Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization

Dominic W. Berry1, Craig Gidney2, Mario Motta3, Jarrod R. McClean2, and Ryan Babbush2

1Department of Physics and Astronomy, Macquarie University, Sydney, NSW 2109, Australia
2Google Research, Venice, CA 90291, United States
3Division of Chemistry, California Institute of Technology, Pasadena, CA 91125, United States

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


Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with $\widetilde{\cal O}(N^{3/2} \lambda)$ T complexity, where $N$ is number of orbitals and $\lambda$ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space.

Simulation of quantum chemistry is one of the most important potential applications of quantum computers, because it could be used to design new molecules for a wide range of applications. For example, it could be used to gain understanding of biological Nitrogen fixation by simulation of the FeMoco molecule. We show how to greatly accelerate the simulation of quantum chemistry by taking advantage of the structure of the system, together with several other new advances in quantum algorithms. Our most efficient approach takes advantage of the fact that the description of the energy has many terms that are close to zero and can be ignored. Together with a more efficient way of inputting information about the nonzero terms into the quantum algorithm, for the example of FeMoco we achieve a speedup of about a factor of 700.

► BibTeX data

► References

[1] R. P. Feynman, International Journal of Theoretical Physics 21, 467 (1982).

[2] S. Lloyd, Science 273, 1073 (1996).

[3] M. Mohseni, P. Read, H. Neven, S. Boixo, V. Denchev, R. Babbush, A. Fowler, V. Smelyanskiy, and J. Martinis, Nature 543, 171 (2017).

[4] A. Aspuru-Guzik, A. D. Dutoi, P. J. Love, and M. Head-Gordon, Science 309, 1704 (2005).

[5] A. Y. Kitaev, arXiv:quant-ph/​9511026 (1995).

[6] D. S. Abrams and S. Lloyd, Physical Review Letters 79, 2586 (1997).

[7] R. Babbush, N. Wiebe, J. McClean, J. McClain, H. Neven, and G. K.-L. Chan, Physical Review X 8, 011044 (2018a).

[8] R. Babbush, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, A. Paler, A. Fowler, and H. Neven, Physical Review X 8, 041015 (2018b).

[9] I. D. Kivlichan, C. Gidney, D. W. Berry, N. Wiebe, J. McClean, W. Sun, Z. Jiang, N. Rubin, A. Fowler, A. Aspuru-Guzik, R. Babbush, and H. Neven, arXiv:1902.10673 (2019).

[10] G. H. Low and N. Wiebe, arXiv:1805.00675 (2018).

[11] R. Babbush, D. W. Berry, J. R. McClean, and H. Neven, npj Quantum Information 5, 92 (2019a).

[12] J. D. Whitfield, J. Biamonte, and A. Aspuru-Guzik, Molecular Physics 109, 735 (2011).

[13] D. Wecker, B. Bauer, B. K. Clark, M. B. Hastings, and M. Troyer, Physical Review A 90, 022305 (2014).

[14] R. Babbush, J. McClean, D. Wecker, A. Aspuru-Guzik, and N. Wiebe, Physical Review A 91, 022311 (2015).

[15] D. Poulin, M. B. Hastings, D. Wecker, N. Wiebe, A. C. Doherty, and M. Troyer, Quantum Information and Computation 15, 361 (2015).

[16] J. T. Seeley, M. J. Richard, and P. J. Love, Journal of Chemical Physics 137, 224109 (2012).

[17] K. Setia and J. D. Whitfield, The Journal of Chemical Physics 148, 164104 (2018).

[18] S. Bravyi, J. M. Gambetta, A. Mezzacapo, and K. Temme, arXiv:1701.08213 (2017).

[19] M. Steudtner and S. Wehner, New Journal of Physics 20, 063010 (2018).

[20] Z. Jiang, J. McClean, R. Babbush, and H. Neven, arXiv:1812.08190 (2018).

[21] L. Veis and J. Pittner, Journal of Chemical Physics 140, 214111 (2014).

[22] D. W. Berry, M. Kieferová, A. Scherer, Y. R. Sanders, G. H. Low, N. Wiebe, C. Gidney, and R. Babbush, npj Quantum Information 4, 22 (2018).

[23] D. Poulin, A. Y. Kitaev, D. Steiger, M. Hastings, and M. Troyer, Physical Review Letters 121, 010501 (2017).

[24] N. M. Tubman, C. Mejuto-Zaera, J. M. Epstein, D. Hait, D. S. Levine, W. Huggins, Z. Jiang, J. R. McClean, R. Babbush, M. Head-Gordon, and K. B. Whaley, arXiv:1809.05523 (2018).

[25] G. H. Low and I. L. Chuang, Quantum 3, 163 (2019).

[26] R. Babbush, D. W. Berry, I. D. Kivlichan, A. Y. Wei, P. J. Love, and A. Aspuru-Guzik, New Journal of Physics 18, 33032 (2016).

[27] E. Campbell, Physical Review Letters 123, 070503 (2019).

[28] N. Cody Jones, J. D. Whitfield, P. L. McMahon, M.-H. Yung, R. V. Meter, A. Aspuru-Guzik, and Y. Yamamoto, New Journal of Physics 14, 115023 (2012).

[29] M. Reiher, N. Wiebe, K. M. Svore, D. Wecker, and M. Troyer, Proceedings of the National Academy of Sciences 114, 7555 (2017).

[30] D. Litinski, Quantum 3, 128 (2019a).

[31] I. Kassal, S. P. Jordan, P. J. Love, M. Mohseni, and A. Aspuru-Guzik, Proceedings of the National Academy of Sciences 105, 18681 (2008).

[32] B. Toloui and P. J. Love, arXiv:1312.2579 (2013).

[33] M. B. Hastings, D. Wecker, B. Bauer, and M. Troyer, Quantum Information and Computation 15, 1 (2015).

[34] K. Sugisaki, S. Yamamoto, S. Nakazawa, K. Toyota, K. Sato, D. Shiomi, and T. Takui, The Journal of Physical Chemistry A 120, 6459 (2016).

[35] F. Motzoi, M. P. Kaicher, and F. K. Wilhelm, Physical Review Letters 119, 160503 (2017).

[36] M. Motta, E. Ye, J. R. McClean, Z. Li, A. J. Minnich, R. Babbush, and G. K.-L. Chan, arXiv:1808.02625 (2018).

[37] C. Gidney and A. G. Fowler, Quantum 3, 135 (2019).

[38] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Physical Review A 86, 032324 (2012).

[39] A. G. Fowler and C. Gidney, arXiv:1808.06709 (2018).

[40] H. Beinert, R. Holm, and E. Munck, Science 277, 653 (1997).

[41] M. Szegedy, in 45th Annual IEEE Symposium on Foundations of Computer Science (IEEE, 2004) pp. 32–41.

[42] A. M. Childs and N. Wiebe, Quantum Information and Computation 12, 901 (2012).

[43] A. M. Childs, D. Maslov, Y. Nam, N. J. Ross, and Y. Su, Proceedings of the National Academy of Sciences 115, 9456 (2018).

[44] G. H. Low, V. Kliuchnikov, and L. Schaeffer, arXiv:1812.00954 (2018).

[45] Z. Li, J. Li, N. S. Dattani, C. J. Umrigar, and G. K.-L. Chan, The Journal of Chemical Physics 150, 024302 (2019).

[46] E. G. Hohenstein, S. I. L. Kokkila, R. M. Parrish, and T. J. Martinez, The Journal of Physical Chemistry B 117, 12972 (2013).

[47] J. L. Whitten, The Journal of Chemical Physics 58, 4496 (1973).

[48] E. G. Hohenstein and C. D. Sherrill, The Journal of Chemical Physics 132, 184111 (2010).

[49] N. H. F. Beebe and J. Linderberg, International Journal of Quantum Chemistry 12, 683 (1977).

[50] H. Koch, A. S. de Meras, and T. B. Pedersen, The Journal of Chemical Physics 118, 9481 (2003).

[51] F. Aquilante, L. De Vico, N. Ferré, G. Ghigo, P.-Å. Malmqvist, P. Neogrády, T. B. Pedersen, M. Pitoňák, M. Reiher, B. O. Roos, L. Serrano-Andrés, M. Urban, V. Veryazov, and R. Lindh, Journal of Computational Chemistry 31, 224 (2010).

[52] T. Helgaker, P. Jorgensen, and J. Olsen, Molecular Electronic Structure Theory (Wiley, 2002).

[53] B. Peng and K. Kowalski, Journal of Chemical Theory and Computation 13, 4179 (2017).

[54] D. W. Berry, A. M. Childs, R. Cleve, R. Kothari, and R. D. Somma, in STOC '14 Proceedings of the 46th Annual ACM Symposium on Theory of Computing (2014) pp. 283–292.

[55] G. H. Low and I. L. Chuang, Physical Review Letters 118, 010501 (2017).

[56] I. D. Kivlichan, J. McClean, N. Wiebe, C. Gidney, A. Aspuru-Guzik, G. K.-L. Chan, and R. Babbush, Physical Review Letters 120, 110501 (2018).

[57] D. A. Mazziotti, Physical Review Letters 108, 263002 (2012).

[58] N. Rubin, R. Babbush, and J. McClean, New Journal of Physics 20, 053020 (2018).

[59] W. A. Al-Saidi, S. Zhang, and H. Krakauer, Journal of Chemical Physics 124, 224101 (2006).

[60] D. Vanderbilt, Physical Review B 41, 7892 (1990).

[61] V. Giovannetti, S. Lloyd, and L. Maccone, Physical Review Letters 100, 160501 (2008).

[62] C. Gidney, Quantum 2, 74 (2018).

[63] R. Babbush, D. W. Berry, and H. Neven, Physical Review A 99, 040301 (2019b).

[64] J. R. McClean, R. Babbush, P. J. Love, and A. Aspuru-Guzik, The Journal of Physical Chemistry Letters 5, 4368 (2014).

[65] D. Litinski, arXiv:1905.06903 (2019b).

[66] S. A. Cuccaro, T. G. Draper, S. A. Kutin, and D. P. Moulton, arXiv:quant-ph/​0410184 (2004).

Cited by

[1] Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan, "Quantum computational chemistry", Reviews of Modern Physics 92 1, 015003 (2020).

[2] Matthew Amy and Neil J. Ross, "Phase-state duality in reversible circuit design", Physical Review A 104 5, 052602 (2021).

[3] Yuta Matsuzawa and Yuki Kurashige, "Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits", Journal of Chemical Theory and Computation 16 2, 944 (2020).

[4] Nicholas P. Bauman, Hongbin Liu, Eric J. Bylaska, Sriram Krishnamoorthy, Guang Hao Low, Christopher E. Granade, Nathan Wiebe, Nathan A. Baker, Bo Peng, Martin Roetteler, Matthias Troyer, and Karol Kowalski, "Toward Quantum Computing for High-Energy Excited States in Molecular Systems: Quantum Phase Estimations of Core-Level States", Journal of Chemical Theory and Computation 17 1, 201 (2021).

[5] Jarrod R. McClean, Nicholas C. Rubin, Joonho Lee, Matthew P. Harrigan, Thomas E. O’Brien, Ryan Babbush, William J. Huggins, and Hsin-Yuan Huang, "What the foundations of quantum computer science teach us about chemistry", The Journal of Chemical Physics 155 15, 150901 (2021).

[6] Jeffrey Cohn, Mario Motta, and Robert M. Parrish, "Quantum Filter Diagonalization with Compressed Double-Factorized Hamiltonians", PRX Quantum 2 4, 040352 (2021).

[7] Saad Yalouz, Bruno Senjean, Jakob Günther, Francesco Buda, Thomas E O’Brien, and Lucas Visscher, "A state-averaged orbital-optimized hybrid quantum–classical algorithm for a democratic description of ground and excited states", Quantum Science and Technology 6 2, 024004 (2021).

[8] Andrew M. Childs, Jiaqi Leng, Tongyang Li, Jin-Peng Liu, and Chenyi Zhang, "Quantum simulation of real-space dynamics", Quantum 6, 860 (2022).

[9] Carlos Outeiral, Martin Strahm, Jiye Shi, Garrett M. Morris, Simon C. Benjamin, and Charlotte M. Deane, "The prospects of quantum computing in computational molecular biology", WIREs Computational Molecular Science 11 1(2021).

[10] Thomas E. O'Brien, Michael Streif, Nicholas C. Rubin, Raffaele Santagati, Yuan Su, William J. Huggins, Joshua J. Goings, Nikolaj Moll, Elica Kyoseva, Matthias Degroote, Christofer S. Tautermann, Joonho Lee, Dominic W. Berry, Nathan Wiebe, and Ryan Babbush, "Efficient quantum computation of molecular forces and other energy gradients", Physical Review Research 4 4, 043210 (2022).

[11] 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).

[12] Samuel Jaques and Thomas Häner, "Leveraging State Sparsity for More Efficient Quantum Simulations", ACM Transactions on Quantum Computing 3 3, 1 (2022).

[13] Nicholas H. Stair and Francesco A. Evangelista, "Simulating Many-Body Systems with a Projective Quantum Eigensolver", PRX Quantum 2 3, 030301 (2021).

[14] Sam McArdle, Earl Campbell, and Yuan Su, "Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian", Physical Review A 105 1, 012403 (2022).

[15] 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, 23 (2021).

[16] Bruno Senjean, Saad Yalouz, and Matthieu Saubanère, "Toward density functional theory on quantum computers?", SciPost Physics 14 3, 055 (2023).

[17] 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).

[18] Richard Meister, Simon C. Benjamin, and Earl T. Campbell, "Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries", Quantum 6, 637 (2022).

[19] Javier Argüello-Luengo, Tao Shi, and Alejandro González-Tudela, "Engineering analog quantum chemistry Hamiltonians using cold atoms in optical lattices", Physical Review A 103 4, 043318 (2021).

[20] 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 3, 030305 (2021).

[21] Nicolas P. D. Sawaya, Francesco Paesani, and Daniel P. Tabor, "Near- and long-term quantum algorithmic approaches for vibrational spectroscopy", Physical Review A 104 6, 062419 (2021).

[22] Tyler Takeshita, Nicholas C. Rubin, Zhang Jiang, Eunseok Lee, Ryan Babbush, and Jarrod R. McClean, "Increasing the Representation Accuracy of Quantum Simulations of Chemistry without Extra Quantum Resources", Physical Review X 10 1, 011004 (2020).

[23] Seonghoon Choi and Artur F. Izmaylov, "Measurement Optimization Techniques for Excited Electronic States in Near-Term Quantum Computing Algorithms", Journal of Chemical Theory and Computation acs.jctc.3c00218 (2023).

[24] Ian D. Kivlichan, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Wei Sun, Zhang Jiang, Nicholas Rubin, Austin Fowler, Alán Aspuru-Guzik, Hartmut Neven, and Ryan Babbush, "Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization", Quantum 4, 296 (2020).

[25] 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 38, e2203533119 (2022).

[26] Kosuke Mitarai, Kiichiro Toyoizumi, and Wataru Mizukami, "Perturbation theory with quantum signal processing", Quantum 7, 1000 (2023).

[27] Nicholas H. Stair, Cristian L. Cortes, Robert M. Parrish, Jeffrey Cohn, and Mario Motta, "Stochastic quantum Krylov protocol with double-factorized Hamiltonians", Physical Review A 107 3, 032414 (2023).

[28] Torin F. Stetina, Anthony Ciavarella, Xiaosong Li, and Nathan Wiebe, "Simulating Effective QED on Quantum Computers", Quantum 6, 622 (2022).

[29] BinBin Cai, Fei Gao, and Gregor Leander, "Quantum attacks on two-round even-mansour", Frontiers in Physics 10, 1028014 (2022).

[30] Emiel Koridon, Saad Yalouz, Bruno Senjean, Francesco Buda, Thomas E. O'Brien, and Lucas Visscher, "Orbital transformations to reduce the 1-norm of the electronic structure Hamiltonian for quantum computing applications", Physical Review Research 3 3, 033127 (2021).

[31] Michael P. Kaicher, Simon B. Jäger, Pierre-Luc Dallaire-Demers, and Frank K. Wilhelm, "Roadmap for quantum simulation of the fractional quantum Hall effect", Physical Review A 102 2, 022607 (2020).

[32] Cristian L. Cortes, A. Eugene DePrince, and Stephen K. Gray, "Fast-forwarding quantum simulation with real-time quantum Krylov subspace algorithms", Physical Review A 106 4, 042409 (2022).

[33] Daniel Claudino, "The basics of quantum computing for chemists", International Journal of Quantum Chemistry 122 23(2022).

[34] G. Wendin, Reference Module in Materials Science and Materials Engineering (2023) ISBN:9780128035818.

[35] John M. Martinis, "Saving superconducting quantum processors from decay and correlated errors generated by gamma and cosmic rays", npj Quantum Information 7 1, 90 (2021).

[36] Craig Gidney and Martin Ekerå, "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits", Quantum 5, 433 (2021).

[37] 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 11, 114119 (2023).

[38] 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 2, 020317 (2021).

[39] 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", npj Quantum Information 7 1, 83 (2021).

[40] 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 (2020).

[41] Pablo A. M. Casares, Roberto Campos, and M. A. Martin-Delgado, "TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry", Quantum 6, 768 (2022).

[42] Yingkai Ouyang, David R. White, and Earl T. Campbell, "Compilation by stochastic Hamiltonian sparsification", Quantum 4, 235 (2020).

[43] Kenji Sugisaki, Chikako Sakai, Kazuo Toyota, Kazunobu Sato, Daisuke Shiomi, and Takeji Takui, "Quantum Algorithm for Full Configuration Interaction Calculations without Controlled Time Evolutions", The Journal of Physical Chemistry Letters 12 45, 11085 (2021).

[44] A. K. Fedorov and M. S. Gelfand, "Towards practical applications in quantum computational biology", Nature Computational Science 1 2, 114 (2021).

[45] Yulong Dong, Lin Lin, and Yu Tong, "Ground-State Preparation and Energy Estimation on Early Fault-Tolerant Quantum Computers via Quantum Eigenvalue Transformation of Unitary Matrices", PRX Quantum 3 4, 040305 (2022).

[46] Connor T. Hann, Gideon Lee, S.M. Girvin, and Liang Jiang, "Resilience of Quantum Random Access Memory to Generic Noise", PRX Quantum 2 2, 020311 (2021).

[47] Élie Gouzien and Nicolas Sangouard, "Factoring 2048-bit RSA Integers in 177 Days with 13 436 Qubits and a Multimode Memory", Physical Review Letters 127 14, 140503 (2021).

[48] 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 8 3, 035019 (2023).

[49] 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", Physics Reports 986, 1 (2022).

[50] Christopher Chamberland and Earl T. Campbell, "Universal Quantum Computing with Twist-Free and Temporally Encoded Lattice Surgery", PRX Quantum 3 1, 010331 (2022).

[51] Bill Poirier and Jonathan Jerke, "Full-dimensional Schrödinger wavefunction calculations using tensors and quantum computers: the Cartesian component-separated approach", Physical Chemistry Chemical Physics 24 7, 4437 (2022).

[52] Mathias Soeken and Martin Roetteler, 2020 IEEE International Conference on Quantum Computing and Engineering (QCE) 366 (2020) ISBN:978-1-7281-8969-7.

[53] Seonghoon Choi, Tzu-Ching Yen, and Artur F. Izmaylov, "Improving Quantum Measurements by Introducing “Ghost” Pauli Products", Journal of Chemical Theory and Computation 18 12, 7394 (2022).

[54] Zhendong Li, "Expressibility of comb tensor network states (CTNS) for the P-cluster and the FeMo-cofactor of nitrogenase", Electronic Structure 3 1, 014001 (2021).

[55] Bin-Lin Chen and Dan-Bo Zhang, "Variational Quantum Eigensolver with Mutual Variance-Hamiltonian Optimization", Chinese Physics Letters 40 1, 010303 (2023).

[56] Yuan Su, Dominic W. Berry, Nathan Wiebe, Nicholas Rubin, and Ryan Babbush, "Fault-Tolerant Quantum Simulations of Chemistry in First Quantization", PRX Quantum 2 4, 040332 (2021).

[57] Yuan Su, Hsin-Yuan Huang, and Earl T. Campbell, "Nearly tight Trotterization of interacting electrons", Quantum 5, 495 (2021).

[58] Nick S. Blunt, Joan Camps, Ophelia Crawford, Róbert Izsák, Sebastian Leontica, Arjun Mirani, Alexandra E. Moylett, Sam A. Scivier, Christoph Sünderhauf, Patrick Schopf, Jacob M. Taylor, and Nicole Holzmann, "Perspective on the Current State-of-the-Art of Quantum Computing for Drug Discovery Applications", Journal of Chemical Theory and Computation 18 12, 7001 (2022).

[59] Mohsen Bagherimehrab, Yuval R. Sanders, Dominic W. Berry, Gavin K. Brennen, and Barry C. Sanders, "Nearly Optimal Quantum Algorithm for Generating the Ground State of a Free Quantum Field Theory", PRX Quantum 3 2, 020364 (2022).

[60] Kianna Wan, Mario Berta, and Earl T. Campbell, "Randomized Quantum Algorithm for Statistical Phase Estimation", Physical Review Letters 129 3, 030503 (2022).

[61] Thomas E. O’Brien, Lev B. Ioffe, Yuan Su, David Fushman, Hartmut Neven, Ryan Babbush, and Vadim Smelyanskiy, "Quantum Computation of Molecular Structure Using Data from Challenging-To-Classically-Simulate Nuclear Magnetic Resonance Experiments", PRX Quantum 3 3, 030345 (2022).

[62] Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Darío Gil, and Zaira Nazario, "The future of quantum computing with superconducting qubits", Journal of Applied Physics 132 16, 160902 (2022).

[63] Isaac H. Kim, Ye-Hua Liu, Sam Pallister, William Pol, Sam Roberts, and Eunseok Lee, "Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules", Physical Review Research 4 2, 023019 (2022).

[64] Yuval R. Sanders, Dominic W. Berry, Pedro C.S. Costa, Louis W. Tessler, Nathan Wiebe, Craig Gidney, Hartmut Neven, and Ryan Babbush, "Compilation of Fault-Tolerant Quantum Heuristics for Combinatorial Optimization", PRX Quantum 1 2, 020312 (2020).

[65] Mark Webber, Vincent Elfving, Sebastian Weidt, and Winfried K. Hensinger, "The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime", AVS Quantum Science 4 1, 013801 (2022).

[66] Vera von Burg, Guang Hao Low, Thomas Häner, Damian S. Steiger, Markus Reiher, Martin Roetteler, and Matthias Troyer, "Quantum computing enhanced computational catalysis", Physical Review Research 3 3, 033055 (2021).

[67] Mario Motta and Julia E. Rice, "Emerging quantum computing algorithms for quantum chemistry", WIREs Computational Molecular Science 12 3(2022).

[68] Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran, "Complexity of Implementing Trotter Steps", PRX Quantum 4 2, 020323 (2023).

[69] Aleksei V. Ivanov, Christoph Sünderhauf, Nicole Holzmann, Tom Ellaby, Rachel N. Kerber, Glenn Jones, and Joan Camps, "Quantum computation for periodic solids in second quantization", Physical Review Research 5 1, 013200 (2023).

[70] Alexander Miessen, Pauline J. Ollitrault, Francesco Tacchino, and Ivano Tavernelli, "Quantum algorithms for quantum dynamics", Nature Computational Science 3 1, 25 (2022).

[71] Jonathan Wei Zhong Lau, Kian Hwee Lim, Harshank Shrotriya, and Leong Chuan Kwek, "NISQ computing: where are we and where do we go?", AAPPS Bulletin 32 1, 27 (2022).

[72] Ryan Babbush, Dominic W. Berry, Jarrod R. McClean, and Hartmut Neven, "Quantum simulation of chemistry with sublinear scaling in basis size", npj Quantum Information 5 1, 92 (2019).

[73] Jorge Chávez-Saab, Jesús-Javier Chi-Domínguez, Samuel Jaques, and Francisco Rodríguez-Henríquez, "The SQALE of CSIDH: sublinear Vélu quantum-resistant isogeny action with low exponents", Journal of Cryptographic Engineering 12 3, 349 (2022).

[74] Jarrod R. McClean, Kevin J. Sung, Ian D. Kivlichan, Yudong Cao, Chengyu Dai, E. Schuyler Fried, Craig Gidney, Brendan Gimby, Pranav Gokhale, Thomas Häner, Tarini Hardikar, Vojtěch Havlíček, Oscar Higgott, Cupjin Huang, Josh Izaac, Zhang Jiang, Xinle Liu, Sam McArdle, Matthew Neeley, Thomas O'Brien, Bryan O'Gorman, Isil Ozfidan, Maxwell D. Radin, Jhonathan Romero, Nicholas Rubin, Nicolas P. D. Sawaya, Kanav Setia, Sukin Sim, Damian S. Steiger, Mark Steudtner, Qiming Sun, Wei Sun, Daochen Wang, Fang Zhang, and Ryan Babbush, "OpenFermion: The Electronic Structure Package for Quantum Computers", arXiv:1710.07629, (2017).

[75] Craig Gidney and Martin Ekerå, "How to factor 2048 bit RSA integers in 8 hours using 20 million noisy qubits", arXiv:1905.09749, (2019).

[76] Sam McArdle, Suguru Endo, Alan Aspuru-Guzik, Simon Benjamin, and Xiao Yuan, "Quantum computational chemistry", arXiv:1808.10402, (2018).

[77] Guang Hao Low, Yuan Su, Yu Tong, and Minh C. Tran, "On the complexity of implementing Trotter steps", arXiv:2211.09133, (2022).

[78] Ryan Babbush, Dominic W. Berry, and Hartmut Neven, "Quantum simulation of the Sachdev-Ye-Kitaev model by asymmetric qubitization", Physical Review A 99 4, 040301 (2019).

[79] G. Wendin, "Quantum information processing with superconducting circuits: a perspective", arXiv:2302.04558, (2023).

[80] Ignacio Loaiza, Alireza Marefat Khah, Nathan Wiebe, and Artur F. Izmaylov, "Reducing molecular electronic Hamiltonian simulation cost for Linear Combination of Unitaries approaches", arXiv:2208.08272, (2022).

[81] Craig Gidney and Austin G. Fowler, "Flexible layout of surface code computations using AutoCCZ states", arXiv:1905.08916, (2019).

[82] William M. Kirby and Peter J. Love, "Contextuality Test of the Nonclassicality of Variational Quantum Eigensolvers", Physical Review Letters 123 20, 200501 (2019).

[83] Craig Gidney, "Windowed quantum arithmetic", arXiv:1905.07682, (2019).

[84] Jarrod R. McClean, Fabian M. Faulstich, Qinyi Zhu, Bryan O'Gorman, Yiheng Qiu, Steven R. White, Ryan Babbush, and Lin Lin, "Discontinuous Galerkin discretization for quantum simulation of chemistry", New Journal of Physics 22 9, 093015 (2020).

[85] Élie Gouzien, Diego Ruiz, Francois-Marie Le Régent, Jérémie Guillaud, and Nicolas Sangouard, "Computing 256-bit Elliptic Curve Logarithm in 9 Hours with 126133 Cat Qubits", arXiv:2302.06639, (2023).

[86] Zhicheng Zhang, Qisheng Wang, and Mingsheng Ying, "Parallel Quantum Algorithm for Hamiltonian Simulation", arXiv:2105.11889, (2021).

[87] Sam McArdle, "Learning from Physics Experiments with Quantum Computers: Applications in Muon Spectroscopy", PRX Quantum 2 2, 020349 (2021).

[88] Yuta Matsuzawa and Yuki Kurashige, "A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits", arXiv:1909.12410, (2019).

[89] Kenji Sugisaki, Shigeaki Nakazawa, Kazuo Toyota, Kazunobu Sato, Daisuke Shiomi, and Takeji Takui, "Quantum chemistry on quantum computers: quantum simulations of the time evolution of wave functions under the S2 operator and determination of the spin quantum number S", Physical Chemistry Chemical Physics (Incorporating Faraday Transactions) 21 28, 15356 (2019).

[90] Guang Hao Low, "Halving the cost of quantum multiplexed rotations", arXiv:2110.13439, (2021).

[91] Michal Krompiec and David Muñoz Ramo, "Strongly Contracted N-Electron Valence State Perturbation Theory Using Reduced Density Matrices from a Quantum Computer", arXiv:2210.05702, (2022).

The above citations are from Crossref's cited-by service (last updated successfully 2023-05-29 19:01:35) and SAO/NASA ADS (last updated successfully 2023-05-29 19:01:37). The list may be incomplete as not all publishers provide suitable and complete citation data.