Symmetry enhanced variational quantum spin eigensolver

Symmetry enhanced variational quantum spin eigensolver

Symmetry enhanced variational quantum spin eigensolver PlatoBlockchain Data Intelligence. Vertical Search. Ai.

Chufan Lyu1, Xusheng Xu2, Man-Hong Yung2,3,4, and Abolfazl Bayat1

1Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610051, China
2Central Research Institute, 2012 Labs, Huawei Technologies
3Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
4Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China

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Abstract

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

Quantum simulators are rapidly emerging in various physical platforms. However, the current noisy Intermediate-Scale Quantum (NISQ) simulators suffer from imperfect initialization, noisy operation and faulty readout. Variational quantum algorithms have been proposed as the most promising approach for achieving quantum advantage on NISQ devices. In these algorithms, the complexity is divided between a parameterized quantum simulator and a classical optimizer for optimizing the parameters of the circuit. Therefore, in variational quantum algorithms we deal with both quantum and classical resources, for both of which we have to be efficient. Here, we focus on Variational Quantum Eigensolver (VQE) algorithm, which has been designed to variationally generate the low-energy eigenstates of a many-body system on a quantum simulator. We exploit symmetries of the system to improve resource efficiency in a VQE algorithm. Two methods are investigated: (i) incorporating the symmetries in the design of the circuit that naturally generates quantum states with desired symmetry; and (ii) adding extra terms to the cost function to penalize the quantum states without the relevant symmetry. Through extensive analysis, we show that the first approach is far more resource efficient, with respect to both quantum and classical resources. In realistic scenarios, one may need to use a hybrid scheme in which some symmetries are incorporated in the hardware and some are targeted through the cost function.

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► References

[1] Christian Kokail, Christine Maier, Rick van Bijnen, Tiff Brydges, Manoj K Joshi, Petar Jurcevic, Christine A Muschik, Pietro Silvi, Rainer Blatt, Christian F Roos, et al. “Self-verifying variational quantum simulation of lattice models”. Nature 569, 355–360 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-1177-4

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

[3] Trygve Helgaker, Poul Jorgensen, and Jeppe Olsen. “Molecular electronic-structure theory”. John Wiley & Sons, Ltd. (2013).
https:/​/​doi.org/​10.1002/​9781119019572

[4] Roman Orus, Samuel Mugel, and Enrique Lizaso. “Quantum computing for finance: Overview and prospects”. Reviews in Physics 4, 100028 (2019).
https:/​/​doi.org/​10.1016/​j.revip.2019.100028

[5] Patrick Rebentrost, Brajesh Gupt, and Thomas R Bromley. “Quantum computational finance: Monte carlo pricing of financial derivatives”. Phys. Rev. A 98, 022321 (2018).
https:/​/​doi.org/​10.1103/​physreva.98.022321

[6] Daniel J Egger, Claudio Gambella, Jakub Marecek, Scott McFaddin, Martin Mevissen, Rudy Raymond, Andrea Simonetto, Stefan Woerner, and Elena Yndurain. “Quantum computing for finance: state of the art and future prospects”. IEEE Transactions on Quantum Engineering (2020).
https:/​/​doi.org/​10.1109/​tqe.2020.3030314

[7] Pranjal Bordia, Henrik Lüschen, Sebastian Scherg, Sarang Gopalakrishnan, Michael Knap, Ulrich Schneider, and Immanuel Bloch. “Probing slow relaxation and many-body localization in two-dimensional quasiperiodic systems”. Phys. Rev. X 7, 041047 (2017).
https:/​/​doi.org/​10.1103/​physrevx.7.041047

[8] Michael Schreiber, Sean S Hodgman, Pranjal Bordia, Henrik P Lüschen, Mark H Fischer, Ronen Vosk, Ehud Altman, Ulrich Schneider, and Immanuel Bloch. “Observation of many-body localization of interacting fermions in a quasirandom optical lattice”. Science 349, 842–845 (2015).
https:/​/​doi.org/​10.1126/​science.aaa7432

[9] Christian Gross and Immanuel Bloch. “Quantum simulations with ultracold atoms in optical lattices”. Science 357, 995–1001 (2017).
https:/​/​doi.org/​10.1126/​science.aal3837

[10] Cornelius Hempel, Christine Maier, Jonathan Romero, Jarrod McClean, Thomas Monz, Heng Shen, Petar Jurcevic, Ben P Lanyon, Peter Love, Ryan Babbush, et al. “Quantum chemistry calculations on a trapped-ion quantum simulator”. Phys. Rev. X 8, 031022 (2018).
https:/​/​doi.org/​10.1103/​PhysRevX.8.031022

[11] Ben P Lanyon, Cornelius Hempel, Daniel Nigg, Markus Müller, Rene Gerritsma, F Zähringer, Philipp Schindler, Julio T Barreiro, Markus Rambach, Gerhard Kirchmair, et al. “Universal digital quantum simulation with trapped ions”. Science 334, 57–61 (2011).
https:/​/​doi.org/​10.1126/​science.1208001

[12] Alán Aspuru-Guzik and Philip Walther. “Photonic quantum simulators”. Nat. Phys. 8, 285–291 (2012).
https:/​/​doi.org/​10.1038/​nphys2253

[13] Jianwei Wang, Fabio Sciarrino, Anthony Laing, and Mark G Thompson. “Integrated photonic quantum technologies”. Nat. Photonics 14, 273–284 (2020).
https:/​/​doi.org/​10.1038/​s41566-019-0532-1

[14] Toivo Hensgens, Takafumi Fujita, Laurens Janssen, Xiao Li, CJ Van Diepen, Christian Reichl, Werner Wegscheider, S Das Sarma, and Lieven MK Vandersypen. “Quantum simulation of a fermi–hubbard model using a semiconductor quantum dot array”. Nature 548, 70–73 (2017).
https:/​/​doi.org/​10.1038/​nature23022

[15] J Salfi, JA Mol, R Rahman, G Klimeck, MY Simmons, LCL Hollenberg, and S Rogge. “Quantum simulation of the hubbard model with dopant atoms in silicon”. Nat. Commun. 7, 1–6 (2016).
https:/​/​doi.org/​10.1038/​ncomms11342

[16] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Sergio Boixo, Michael Broughton, Bob B Buckley, David A Buell, et al. “Hartree-fock on a superconducting qubit quantum computer”. Science 369, 1084–1089 (2020).
https:/​/​doi.org/​10.1126/​science.abb9811

[17] Rami Barends, Alireza Shabani, Lucas Lamata, Julian Kelly, Antonio Mezzacapo, Urtzi Las Heras, Ryan Babbush, Austin G Fowler, Brooks Campbell, Yu Chen, et al. “Digitized adiabatic quantum computing with a superconducting circuit”. Nature 534, 222–226 (2016).
https:/​/​doi.org/​10.1038/​nature17658

[18] John Preskill. “Quantum computing in the nisq era and beyond”. Quantum 2, 79 (2018).
https:/​/​doi.org/​10.22331/​q-2018-08-06-79

[19] 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 (2022).
https:/​/​doi.org/​10.1103/​revmodphys.94.015004

[20] 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”. Nat. Commun. 5, 1–7 (2014).
https:/​/​doi.org/​10.1038/​ncomms5213

[21] Marco Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, et al. “Variational quantum algorithms”. Nat. Rev. Phys.Pages 1–20 (2021).
https:/​/​doi.org/​10.1038/​s42254-021-00348-9

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

[23] Xiao Yuan, Suguru Endo, Qi Zhao, Ying Li, and Simon C Benjamin. “Theory of variational quantum simulation”. Quantum 3, 191 (2019).
https:/​/​doi.org/​10.22331/​q-2019-10-07-191

[24] Tao Xin, Xinfang Nie, Xiangyu Kong, Jingwei Wen, Dawei Lu, and Jun Li. “Quantum pure state tomography via variational hybrid quantum-classical method”. Phys. Rev. Applied 13, 024013 (2020).
https:/​/​doi.org/​10.1103/​PhysRevApplied.13.024013

[25] Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd. “Quantum machine learning”. Nature 549, 195–202 (2017).
https:/​/​doi.org/​10.1038/​nature23474

[26] Srinivasan Arunachalam and Ronald de Wolf. “A survey of quantum learning theory” (2017). arXiv:1701.06806.
arXiv:1701.06806

[27] Carlo Ciliberto, Mark Herbster, Alessandro Davide Ialongo, Massimiliano Pontil, Andrea Rocchetto, Simone Severini, and Leonard Wossnig. “Quantum machine learning: a classical perspective”. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, 20170551 (2018).
https:/​/​doi.org/​10.1098/​rspa.2017.0551

[28] Vedran Dunjko and Hans J Briegel. “Machine learning & artificial intelligence in the quantum domain: a review of recent progress”. Reports on Progress in Physics 81, 074001 (2018).
https:/​/​doi.org/​10.1088/​1361-6633/​aab406

[29] Edward Farhi and Hartmut Neven. “Classification with quantum neural networks on near term processors” (2018). arXiv:1802.06002.
arXiv:1802.06002

[30] Maria Schuld and Nathan Killoran. “Quantum machine learning in feature hilbert spaces”. Phys. Rev. Lett. 122, 040504 (2019).
https:/​/​doi.org/​10.1103/​physrevlett.122.040504

[31] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. “A quantum approximate optimization algorithm” (2014). arXiv:1411.4028.
arXiv:1411.4028

[32] Sergey Bravyi, Alexander Kliesch, Robert Koenig, and Eugene Tang. “Obstacles to variational quantum optimization from symmetry protection”. Phys. Rev. Lett. 125, 260505 (2020).
https:/​/​doi.org/​10.1103/​physrevlett.125.260505

[33] Cristina Cirstoiu, Zoe Holmes, Joseph Iosue, Lukasz Cincio, Patrick J Coles, and Andrew Sornborger. “Variational fast forwarding for quantum simulation beyond the coherence time”. Npj Quantum Inf. 6, 1–10 (2020).
https:/​/​doi.org/​10.1038/​s41534-020-00302-0

[34] Joe Gibbs, Kaitlin Gili, Zoë Holmes, Benjamin Commeau, Andrew Arrasmith, Lukasz Cincio, Patrick J. Coles, and Andrew Sornborger. “Long-time simulations with high fidelity on quantum hardware” (2021). arXiv:2102.04313.
arXiv:2102.04313

[35] Sam McArdle, Tyson Jones, Suguru Endo, Ying Li, Simon C Benjamin, and Xiao Yuan. “Variational ansatz-based quantum simulation of imaginary time evolution”. Npj Quantum Inf. 5, 1–6 (2019).
https:/​/​doi.org/​10.1038/​s41534-019-0187-2

[36] Kentaro Heya, Ken M Nakanishi, Kosuke Mitarai, and Keisuke Fujii. “Subspace variational quantum simulator” (2019). arXiv:1904.08566.
arXiv:1904.08566

[37] Joonsuk Huh, Sarah Mostame, Takatoshi Fujita, Man-Hong Yung, and Alán Aspuru-Guzik. “Linear-algebraic bath transformation for simulating complex open quantum systems”. New J. Phys. 16, 123008 (2014).
https:/​/​doi.org/​10.1088/​1367-2630/​16/​12/​123008

[38] Zixuan Hu, Rongxin Xia, and Sabre Kais. “A quantum algorithm for evolving open quantum dynamics on quantum computing devices”. Sci. Rep. 10, 1–9 (2020).
https:/​/​doi.org/​10.1038/​s41598-020-60321-x

[39] Suguru Endo, Jinzhao Sun, Ying Li, Simon C Benjamin, and Xiao Yuan. “Variational quantum simulation of general processes”. Phys. Rev. Lett. 125, 010501 (2020).
https:/​/​doi.org/​10.1103/​physrevlett.125.010501

[40] Tobias Haug and Kishor Bharti. “Generalized quantum assisted simulator” (2020). arXiv:2011.14737.
arXiv:2011.14737

[41] Johannes Jakob Meyer, Johannes Borregaard, and Jens Eisert. “A variational toolbox for quantum multi-parameter estimation”. Npj Quantum Inf. 7, 1–5 (2021).
https:/​/​doi.org/​10.1038/​s41534-021-00425-y

[42] Johannes Jakob Meyer. “Fisher information in noisy intermediate-scale quantum applications”. Quantum 5, 539 (2021).
https:/​/​doi.org/​10.22331/​q-2021-09-09-539

[43] Jacob L. Beckey, M. Cerezo, Akira Sone, and Patrick J. Coles. “Variational quantum algorithm for estimating the quantum fisher information”. Phys. Rev. Res. 4 (2022).
https:/​/​doi.org/​10.1103/​physrevresearch.4.013083

[44] Raphael Kaubruegger, Pietro Silvi, Christian Kokail, Rick van Bijnen, Ana Maria Rey, Jun Ye, Adam M Kaufman, and Peter Zoller. “Variational spin-squeezing algorithms on programmable quantum sensors”. Phys. Rev. Lett. 123, 260505 (2019).
https:/​/​doi.org/​10.1103/​physrevlett.123.260505

[45] Bálint Koczor, Suguru Endo, Tyson Jones, Yuichiro Matsuzaki, and Simon C Benjamin. “Variational-state quantum metrology”. New J. Phys. 22, 083038 (2020).
https:/​/​doi.org/​10.1088/​1367-2630/​ab965e

[46] Ziqi Ma, Pranav Gokhale, Tian-Xing Zheng, Sisi Zhou, Xiaofei Yu, Liang Jiang, Peter Maurer, and Frederic T. Chong. “Adaptive circuit learning for quantum metrology”. In 2021 IEEE International Conference on Quantum Computing and Engineering (QCE). IEEE (2021).

[47] Tobias Haug and M. S. Kim. “Natural parametrized quantum circuit”. Phys. Rev. A 106, 052611 (2022).
https:/​/​doi.org/​10.1103/​PhysRevA.106.052611

[48] 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” (2021). arXiv:2109.02110.
arXiv:2109.02110

[49] 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

[50] Yunseong Nam, Jwo-Sy Chen, Neal C Pisenti, Kenneth Wright, Conor Delaney, Dmitri Maslov, Kenneth R Brown, Stewart Allen, Jason M Amini, Joel Apisdorf, et al. “Ground-state energy estimation of the water molecule on a trapped-ion quantum computer”. Npj Quantum Inf. 6, 1–6 (2020).
https:/​/​doi.org/​10.1038/​s41534-020-0259-3

[51] Carlos Bravo-Prieto, Josep Lumbreras-Zarapico, Luca Tagliacozzo, and José I. Latorre. “Scaling of variational quantum circuit depth for condensed matter systems”. Quantum 4, 272 (2020).
https:/​/​doi.org/​10.22331/​q-2020-05-28-272

[52] Chufan Lyu, Victor Montenegro, and Abolfazl Bayat. “Accelerated variational algorithms for digital quantum simulation of many-body ground states”. Quantum 4, 324 (2020).
https:/​/​doi.org/​10.22331/​q-2020-09-16-324

[53] Alexey Uvarov, Jacob D Biamonte, and Dmitry Yudin. “Variational quantum eigensolver for frustrated quantum systems”. Phys. Rev. B 102, 075104 (2020).
https:/​/​doi.org/​10.1103/​physrevb.102.075104

[54] Ken N. Okada, Keita Osaki, Kosuke Mitarai, and Keisuke Fujii. “Identification of topological phases using classically-optimized variational quantum eigensolver” (2022). arXiv:2202.02909.
arXiv:2202.02909

[55] Ming-Cheng Chen, Ming Gong, Xiaosi Xu, Xiao Yuan, Jian-Wen Wang, Can Wang, Chong Ying, Jin Lin, Yu Xu, Yulin Wu, et al. “Demonstration of adiabatic variational quantum computing with a superconducting quantum coprocessor”. Phys. Rev. Lett. 125, 180501 (2020).
https:/​/​doi.org/​10.1103/​physrevlett.125.180501

[56] Matthew P Harrigan, Kevin J Sung, Matthew Neeley, Kevin J Satzinger, Frank Arute, Kunal Arya, Juan Atalaya, Joseph C Bardin, Rami Barends, Sergio Boixo, et al. “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor”. Nat. Phys. 17, 332–336 (2021).
https:/​/​doi.org/​10.1038/​s41567-020-01105-y

[57] Guido Pagano, Aniruddha Bapat, Patrick Becker, Katherine S Collins, Arinjoy De, Paul W Hess, Harvey B Kaplan, Antonis Kyprianidis, Wen Lin Tan, Christopher Baldwin, et al. “Quantum approximate optimization of the long-range ising model with a trapped-ion quantum simulator”. Proceedings of the National Academy of Sciences 117, 25396–25401 (2020).
https:/​/​doi.org/​10.1073/​pnas.2006373117

[58] Andrew Zhao, Andrew Tranter, William M Kirby, Shu Fay Ung, Akimasa Miyake, and Peter J Love. “Measurement reduction in variational quantum algorithms”. Phys. Rev. A 101, 062322 (2020).
https:/​/​doi.org/​10.1103/​physreva.101.062322

[59] 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”. J. Chem. Theory Comput. 16, 190–195 (2019).
https:/​/​doi.org/​10.1021/​acs.jctc.9b00791

[60] Vladyslav Verteletskyi, Tzu-Ching Yen, and Artur F Izmaylov. “Measurement optimization in the variational quantum eigensolver using a minimum clique cover”. J. Chem. Phys. 152, 124114 (2020).
https:/​/​doi.org/​10.1063/​1.5141458

[61] Pranav Gokhale, Olivia Angiuli, Yongshan Ding, Kaiwen Gui, Teague Tomesh, Martin Suchara, Margaret Martonosi, and Frederic T. Chong. “$o(n^3)$ measurement cost for variational quantum eigensolver on molecular hamiltonians”. IEEE Transactions on Quantum Engineering 1, 1–24 (2020).
https:/​/​doi.org/​10.1109/​TQE.2020.3035814

[62] Alexis Ralli, Peter J Love, Andrew Tranter, and Peter V Coveney. “Implementation of measurement reduction for the variational quantum eigensolver”. Phys. Rev. Res. 3, 033195 (2021).
https:/​/​doi.org/​10.1103/​physrevresearch.3.033195

[63] Barnaby van Straaten and Bálint Koczor. “Measurement cost of metric-aware variational quantum algorithms”. PRX Quantum 2, 030324 (2021).
https:/​/​doi.org/​10.1103/​prxquantum.2.030324

[64] Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, and Marcello Benedetti. “An initialization strategy for addressing barren plateaus in parametrized quantum circuits”. Quantum 3, 214 (2019).
https:/​/​doi.org/​10.22331/​q-2019-12-09-214

[65] Tyler Volkoff and Patrick J Coles. “Large gradients via correlation in random parameterized quantum circuits”. Quantum Sci. Technol. 6, 025008 (2021).
https:/​/​doi.org/​10.1088/​2058-9565/​abd891

[66] James Stokes, Josh Izaac, Nathan Killoran, and Giuseppe Carleo. “Quantum natural gradient”. Quantum 4, 269 (2020).
https:/​/​doi.org/​10.22331/​q-2020-05-25-269

[67] Sami Khairy, Ruslan Shaydulin, Lukasz Cincio, Yuri Alexeev, and Prasanna Balaprakash. “Learning to optimize variational quantum circuits to solve combinatorial problems”. Proceedings of the AAAI Conference on Artificial Intelligence 34, 2367–2375 (2020).
https:/​/​doi.org/​10.1609/​aaai.v34i03.5616

[68] András Gilyén, Srinivasan Arunachalam, and Nathan Wiebe. “Optimizing quantum optimization algorithms via faster quantum gradient computation”. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms. Pages 1425–1444. Society for Industrial and Applied Mathematics (2019).
https:/​/​doi.org/​10.1137/​1.9781611975482.87

[69] Mateusz Ostaszewski, Lea M. Trenkwalder, Wojciech Masarczyk, Eleanor Scerri, and Vedran Dunjko. “Reinforcement learning for optimization of variational quantum circuit architectures” (2021). arXiv:2103.16089.
arXiv:2103.16089

[70] Mohammad Pirhooshyaran and Tamas Terlaky. “Quantum circuit design search” (2020). arXiv:2012.04046.
arXiv:2012.04046

[71] Thomas Fösel, Murphy Yuezhen Niu, Florian Marquardt, and Li Li. “Quantum circuit optimization with deep reinforcement learning” (2021). arXiv:2103.07585.
arXiv:2103.07585

[72] Arthur G. Rattew, Shaohan Hu, Marco Pistoia, Richard Chen, and Steve Wood. “A domain-agnostic, noise-resistant, hardware-efficient evolutionary variational quantum eigensolver” (2019). arXiv:1910.09694.
arXiv:1910.09694

[73] D. Chivilikhin, A. Samarin, V. Ulyantsev, I. Iorsh, A. R. Oganov, and O. Kyriienko. “Mog-vqe: Multiobjective genetic variational quantum eigensolver” (2020). arXiv:2007.04424.
arXiv:2007.04424

[74] Yuhan Huang, Qingyu Li, Xiaokai Hou, Rebing Wu, Man-Hong Yung, Abolfazl Bayat, and Xiaoting Wang. “Robust resource-efficient quantum variational ansatz through an evolutionary algorithm”. Phys. Rev. A 105, 052414 (2022).
https:/​/​doi.org/​10.1103/​PhysRevA.105.052414

[75] János K Asbóth, László Oroszlány, and András Pályi. “The su-schrieffer-heeger (ssh) model”. In A Short Course on Topological Insulators. Pages 1–22. Springer (2016).
https:/​/​doi.org/​10.1007/​978-3-319-25607-8

[76] Ken M Nakanishi, Kosuke Mitarai, and Keisuke Fujii. “Subspace-search variational quantum eigensolver for excited states”. Phys. Rev. Res. 1, 033062 (2019).
https:/​/​doi.org/​10.1103/​physrevresearch.1.033062

[77] Oscar Higgott, Daochen Wang, and Stephen Brierley. “Variational quantum computation of excited states”. Quantum 3, 156 (2019).
https:/​/​doi.org/​10.22331/​q-2019-07-01-156

[78] Jarrod R McClean, Mollie E Kimchi-Schwartz, Jonathan Carter, and Wibe A De Jong. “Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states”. Phys. Rev. A 95, 042308 (2017).
https:/​/​doi.org/​10.1103/​physreva.95.042308

[79] Raffaele Santagati, Jianwei Wang, Antonio A Gentile, Stefano Paesani, Nathan Wiebe, Jarrod R McClean, Sam Morley-Short, Peter J Shadbolt, Damien Bonneau, Joshua W Silverstone, et al. “Witnessing eigenstates for quantum simulation of hamiltonian spectra”. Sci. Adv. 4, eaap9646 (2018).
https:/​/​doi.org/​10.1126/​sciadv.aap9646

[80] Walter Greiner and Berndt Müller. “Quantum mechanics: symmetries”. Springer Science & Business Media. (2012).
https:/​/​doi.org/​10.1007/​978-3-662-00902-4

[81] Roy McWeeny. “Symmetry: An introduction to group theory and its applications”. Courier Corporation. (2002).

[82] Ramiro Sagastizabal, Xavier Bonet-Monroig, Malay Singh, M Adriaan Rol, CC Bultink, Xiang Fu, CH Price, VP Ostroukh, N Muthusubramanian, A Bruno, et al. “Experimental error mitigation via symmetry verification in a variational quantum eigensolver”. Phys. Rev. A 100, 010302 (2019).
https:/​/​doi.org/​10.1103/​physreva.100.010302

[83] Johannes Jakob Meyer, Marian Mularski, Elies Gil-Fuster, Antonio Anna Mele, Francesco Arzani, Alissa Wilms, and Jens Eisert. “Exploiting symmetry in variational quantum machine learning” (2022). arXiv:2205.06217.
arXiv:2205.06217

[84] Jin-Guo Liu, Yi-Hong Zhang, Yuan Wan, and Lei Wang. “Variational quantum eigensolver with fewer qubits”. Phys. Rev. Res. 1, 023025 (2019).
https:/​/​doi.org/​10.1103/​physrevresearch.1.023025

[85] Panagiotis Kl Barkoutsos, Jerome F Gonthier, Igor Sokolov, Nikolaj Moll, Gian Salis, Andreas Fuhrer, Marc Ganzhorn, Daniel J Egger, Matthias Troyer, Antonio Mezzacapo, et al. “Quantum algorithms for electronic structure calculations: Particle-hole hamiltonian and optimized wave-function expansions”. Phys. Rev. A 98, 022322 (2018).
https:/​/​doi.org/​10.1103/​physreva.98.022322

[86] Hefeng Wang, S Ashhab, and Franco Nori. “Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer”. Phys. Rev. A 79, 042335 (2009).
https:/​/​doi.org/​10.1103/​physreva.79.042335

[87] Kazuhiro Seki, Tomonori Shirakawa, and Seiji Yunoki. “Symmetry-adapted variational quantum eigensolver”. Phys. Rev. A 101, 052340 (2020).
https:/​/​doi.org/​10.1103/​physreva.101.052340

[88] 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 Inf. 6, 10 (2020).
https:/​/​doi.org/​10.1038/​s41534-019-0240-1

[89] George S Barron, Bryan T Gard, Orien J Altman, Nicholas J Mayhall, Edwin Barnes, and Sophia E Economou. “Preserving symmetries for variational quantum eigensolvers in the presence of noise”. Phys. Rev. Appl. 16, 034003 (2021).
https:/​/​doi.org/​10.1103/​physrevapplied.16.034003

[90] Feng Zhang, Niladri Gomes, Noah F Berthusen, Peter P Orth, Cai-Zhuang Wang, Kai-Ming Ho, and Yong-Xin Yao. “Shallow-circuit variational quantum eigensolver based on symmetry-inspired hilbert space partitioning for quantum chemical calculations”. Phys. Rev. Res. 3, 013039 (2021).
https:/​/​doi.org/​10.1103/​physrevresearch.3.013039

[91] Han Zheng, Zimu Li, Junyu Liu, Sergii Strelchuk, and Risi Kondor. “Speeding up learning quantum states through group equivariant convolutional quantum ansätze” (2021). arXiv:2112.07611.
arXiv:2112.07611

[92] Ilya G Ryabinkin, Scott N Genin, and Artur F Izmaylov. “Constrained variational quantum eigensolver: Quantum computer search engine in the fock space”. J. Chem. Theory Comput. 15, 249–255 (2018).
https:/​/​doi.org/​10.1021/​acs.jctc.8b00943

[93] Andrew G Taube and Rodney J Bartlett. “New perspectives on unitary coupled-cluster theory”. International journal of quantum chemistry 106, 3393–3401 (2006).
https:/​/​doi.org/​10.1002/​qua.21198

[94] Peter JJ O’Malley, Ryan Babbush, Ian D Kivlichan, Jonathan Romero, Jarrod R McClean, Rami Barends, Julian Kelly, Pedram Roushan, Andrew Tranter, Nan Ding, et al. “Scalable quantum simulation of molecular energies”. Phys. Rev. X 6, 031007 (2016).
https:/​/​doi.org/​10.1103/​physrevx.6.031007

[95] 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 Sci. Technol. 4, 014008 (2018).
https:/​/​doi.org/​10.1088/​2058-9565/​aad3e4

[96] Dave Wecker, Matthew B Hastings, and Matthias Troyer. “Progress towards practical quantum variational algorithms”. Phys. Rev. A 92, 042303 (2015).
https:/​/​doi.org/​10.1103/​physreva.92.042303

[97] Dong C. Liu and Jorge Nocedal. “On the limited memory bfgs method for large scale optimization”. Mathematical Programming 45, 503–528 (1989).
https:/​/​doi.org/​10.1007/​BF01589116

[98] Jarrod R McClean, Sergio Boixo, Vadim N Smelyanskiy, Ryan Babbush, and Hartmut Neven. “Barren plateaus in quantum neural network training landscapes”. Nat. Commun. 9, 1–6 (2018).
https:/​/​doi.org/​10.1038/​s41467-018-07090-4

[99] Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, and Andreas Winter. “Unitary 2-designs from random x-and z-diagonal unitaries”. J. Math. Phys. 58, 052203 (2017).
https:/​/​doi.org/​10.1063/​1.4983266

[100] Farrokh Vatan and Colin Williams. “Optimal quantum circuits for general two-qubit gates”. Phys. Rev. A 69, 032315 (2004).
https:/​/​doi.org/​10.1103/​PhysRevA.69.032315

[101] Vojtěch Havlíček, Antonio D Córcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, and Jay M Gambetta. “Supervised learning with quantum-enhanced feature spaces”. Nature 567, 209–212 (2019).
https:/​/​doi.org/​10.1038/​s41586-019-0980-2

[102] Juan Carlos Garcia-Escartin and Pedro Chamorro-Posada. “Swap test and hong-ou-mandel effect are equivalent”. Phys. Rev. A 87, 052330 (2013).
https:/​/​doi.org/​10.1103/​physreva.87.052330

[103] Lukasz Cincio, Yiğit Subaşı, Andrew T Sornborger, and Patrick J Coles. “Learning the quantum algorithm for state overlap”. New J. Phys. 20, 113022 (2018).
https:/​/​doi.org/​10.1088/​1367-2630/​aae94a

[104] Kohdai Kuroiwa and Yuya O Nakagawa. “Penalty methods for a variational quantum eigensolver”. Phys. Rev. Res. 3, 013197 (2021).
https:/​/​doi.org/​10.1103/​physrevresearch.3.013197

[105] Chufan Lyu, Xiaoyu Tang, Junning Li, Xusheng Xu, Man-Hong Yung, and Abolfazl Bayat. “Variational quantum simulation of long-range interacting systems” (2022). arXiv:2203.14281.
arXiv:2203.14281

[106] Chufan Lyu. “Codes for symmetry enhanced variational quantum spin eigensolver”. https:/​/​gitee.com/​mindspore/​mindquantum/​tree/​research/​paper_with_code/​symmetry_enhanced_variational_quantum_spin_eigensolver (2022).
https:/​/​gitee.com/​mindspore/​mindquantum/​tree/​research/​paper_with_code/​symmetry_enhanced_variational_quantum_spin_eigensolver

Cited by

[1] Yuhan Huang, Qingyu Li, Xiaokai Hou, Rebing Wu, Man-Hong Yung, Abolfazl Bayat, and Xiaoting Wang, “Robust resource-efficient quantum variational ansatz through an evolutionary algorithm”, Physical Review A 105 5, 052414 (2022).

[2] Margarite L. LaBorde and Mark M. Wilde, “Quantum Algorithms for Testing Hamiltonian Symmetry”, Physical Review Letters 129 16, 160503 (2022).

[3] Chufan Lyu, Xiaoyu Tang, Junning Li, Xusheng Xu, Man-Hong Yung, and Abolfazl Bayat, “Variational quantum simulation of long-range interacting systems”, arXiv:2203.14281.

[4] Arunava Majumder, Dylan Lewis, and Sougato Bose, “Variational Quantum Circuits for Multi-Qubit Gate Automata”, arXiv:2209.00139.

[5] Raphael César de Souza Pimenta and Anibal Thiago Bezerra, “Revisiting semiconductor bulk hamiltonians using quantum computers”, arXiv:2208.10323.

The above citations are from SAO/NASA ADS (last updated successfully 2023-01-21 01:01:04). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref’s cited-by service no data on citing works was found (last attempt 2023-01-21 01:01:02).

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