.org/10.1103/PhysRevResearch.3.033055
[17] Joonho Lee, Dominic W. Berry, Craig Gidney, William J. Huggins, Jarrod R. McClean, Nathan Wiebe, and Ryan Babbush. ``Even more efficient quantum computations of chemistry through tensor hypercontraction''. PRX Quantum 2, 030305 (2021).
https://doi.org/10.1103/PRXQuantum.2.030305
[18] Robert M. Parrish and Peter L. McMahon. ``Quantum filter diagonalization: Quantum eigendecomposition without full quantum phase estimation'' (2019). arXiv:1909.08925.
arXiv:1909.08925
[19] Ignacio Loaiza, Alireza Marefat Khah, Nathan Wiebe, and Artur F Izmaylov. ``Reducing molecular electronic hamiltonian simulation cost for linear combination of unitaries approaches''. Quantum Science and Technology (2022).
https://doi.org/10.1088/2058-9565/acd577
[20] Tzu-Ching Yen and Artur F Izmaylov. ``Cartan subalgebra approach to efficient measurements of quantum observables''. PRX Quantum 2, 040320 (2021).
https://doi.org/10.1103/PRXQuantum.2.040320
[21] Seonghoon Choi, Ignacio Loaiza, and Artur F. Izmaylov. ``Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver''. Quantum 7, 889 (2023).
https://doi.org/10.22331/q-2023-01-03-889
[22] Artur F Izmaylov, Tzu-Ching Yen, Robert A Lang, and Vladyslav Verteletskyi. ``Unitary partitioning approach to the measurement problem in the variational quantum eigensolver method''. Journal of chemical theory and computation 16, 190–195 (2019).
https://doi.org/10.1021/acs.jctc.9b00791
[23] Mario Motta, Erika Ye, Jarrod R McClean, Zhendong Li, Austin J Minnich, Ryan Babbush, and Garnet Kin Chan. ``Low rank representations for quantum simulation of electronic structure''. npj Quantum Information 7, 1–7 (2021).
https://doi.org/10.1038/s41534-021-00416-z
[24] Edvin Deadman, Nicholas J Higham, and Rui Ralha. ``Blocked schur algorithms for computing the matrix square root''. In International Workshop on Applied Parallel Computing. Pages 171–182. Springer (2012).
https://doi.org/10.1007/978-3-642-36803-5_12
[25] Mario Barbatti, Adélia JA Aquino, and Hans Lischka. ``Ultrafast two-step process in the non-adiabatic relaxation of the ch2 molecule''. Molecular Physics 104, 1053–1060 (2006).
https://doi.org/10.1080/00268970500417945
[26] Bernhard Sellner, Mario Barbatti, Thomas Müller, Wolfgang Domcke, and Hans Lischka. ``Ultrafast non-adiabatic dynamics of ethylene including rydberg states''. Molecular physics 111, 2439–2450 (2013).
https://doi.org/10.1080/00268976.2013.813590
[27] Thom H. Dunning. ``Gaussian basis sets for use in correlated molecular calculations. i. the atoms boron through neon and hydrogen''. J. Chem. Phys. 90, 1007–1023 (1989).
https://doi.org/10.1063/1.456153
[28] 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, 242–246 (2017).
https://doi.org/10.1038/nature23879
[29] Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, Shahnawaz Ahmed, Vishnu Ajith, M. Sohaib Alam, Guillermo Alonso-Linaje, B. AkashNarayanan, Ali Asadi, Juan Miguel Arrazola, Utkarsh Azad, Sam Banning, Carsten Blank, Thomas R Bromley, Benjamin A. Cordier, Jack Ceroni, Alain Delgado, Olivia Di Matteo, Amintor Dusko, Tanya Garg, Diego Guala, Anthony Hayes, Ryan Hill, Aroosa Ijaz, Theodor Isacsson, David Ittah, Soran Jahangiri, Prateek Jain, Edward Jiang, Ankit Khandelwal, Korbinian Kottmann, Robert A. Lang, Christina Lee, Thomas Loke, Angus Lowe, Keri McKiernan, Johannes Jakob Meyer, J. A. Montañez-Barrera, Romain Moyard, Zeyue Niu, Lee James O'Riordan, Steven Oud, Ashish Panigrahi, Chae-Yeun Park, Daniel Polatajko, Nicolás Quesada, Chase Roberts, Nahum Sá, Isidor Schoch, Borun Shi, Shuli Shu, Sukin Sim, Arshpreet Singh, Ingrid Strandberg, Jay Soni, Antal Száva, Slimane Thabet, Rodrigo A. Vargas-Hernández, Trevor Vincent, Nicola Vitucci, Maurice Weber, David Wierichs, Roeland Wiersema, Moritz Willmann, Vincent Wong, Shaoming Zhang, and Nathan Killoran. ``Pennylane: Automatic differentiation of hybrid quantum-classical computations'' (2018).
[30] Elvira R. Sayfutyarova, Qiming Sun, Garnet Kin-Lic Chan, and Gerald Knizia. ``Automated construction of molecular active spaces from atomic valence orbitals''. Journal of Chemical Theory and Computation 13, 4063–4078 (2017).
https://doi.org/10.1021/acs.jctc.7b00128
[31] 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, e1340 (2018).
https://doi.org/10.1002/wcms.1340
[32] Qiming Sun, Xing Zhang, Samragni Banerjee, Peng Bao, Marc Barbry, Nick S. Blunt, Nikolay A. Bogdanov, George H. Booth, Jia Chen, Zhi-Hao Cui, Janus J. Eriksen, Yang Gao, Sheng Guo, Jan Hermann, Matthew R. Hermes, Kevin Koh, Peter Koval, Susi Lehtola, Zhendong Li, Junzi Liu, Narbe Mardirossian, James D. McClain, Mario Motta, Bastien Mussard, Hung Q. Pham, Artem Pulkin, Wirawan Purwanto, Paul J. Robinson, Enrico Ronca, Elvira R. Sayfutyarova, Maximilian Scheurer, Henry F. Schurkus, James E. T. Smith, Chong Sun, Shi-Ning Sun, Shiv Upadhyay, Lucas K. Wagner, Xiao Wang, Alec White, James Daniel Whitfield, Mark J. Williamson, Sebastian Wouters, Jun Yang, Jason M. Yu, Tianyu Zhu, Timothy C. Berkelbach, Sandeep Sharma, Alexander Yu. Sokolov, and Garnet Kin-Lic Chan. ``Recent developments in the pyscf program package''. The Journal of Chemical Physics 153, 024109 (2020).
https://doi.org/10.1063/5.0006074
[33] Florian Weigend and Reinhart Ahlrichs. ``Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for h to rn: Design and assessment of accuracy''. Phys. Chem. Chem. Phys. 7, 3297 (2005).
https://doi.org/10.1039/b508541a
[34] Kianna Wan, William J. Huggins, Joonho Lee, and Ryan Babbush. ``Matchgate shadows for fermionic quantum simulation''. Communications in Mathematical Physics 404, 629–700 (2023).
https://doi.org/10.1007/s00220-023-04844-0
[35] Guang Hao Low. ``Classical shadows of fermions with particle number symmetry'' (2022). arXiv:2208.08964 [quant-ph].
arXiv:2208.08964
[36] Roy Frostig, Matthew Johnson, and Chris Leary. ``Compiling machine learning programs via high-level tracing''. SysML (2018). url: https://mlsys.org/Conferences/doc/2018/146.pdf.
https://mlsys.org/Conferences/doc/2018/146.pdf
[37] Oumarou Oumarou, Maximilian Scheurer, Robert M. Parrish, Edward G. Hohenstein, and Christian Gogolin. ``Data for Accelerating Quantum Computations of Chemistry Through Regularized Compressed Double Factorization''. Zenodo (2023).
https://doi.org/10.5281/zenodo.7866658
[38] Ciyou Zhu, Richard H Byrd, Peihuang Lu, and Jorge Nocedal. ``Algorithm 778: L-bfgs-b: Fortran subroutines for large-scale bound-constrained optimization''. ACM Transactions on mathematical software (TOMS) 23, 550–560 (1997).
https://doi.org/10.1145/279232.279236
[39] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. ``SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python''. Nature Methods 17, 261–272 (2020).
https://doi.org/10.1038/s41592-019-0686-2
[40] Joshua J. Goings, Alec White, Christofer S. Tautermann, Matthias Degroote, Craig Gidney, Toru Shiozaki, Ryan Babbush, and Nicholas C. Rubin. ``Data for reliably assessing the electronic structure of cytochrome p450 on today's classical computers and tomorrow's quantum computers''. Zenodo (2022).
https://doi.org/10.5281/zenodo.5941130
[41] Dougal Maclaurin, David Duvenaud, and Ryan P Adams. ``Autograd: Effortless gradients in numpy''. In ICML 2015 AutoML workshop. Volume 238. (2015). url: https://indico.ijclab.in2p3.fr/event/2914/contributions/6483/subcontributions/180/attachments/6060/7185/automl-short.pdf.
https://indico.ijclab.in2p3.fr/event/2914/contributions/6483/subcontributions/180/attachments/6060/7185/automl-short.pdf
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[1] Smik Patel, Aritra Sankar Brahmachari, Joshua T. Cantin, Linjun Wang, and Artur F. Izmaylov, "Global Minimization of Electronic Hamiltonian 1-Norm via Linear Programming in the Block Invariant Symmetry Shift (BLISS) Method", Journal of Chemical Theory and Computation 21 2, 703 (2025).
[2] Smik Patel, Praveen Jayakumar, Tzu-Ching Yen, and Artur F. Izmaylov, "Quantum Measurement for Quantum Chemistry on a Quantum Computer", Chemical Reviews 125 16, 7490 (2025).
[3] Cristian L. Cortes, Dario Rocca, Jérôme F. Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca R. Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Assessing the query complexity limits of quantum phase estimation using symmetry-aware spectral bounds", Physical Review A 110 2, 022420 (2024).
[4] Ignacio Loaiza and Artur F. Izmaylov, "Block-Invariant Symmetry Shift: Preprocessing Technique for Second-Quantized Hamiltonians to Improve Their Decompositions to Linear Combination of Unitaries", Journal of Chemical Theory and Computation 19 22, 8201 (2023).
[5] Dominic W. Berry, Nicholas C. Rubin, Ahmed O. Elnabawy, Gabriele Ahlers, A. Eugene DePrince, Joonho Lee, Christian Gogolin, and Ryan Babbush, "Quantum simulation of realistic materials in first quantization using non-local pseudopotentials", npj Quantum Information 10 1, 130 (2024).
[6] Guang Hao Low, Robbie King, Dominic W. Berry, Qiushi Han, A. Eugene DePrince, Alec F. White, Ryan Babbush, Rolando D. Somma, and Nicholas C. Rubin, "Fast Quantum Simulation of Electronic Structure by Spectral Amplification", Physical Review X 15 4, 041016 (2025).
[7] Michael A. Jones, Harish J. Vallury, Manolo C. Per, Harry M. Quiney, and Lloyd C. L. Hollenberg, "Moments-based improved quantum computation of the electric dipole moment of molecular systems", Physical Review Applied 25 5, 054001 (2026).
[8] Pauline J. Ollitrault, Cristian L. Cortes, Jérôme F. Gonthier, Robert M. Parrish, Dario Rocca, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Enhancing Initial State Overlap through Orbital Optimization for Faster Molecular Electronic Ground-State Energy Estimation", Physical Review Letters 133 25, 250601 (2024).
[9] Oumarou Oumarou, Pauline J. Ollitrault, Cristian L. Cortes, Maximilian Scheurer, Robert M. Parrish, and Christian Gogolin, "Molecular Properties from Quantum Krylov Subspace Diagonalization", Journal of Chemical Theory and Computation 21 9, 4543 (2025).
[10] Athena Caesura, Cristian L. Cortes, William Pol, Sukin Sim, Mark Steudtner, Gian-Luca R. Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, Michael Streif, and Christofer S. Tautermann, "Faster Quantum Chemistry Simulations on a Quantum Computer with Improved Tensor Factorization and Active Volume Compilation", PRX Quantum 6 3, 030337 (2025).
[11] Pauline J. Ollitrault, Jérôme F. Gonthier, Dario Rocca, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Improving the Runtime of Quantum Phase Estimation for Chemistry through Basis Set Optimization", Journal of Chemical Theory and Computation 21 23, 12034 (2025).
[12] Alexander Kunitsa, Diksha Dhawan, Stepan Fomichev, Juan Miguel Arrazola, Minghao Zhang, and Torin F. Stetina, "Quantum simulation of electron energy loss spectroscopy for battery materials", The Journal of Chemical Physics 163 24, 244110 (2025).
[13] Fotios Gkritsis, Daniel Dux, Jin Zhang, Naman Jain, Christian Gogolin, and Philipp M. Preiss, "Simulating Chemistry with Fermionic Optical Superlattices", PRX Quantum 6 1, 010318 (2025).
[14] Chiara Leadbeater, Nathan Fitzpatrick, David Muñoz Ramo, and Alex J W Thom, "Non-unitary Trotter circuits for imaginary time evolution", Quantum Science and Technology 9 4, 045007 (2024).
[15] Alexey Pyrkov, Alex Aliper, Dmitry Bezrukov, and Alex Zhavoronkov, Applied Artificial Intelligence for Drug Discovery 289 (2026) ISBN:978-3-031-98021-3.
[16] Ludwig Nützel, Michael J Hartmann, Henrik Dreyer, and Etienne Granet, "Ground state energy via adiabatic evolution and phase measurement for a molecular Hamiltonian on an ion-trap quantum computer", Quantum Science and Technology 11 3, 035038 (2026).
[17] Jakob Günther, Freek Witteveen, Alexander Schmidhuber, Marek Miller, Matthias Christandl, and Aram W. Harrow, "Phase Estimation with Partially Randomized Time Evolution", PRX Quantum 7 2, 020332 (2026).
[18] Konrad Deka and Emil Zak, "Simultaneously Optimizing Symmetry Shifts and Tensor Factorizations for Cost-Efficient Fault-Tolerant Quantum Simulations of Electronic Hamiltonians", Journal of Chemical Theory and Computation 21 9, 4458 (2025).
[19] Kieran Dalton, Christopher K. Long, Yordan S. Yordanov, Charles G. Smith, Crispin H. W. Barnes, Normann Mertig, and David R. M. Arvidsson-Shukur, "Quantifying the effect of gate errors on variational quantum eigensolvers for quantum chemistry", npj Quantum Information 10 1, 18 (2024).
[20] Nicholas C. Rubin, Dominic W. Berry, Fionn D. Malone, Alec F. White, Tanuj Khattar, A. Eugene DePrince, Sabrina Sicolo, Michael Küehn, Michael Kaicher, Joonho Lee, and Ryan Babbush, "Fault-Tolerant Quantum Simulation of Materials Using Bloch Orbitals", PRX Quantum 4 4, 040303 (2023).
[21] Cristian L. Cortes, Matthias Loipersberger, Robert M. Parrish, Sam Morley-Short, William Pol, Sukin Sim, Mark Steudtner, Christofer S. Tautermann, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Fault-Tolerant Quantum Algorithm for Symmetry-Adapted Perturbation Theory", PRX Quantum 5 1, 010336 (2024).
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[23] Isaac L. Huidobro-Meezs, Jun Dai, Guillaume Rabusseau, and Rodrigo A. Vargas-Hernández, "GFlowNets for Hamiltonian decomposition in groups of compatible operators", arXiv:2410.16041, (2024).
[24] Pauline J. Ollitrault, Cristian L. Cortes, Jerome F. Gonthier, Robert M. Parrish, Dario Rocca, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Enhancing initial state overlap through orbital optimization for faster molecular electronic ground-state energy estimation", arXiv:2404.08565, (2024).
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[26] Christopher Kang and Yuan Su, "Quantum matrix arithmetics with Hamiltonian evolution", arXiv:2510.06316, (2025).
[27] Ignacio Loaiza and Artur F. Izmaylov, "Block-Invariant Symmetry Shift: Preprocessing technique for second-quantized Hamiltonians to improve their decompositions to Linear Combination of Unitaries", arXiv:2304.13772, (2023).
[28] Dario Rocca, Cristian L. Cortes, Jérôme F. Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Reducing the Runtime of Fault-Tolerant Quantum Simulations in Chemistry through Symmetry-Compressed Double Factorization", Journal of Chemical Theory and Computation 20 11, 4639 (2024).
[29] Dario Rocca, Cristian L. Cortes, Jerome Gonthier, Pauline J. Ollitrault, Robert M. Parrish, Gian-Luca Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Reducing the runtime of fault-tolerant quantum simulations in chemistry through symmetry-compressed double factorization", arXiv:2403.03502, (2024).
[30] Pablo Antonio Moreno Casares, "Fault-tolerant quantum algorithms", arXiv:2301.08057, (2023).
[31] Pauline J. Ollitrault, Matthias Loipersberger, Robert M. Parrish, Alexander Erhard, Christine Maier, Christian Sommer, Juris Ulmanis, Thomas Monz, Christian Gogolin, Christofer S. Tautermann, Gian-Luca R. Anselmetti, Matthias Degroote, Nikolaj Moll, Raffaele Santagati, and Michael Streif, "Estimation of electrostatic interaction energies on a trapped-ion quantum computer", arXiv:2312.14739, (2023).
[32] V. Anurag K. S., Ashish Kumar Patra, Manas Mukherjee, Alok Shukla, Sai Shankar P., Ruchika Bhat, L. Radhika T. S., and Jaiganesh G, "Towards Chemically Accurate and Scalable Quantum Simulations on IQM Quantum Hardware: A Quantum-HPC Hybrid Approach", arXiv:2604.01983, (2026).
[33] Pooja Rao, Dimitar Trenev, Jerome Gonthier, Taylor Patti, Sebastian Stern, Tyler Takeshita, Yuri Alexeev, Cedric Lin, Sam McArdle, Justin Lietz, Katherine Klymko, Ermal Rrapaj, Norm Tubman, Krysta Svore, Peter Komar, and Elica Kyoseva, "Performance Model for Hybrid Quantum-Classical Workflows", arXiv:2607.15426, (2026).
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