Structure optimization for parameterized quantum circuits

Mateusz Ostaszewski; Edward Grant; Marcello Benedetti

doi:10.22331/q-2021-01-28-391

Structure optimization for parameterized quantum circuits

Mateusz Ostaszewski^1,2, Edward Grant^2,3, and Marcello Benedetti^2,4

¹Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, Bałtycka 5, 44-100 Gliwice, Poland
²Department of Computer Science, University College London, WC1E 6BT London, United Kingdom
³Rahko Limited, N4 3JP London, United Kingdom
⁴Cambridge Quantum Computing Limited, CB2 1UB Cambridge, United Kingdom

Published:	2021-01-28, volume 5, page 391
Eprint:	arXiv:1905.09692v3
Doi:	https://doi.org/10.22331/q-2021-01-28-391
Citation:	Quantum 5, 391 (2021).

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Abstract

We propose an efficient method for simultaneously optimizing both the structure and parameter values of quantum circuits with only a small computational overhead. Shallow circuits that use structure optimization perform significantly better than circuits that use parameter updates alone, making this method particularly suitable for noisy intermediate-scale quantum computers. We demonstrate the method for optimizing a variational quantum eigensolver for finding the ground states of Lithium Hydride and the Heisenberg model in simulation, and for finding the ground state of Hydrogen gas on the IBM Melbourne quantum computer.

► BibTeX data

@article{Ostaszewski2021structure,
  doi = {10.22331/q-2021-01-28-391},
  url = {https://doi.org/10.22331/q-2021-01-28-391},
  title = {Structure optimization for parameterized quantum circuits},
  author = {Ostaszewski, Mateusz and Grant, Edward and Benedetti, Marcello},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {391},
  month = jan,
  year = {2021}
}

► References

[1] 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, 4213 (2014).
https://doi.org/10.1038/ncomms5213

[2] E. Farhi, J. Goldstone, S. Gutmann, and H. Neven, ``Quantum Algorithms for Fixed Qubit Architectures'' (2017).
arXiv:1703.06199

[3] Edward Farhiand Hartmut Neven ``Classification with Quantum Neural Networks on Near Term Processors'' (2018).
arXiv:1802.06002

[4] Marcello Benedetti, Delfina Garcia-Pintos, Oscar Perdomo, Vicente Leyton-Ortega, Yunseong Nam, and Alejandro Perdomo-Ortiz, ``A generative modeling approach for benchmarking and training shallow quantum circuits'' npj Quantum Information 5 (2019).
https://doi.org/10.1038/s41534-019-0157-8

[5] Marcello Benedetti, Edward Grant, Leonard Wossnig, and Simone Severini, ``Adversarial quantum circuit learning for pure state approximation'' New Journal of Physics 21, 043023 (2019).
https://doi.org/10.1088/1367-2630/ab14b5

[6] Hongxiang Chen, Leonard Wossnig, Simone Severini, Hartmut Neven, and Masoud Mohseni, ``Universal discriminative quantum neural networks'' (2018).
arXiv:1805.08654

[7] Edward Grant, Marcello Benedetti, Shuxiang Cao, Andrew Hallam, Joshua Lockhart, Vid Stojevic, Andrew G Green, and Simone Severini, ``Hierarchical quantum classifiers'' npj Quantum Information 4, 1–8 (2018).
https://doi.org/10.1038/s41534-018-0116-9

[8] Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini, ``Parameterized quantum circuits as machine learning models'' Quantum Science and Technology 4, 043001 (2019).
https://doi.org/10.1088/2058-9565/ab4eb5

[9] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, ``Quantum circuit learning'' Phys. Rev. A 98, 032309 (2018).
https://doi.org/10.1103/PhysRevA.98.032309

[10] 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

[11] Kosuke Mitarai, Tennin Yan, and Keisuke Fujii, ``Generalization of the Output of a Variational Quantum Eigensolver by Parameter Interpolation with a Low-depth Ansatz'' Phys. Rev. Applied 11, 044087 (2019).
https://doi.org/10.1103/PhysRevApplied.11.044087

[12] Artur F. Izmaylov, Tzu-Ching Yen, and Ilya G. Ryabinkin, ``Revising the measurement process in the variational quantum eigensolver: is it possible to reduce the number of separately measured operators?'' Chem. Sci. 10, 3746–3755 (2019).
https://doi.org/10.1039/C8SC05592K

[13] 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

[14] Rui Li, Unai Alvarez-Rodriguez, Lucas Lamata, and Enrique Solano, ``Approximate Quantum Adders with Genetic Algorithms: An IBM Quantum Experience'' Quantum Measurements and Quantum Metrology 4, 1 –7 (26 Jul. 2017).
https://doi.org/10.1515/qmetro-2017-0001
https://www.degruyter.com/view/journals/qmetro/4/1/article-p1.xml

[15] 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 (2019).
https://doi.org/10.1038/s41467-019-10988-2

[16] Ken M. Nakanishi, Keisuke Fujii, and Synge Todo, ``Sequential minimal optimization for quantum-classical hybrid algorithms'' Phys. Rev. Research 2, 043158 (2020).
https://doi.org/10.1103/PhysRevResearch.2.043158

[17] Robert M. Parrish, Joseph T. Iosue, Asier Ozaeta, and Peter L. McMahon, ``A Jacobi Diagonalization and Anderson Acceleration Algorithm For Variational Quantum Algorithm Parameter Optimization'' (2019).
arXiv:1904.03206

[18] D.P. Bertsekas ``Nonlinear Programming'' Athena Scientific (1999).

[19] Ankan Sahaand Ambuj Tewari ``On the Finite Time Convergence of Cyclic Coordinate Descent Methods'' (2010).
arXiv:1005.2146

[20] Stephen J Wright ``Coordinate descent algorithms'' Mathematical Programming 151, 3–34 (2015).
https://doi.org/10.1007/s10107-015-0892-3

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

[22] Héctor Abraham, Ismail Yunus Akhalwaya, Gadi Aleksandrowicz, Thomas Alexander, Eli Arbel, Abraham Asfaw, Carlos Azaustre, Panagiotis Barkoutsos, George Barron, and Luciano Bello, ``Qiskit: An Open-source Framework for Quantum Computing'' (2019).
https://doi.org/10.5281/zenodo.2562110

[23] Sukin Sim, Peter D. Johnson, and Alán Aspuru-Guzik, ``Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum-Classical Algorithms'' Advanced Quantum Technologies 2, 1900070 (2019).
https://doi.org/10.1002/qute.201900070

[24] J. C. Spall ``Multivariate stochastic approximation using a simultaneous perturbation gradient approximation'' IEEE Transactions on Automatic Control 37, 332–341 (1992).
https://doi.org/10.1109/9.119632

[25] Diederik P. Kingmaand Jimmy Ba ``Adam: A Method for Stochastic Optimization'' (2014).
arXiv:1412.6980

[26] Anders Sørensenand Klaus Mølmer ``Quantum Computation with Ions in Thermal Motion'' Phys. Rev. Lett. 82, 1971–1974 (1999).
https://doi.org/10.1103/PhysRevLett.82.1971

[27] Norbert M. Linke, Dmitri Maslov, Martin Roetteler, Shantanu Debnath, Caroline Figgatt, Kevin A. Landsman, Kenneth Wright, and Christopher Monroe, ``Experimental comparison of two quantum computing architectures'' Proceedings of the National Academy of Sciences 114, 3305–3310 (2017).
https://doi.org/10.1073/pnas.1618020114
https://www.pnas.org/content/114/13/3305

Cited by

[1] Ran-Yi-Liu Chen, Ben-Chi Zhao, Zhi-Xin Song, Xuan-Qiang Zhao, Kun Wang, and Xin Wang, "Hybrid quantum-classical algorithms: Foundation, design and applications", Acta Physica Sinica 70 21, 210302 (2021).

[2] Roeland Wiersema and Nathan Killoran, "Optimizing quantum circuits with Riemannian gradient flow", Physical Review A 107 6, 062421 (2023).

[3] M. Bilkis, M. Cerezo, Guillaume Verdon, Patrick J. Coles, and Lukasz Cincio, "A semi-agnostic ansatz with variable structure for variational quantum algorithms", Quantum Machine Intelligence 5 2, 43 (2023).

[4] Dylan Herman, Rudy Raymond, Muyuan Li, Nicolas Robles, Antonio Mezzacapo, and Marco Pistoia, "Expressivity of Variational Quantum Machine Learning on the Boolean Cube", IEEE Transactions on Quantum Engineering 4, 1 (2023).

[5] 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).

[6] Nam Nguyen and Kwang-Cheng Chen, "Quantum Embedding Search for Quantum Machine Learning", IEEE Access 10, 41444 (2022).

[7] Ranyiliu Chen, Benchi Zhao, and Xin Wang, "Near-Term Efficient Quantum Algorithms for Entanglement Analysis", Physical Review Applied 20 2, 024071 (2023).

[8] Noah F. Berthusen, Thaís V. Trevisan, Thomas Iadecola, and Peter P. Orth, "Quantum dynamics simulations beyond the coherence time on noisy intermediate-scale quantum hardware by variational Trotter compression", Physical Review Research 4 2, 023097 (2022).

[9] Nikita Astrakhantsev, Sheng-Hsuan Lin, Frank Pollmann, and Adam Smith, "Time evolution of uniform sequential circuits", Physical Review Research 5 3, 033187 (2023).

[10] Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, and Hong Yao, "Differentiable quantum architecture search", Quantum Science and Technology 7 4, 045023 (2022).

[11] Xin Wang, Zhixin Song, and Youle Wang, "Variational Quantum Singular Value Decomposition", Quantum 5, 483 (2021).

[12] Xavier Bonet-Monroig, Hao Wang, Diederick Vermetten, Bruno Senjean, Charles Moussa, Thomas Bäck, Vedran Dunjko, and Thomas E. O'Brien, "Performance comparison of optimization methods on variational quantum algorithms", Physical Review A 107 3, 032407 (2023).

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

[14] Bálint Koczor and Simon C. Benjamin, "Quantum analytic descent", Physical Review Research 4 2, 023017 (2022).

[15] Thomas Ayral, Pauline Besserve, Denis Lacroix, and Edgar Andres Ruiz Guzman, "Quantum computing with and for many-body physics", The European Physical Journal A 59 10, 227 (2023).

[16] Kirill Plekhanov, Matthias Rosenkranz, Mattia Fiorentini, and Michael Lubasch, "Variational quantum amplitude estimation", Quantum 6, 670 (2022).

[17] Stefan H. Sack, Raimel A. Medina, Alexios A. Michailidis, Richard Kueng, and Maksym Serbyn, "Avoiding Barren Plateaus Using Classical Shadows", PRX Quantum 3 2, 020365 (2022).

[18] Carlos Bravo-Prieto, Julien Baglio, Marco Cè, Anthony Francis, Dorota M. Grabowska, and Stefano Carrazza, "Style-based quantum generative adversarial networks for Monte Carlo events", Quantum 6, 777 (2022).

[19] Ruilin Liu, Sebastián V. Romero, Izaskun Oregi, Eneko Osaba, Esther Villar-Rodriguez, and Yue Ban, "Digital Quantum Simulation and Circuit Learning for the Generation of Coherent States", Entropy 24 11, 1529 (2022).

[20] Kaito Wada, Rudy Raymond, Yu-ya Ohnishi, Eriko Kaminishi, Michihiko Sugawara, Naoki Yamamoto, and Hiroshi C. Watanabe, "Simulating time evolution with fully optimized single-qubit gates on parametrized quantum circuits", Physical Review A 105 6, 062421 (2022).

[21] Li Ding and Lee Spector, Proceedings of the Genetic and Evolutionary Computation Conference Companion 2190 (2022) ISBN:9781450392686.

[22] Zhimin He, Chuangtao Chen, Lvzhou Li, Shenggen Zheng, and Haozhen Situ, "Quantum Architecture Search with Meta‐Learning", Advanced Quantum Technologies 5 8, 2100134 (2022).

[23] Jinkai Tian, Xiaoyu Sun, Yuxuan Du, Shanshan Zhao, Qing Liu, Kaining Zhang, Wei Yi, Wanrong Huang, Chaoyue Wang, Xingyao Wu, Min-Hsiu Hsieh, Tongliang Liu, Wenjing Yang, and Dacheng Tao, "Recent Advances for Quantum Neural Networks in Generative Learning", IEEE Transactions on Pattern Analysis and Machine Intelligence 1 (2023).

[24] Shi-Xin Zhang, Jonathan Allcock, Zhou-Quan Wan, Shuo Liu, Jiace Sun, Hao Yu, Xing-Han Yang, Jiezhong Qiu, Zhaofeng Ye, Yu-Qin Chen, Chee-Kong Lee, Yi-Cong Zheng, Shao-Kai Jian, Hong Yao, Chang-Yu Hsieh, and Shengyu Zhang, "TensorCircuit: a Quantum Software Framework for the NISQ Era", Quantum 7, 912 (2023).

[25] Manpreet Singh Jattana, Fengping Jin, Hans De Raedt, and Kristel Michielsen, "Assessment of the Variational Quantum Eigensolver: Application to the Heisenberg Model", Frontiers in Physics 10, 907160 (2022).

[26] Bhaskara Narottama and Sonia Aïssa, 2023 IEEE 34th Annual International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) 1 (2023) ISBN:978-1-6654-6483-3.

[27] Thomas Hubregtsen, Frederik Wilde, Shozab Qasim, and Jens Eisert, "Single-component gradient rules for variational quantum algorithms", Quantum Science and Technology 7 3, 035008 (2022).

[28] Agustin Silva, Omar Gustavo Zabaleta, and Constancio Miguel Arizmendi, "Learning Mixed Strategies in Quantum Games with Imperfect Information", Quantum Reports 4 4, 462 (2022).

[29] Zhimin He, Maijie Deng, Shenggen Zheng, Lvzhou Li, and Haozhen Situ, "GSQAS: Graph Self-supervised Quantum Architecture Search", Physica A: Statistical Mechanics and its Applications 630, 129286 (2023).

[30] A. M. Romero, J. Engel, Ho Lun Tang, and Sophia E. Economou, "Solving nuclear structure problems with the adaptive variational quantum algorithm", Physical Review C 105 6, 064317 (2022).

[31] Péter Mernyei, Konstantinos Meichanetzidis, and İsmail İlkan Ceylan, "Equivariant quantum graph circuits: constructions for universal approximation over graphs", Quantum Machine Intelligence 5 1, 6 (2023).

[32] Bojia Duan and Chang-Yu Hsieh, "Hamiltonian-based data loading with shallow quantum circuits", Physical Review A 106 5, 052422 (2022).

[33] Shiro Tamiya and Hayata Yamasaki, "Stochastic gradient line Bayesian optimization for efficient noise-robust optimization of parameterized quantum circuits", npj Quantum Information 8 1, 90 (2022).

[34] Yuxuan Du, Tao Huang, Shan You, Min-Hsiu Hsieh, and Dacheng Tao, "Quantum circuit architecture search for variational quantum algorithms", npj Quantum Information 8 1, 62 (2022).

[35] Trung Q. Duong, Long D. Nguyen, Bhaskara Narottama, James Adu Ansere, Dang Van Huynh, and Hyundong Shin, "Quantum-Inspired Real-Time Optimization for 6G Networks: Opportunities, Challenges, and the Road Ahead", IEEE Open Journal of the Communications Society 3, 1347 (2022).

[36] Benjamin Jaderberg, Alexander Eisfeld, Dieter Jaksch, and Sarah Mostame, "Recompilation-enhanced simulation of electron–phonon dynamics on IBM quantum computers", New Journal of Physics 24 9, 093017 (2022).

[37] Zhimin He, Xuefen Zhang, Chuangtao Chen, Zhiming Huang, Yan Zhou, and Haozhen Situ, "A GNN-based predictor for quantum architecture search", Quantum Information Processing 22 2, 128 (2023).

[38] S. Mangini, F. Tacchino, D. Gerace, D. Bajoni, and C. Macchiavello, "Quantum computing models for artificial neural networks", Europhysics Letters 134 1, 10002 (2021).

[39] Weikang Li and Dong-Ling Deng, "Recent advances for quantum classifiers", Science China Physics, Mechanics & Astronomy 65 2, 220301 (2022).

[40] Jules Tilly, P. V. Sriluckshmy, Akashkumar Patel, Enrico Fontana, Ivan Rungger, Edward Grant, Robert Anderson, Jonathan Tennyson, and George H. Booth, "Reduced density matrix sampling: Self-consistent embedding and multiscale electronic structure on current generation quantum computers", Physical Review Research 3 3, 033230 (2021).

[41] Brian Coyle, Mina Doosti, Elham Kashefi, and Niraj Kumar, "Progress toward practical quantum cryptanalysis by variational quantum cloning", Physical Review A 105 4, 042604 (2022).

[42] Kentaro Yamamoto, David Zsolt Manrique, Irfan T. Khan, Hideaki Sawada, and David Muñoz Ramo, "Quantum hardware calculations of periodic systems with partition-measurement symmetry verification: Simplified models of hydrogen chain and iron crystals", Physical Review Research 4 3, 033110 (2022).

[43] F. Barratt, James Dborin, Matthias Bal, Vid Stojevic, Frank Pollmann, and A. G. Green, "Parallel quantum simulation of large systems on small NISQ computers", npj Quantum Information 7 1, 79 (2021).

[44] Matt Lourens, Ilya Sinayskiy, Daniel K. Park, Carsten Blank, and Francesco Petruccione, "Hierarchical quantum circuit representations for neural architecture search", npj Quantum Information 9 1, 79 (2023).

[45] Sergio Altares-López, Angela Ribeiro, and Juan José García-Ripoll, "Automatic design of quantum feature maps", Quantum Science and Technology 6 4, 045015 (2021).

[46] Maria Schuld, Ryan Sweke, and Johannes Jakob Meyer, "Effect of data encoding on the expressive power of variational quantum-machine-learning models", Physical Review A 103 3, 032430 (2021).

[47] Yuki Sato, Hiroshi C. Watanabe, Rudy Raymond, Ruho Kondo, Kaito Wada, Katsuhiro Endo, Michihiko Sugawara, and Naoki Yamamoto, "Variational quantum algorithm for generalized eigenvalue problems and its application to the finite-element method", Physical Review A 108 2, 022429 (2023).

[48] Hugh G. A. Burton, Daniel Marti-Dafcik, David P. Tew, and David J. Wales, "Exact electronic states with shallow quantum circuits from global optimisation", npj Quantum Information 9 1, 75 (2023).

[49] David Wierichs, Josh Izaac, Cody Wang, and Cedric Yen-Yu Lin, "General parameter-shift rules for quantum gradients", Quantum 6, 677 (2022).

[50] Zhimin He, Junjian Su, Chuangtao Chen, Minghua Pan, and Haozhen Situ, "Search space pruning for quantum architecture search", The European Physical Journal Plus 137 4, 491 (2022).

[51] Tatiana A. Bespalova and Oleksandr Kyriienko, "Hamiltonian Operator Approximation for Energy Measurement and Ground-State Preparation", PRX Quantum 2 3, 030318 (2021).

[52] Javier Mancilla and Christophe Pere, "A Preprocessing Perspective for Quantum Machine Learning Classification Advantage in Finance Using NISQ Algorithms", Entropy 24 11, 1656 (2022).

[53] Aikaterini Gratsea and Patrick Huembeli, "The effect of the processing and measurement operators on the expressive power of quantum models", Quantum Machine Intelligence 5 2, 32 (2023).

[54] Davide Castaldo, Soran Jahangiri, Alain Delgado, and Stefano Corni, "Quantum Simulation of Molecules in Solution", Journal of Chemical Theory and Computation 18 12, 7457 (2022).

[55] Hiroshi C. Watanabe, Rudy Raymond, Yu-Ya Ohnishi, Eriko Kaminishi, and Michihiko Sugawara, "Optimizing Parameterized Quantum Circuits With Free-Axis Single-Qubit Gates", IEEE Transactions on Quantum Engineering 4, 1 (2023).

[56] Anqi 安琪 Zhang 张, Kelun 可伦 Wang 王, Yihua 逸华 Wu 吴, and Sheng-Mei 生妹 Zhao 赵, "Single-qubit quantum classifier based on gradient-free optimization algorithm", Chinese Physics B 32 10, 100308 (2023).

[57] P. Besserve and T. Ayral, "Unraveling correlated material properties with noisy quantum computers: Natural orbitalized variational quantum eigensolving of extended impurity models within a slave-boson approach", Physical Review B 105 11, 115108 (2022).

[58] Tomislav Piskor, Jan-Michael Reiner, Sebastian Zanker, Nicolas Vogt, Michael Marthaler, Frank K. Wilhelm, and Florian G. Eich, "Using gradient-based algorithms to determine ground-state energies on a quantum computer", Physical Review A 105 6, 062415 (2022).

[59] Maria Schuld and Nathan Killoran, "Is Quantum Advantage the Right Goal for Quantum Machine Learning?", PRX Quantum 3 3, 030101 (2022).

[60] Marcello Benedetti, Mattia Fiorentini, and Michael Lubasch, "Hardware-efficient variational quantum algorithms for time evolution", Physical Review Research 3 3, 033083 (2021).

[61] Hrushikesh Patil, Yulun Wang, and Predrag S. Krstić, "Variational quantum linear solver with a dynamic ansatz", Physical Review A 105 1, 012423 (2022).

[62] Hiroshi C. Watanabe, Rudy Raymond, Yu-Ya Ohnishi, Eriko Kaminishi, and Michihiko Sugawara, 2021 IEEE International Conference on Quantum Computing and Engineering (QCE) 100 (2021) ISBN:978-1-6654-1691-7.

[63] Adam Glos, Aleksandra Krawiec, and Zoltán Zimborás, "Space-efficient binary optimization for variational quantum computing", npj Quantum Information 8 1, 39 (2022).

[64] Maijie Deng, Zhimin He, Shenggen Zheng, Yan Zhou, Fei Zhang, and Haozhen Situ, "A progressive predictor-based quantum architecture search with active learning", The European Physical Journal Plus 138 10, 905 (2023).

[65] Bowen Li, Ting Li, and Fei Li, "A design method for efficient variational quantum models based on specific Pauli axis", Quantum Information Processing 22 10, 387 (2023).

[66] Katsuhiro Endo, Yuki Sato, Rudy Raymond, Kaito Wada, Naoki Yamamoto, and Hiroshi C. Watanabe, "Optimal parameter configurations for sequential optimization of the variational quantum eigensolver", Physical Review Research 5 4, 043136 (2023).

[67] Asahi Chikaoka and Haozhao Liang, "Quantum computing for the Lipkin model with unitary coupled cluster and structure learning ansatz * ", Chinese Physics C 46 2, 024106 (2022).

[68] Yuto Takaki, Kosuke Mitarai, Makoto Negoro, Keisuke Fujii, and Masahiro Kitagawa, "Learning temporal data with a variational quantum recurrent neural network", Physical Review A 103 5, 052414 (2021).

[69] Hongxiang Chen, Max Nusspickel, Jules Tilly, and George H. Booth, "Variational quantum eigensolver for dynamic correlation functions", Physical Review A 104 3, 032405 (2021).

[70] L. C. G. Govia, C. Poole, M. Saffman, and H. K. Krovi, "Freedom of the mixer rotation axis improves performance in the quantum approximate optimization algorithm", Physical Review A 104 6, 062428 (2021).

[71] Li Ding and Lee Spector, "Multi-Objective Evolutionary Architecture Search for Parameterized Quantum Circuits", Entropy 25 1, 93 (2023).

[72] Manpreet Singh Jattana, Fengping Jin, Hans De Raedt, and Kristel Michielsen, "Improved Variational Quantum Eigensolver Via Quasidynamical Evolution", Physical Review Applied 19 2, 024047 (2023).

[73] David Amaro, Carlo Modica, Matthias Rosenkranz, Mattia Fiorentini, Marcello Benedetti, and Michael Lubasch, "Filtering variational quantum algorithms for combinatorial optimization", Quantum Science and Technology 7 1, 015021 (2022).

[74] Nils Herrmann, Daanish Arya, Marcus W. Doherty, Angus Mingare, Jason C. Pillay, Florian Preis, and Stefan Prestel, 2023 IEEE International Conference on Quantum Software (QSW) 162 (2023) ISBN:979-8-3503-0479-4.

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

[76] 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", Reviews of Modern Physics 94 1, 015004 (2022).

[77] Marcello Benedetti, Erika Lloyd, Stefan Sack, and Mattia Fiorentini, "Parameterized quantum circuits as machine learning models", Quantum Science and Technology 4 4, 043001 (2019).

[78] Ken M. Nakanishi, Keisuke Fujii, and Synge Todo, "Sequential minimal optimization for quantum-classical hybrid algorithms", Physical Review Research 2 4, 043158 (2020).

[79] Arthur G. Rattew, Shaohan Hu, Marco Pistoia, Richard Chen, and Steve Wood, "A Domain-agnostic, Noise-resistant, Hardware-efficient Evolutionary Variational Quantum Eigensolver", arXiv:1910.09694, (2019).

[80] Ryan LaRose and Brian Coyle, "Robust data encodings for quantum classifiers", Physical Review A 102 3, 032420 (2020).

[81] Chris Cade, Lana Mineh, Ashley Montanaro, and Stasja Stanisic, "Strategies for solving the Fermi-Hubbard model on near-term quantum computers", Physical Review B 102 23, 235122 (2020).

[82] D. Chivilikhin, A. Samarin, V. Ulyantsev, I. Iorsh, A. R. Oganov, and O. Kyriienko, "MoG-VQE: Multiobjective genetic variational quantum eigensolver", arXiv:2007.04424, (2020).

[83] David Wierichs, Christian Gogolin, and Michael Kastoryano, "Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer", Physical Review Research 2 4, 043246 (2020).

[84] Andrea Mari, Thomas R. Bromley, and Nathan Killoran, "Estimating the gradient and higher-order derivatives on quantum hardware", Physical Review A 103 1, 012405 (2021).

[85] I. Rungger, N. Fitzpatrick, H. Chen, C. H. Alderete, H. Apel, A. Cowtan, A. Patterson, D. Munoz Ramo, Y. Zhu, N. H. Nguyen, E. Grant, S. Chretien, L. Wossnig, N. M. Linke, and R. Duncan, "Dynamical mean field theory algorithm and experiment on quantum computers", arXiv:1910.04735, (2019).

[86] Jules Tilly, Glenn Jones, Hongxiang Chen, Leonard Wossnig, and Edward Grant, "Computation of molecular excited states on IBM quantum computers using a discriminative variational quantum eigensolver", Physical Review A 102 6, 062425 (2020).

[87] Oinam Romesh Meitei, Bryan T. Gard, George S. Barron, David P. Pappas, Sophia E. Economou, Edwin Barnes, and Nicholas J. Mayhall, "Gate-free state preparation for fast variational quantum eigensolver simulations: ctrl-VQE", arXiv:2008.04302, (2020).

[88] Youle Wang, Guangxi Li, and Xin Wang, "Variational quantum Gibbs state preparation with a truncated Taylor series", arXiv:2005.08797, (2020).

[89] 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 (2021).

[90] Youle Wang, Guangxi Li, and Xin Wang, "Variational Quantum Gibbs State Preparation with a Truncated Taylor Series", Physical Review Applied 16 5, 054035 (2021).

[91] Kerstin Beer, "Quantum neural networks", arXiv:2205.08154, (2022).

[92] James Dborin, Fergus Barratt, Vinul Wimalaweera, Lewis Wright, and Andrew G. Green, "Matrix product state pre-training for quantum machine learning", Quantum Science and Technology 7 3, 035014 (2022).

[93] Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, and Hong Yao, "Neural predictor based quantum architecture search", Machine Learning: Science and Technology 2 4, 045027 (2021).

[94] Oinam Romesh Meitei, Bryan T. Gard, George S. Barron, David P. Pappas, Sophia E. Economou, Edwin Barnes, and Nicholas J. Mayhall, "Gate-free state preparation for fast variational quantum eigensolver simulations", npj Quantum Information 7, 155 (2021).

[95] Zhide Lu, Pei-Xin Shen, and Dong-Ling Deng, "Markovian Quantum Neuroevolution for Machine Learning", Physical Review Applied 16 4, 044039 (2021).

[96] Mingrui Jing, Geng Liu, Hongbin Ren, and Xin Wang, "Quantum sequential scattering model for quantum state learning", arXiv:2310.07797, (2023).

[97] Andrew Patterson, Hongxiang Chen, Leonard Wossnig, Simone Severini, Dan Browne, and Ivan Rungger, "Quantum state discrimination using noisy quantum neural networks", Physical Review Research 3 1, 013063 (2021).

[98] Mohammad Pirhooshyaran and Tamas Terlaky, "Quantum Circuit Design Search", arXiv:2012.04046, (2020).

[99] Hao-Kai Zhang, Chengkai Zhu, Geng Liu, and Xin Wang, "Fundamental limitations on optimization in variational quantum algorithms", arXiv:2205.05056, (2022).

[100] Shuxiang Cao, Leonard Wossnig, Brian Vlastakis, Peter Leek, and Edward Grant, "Cost-function embedding and dataset encoding for machine learning with parametrized quantum circuits", Physical Review A 101 5, 052309 (2020).

[101] Santosh Kumar Radha, "Quantum option pricing using Wick rotated imaginary time evolution", arXiv:2101.04280, (2021).

[102] 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", arXiv:2102.01544, (2021).

[103] Thomas Hoffmann and Douglas Brown, "Gradient Estimation with Constant Scaling for Hybrid Quantum Machine Learning", arXiv:2211.13981, (2022).

[104] Kerstin Beer, Daniel List, Gabriel Müller, Tobias J. Osborne, and Christian Struckmann, "Training Quantum Neural Networks on NISQ Devices", arXiv:2104.06081, (2021).

[105] Sheng-Hsuan Lin, Rohit Dilip, Andrew G. Green, Adam Smith, and Frank Pollmann, "Real- and imaginary-time evolution with compressed quantum circuits", arXiv:2008.10322, (2020).

[106] Anton Nykänen, Matteo A. C. Rossi, Elsi-Mari Borrelli, Sabrina Maniscalco, and Guillermo García-Pérez, "Mitigating the measurement overhead of ADAPT-VQE with optimised informationally complete generalised measurements", arXiv:2212.09719, (2022).

[107] Xuchen You and Xiaodi Wu, "Exponentially Many Local Minima in Quantum Neural Networks", arXiv:2110.02479, (2021).

[108] Hongxiang Chen, Michael Vasmer, Nikolas P. Breuckmann, and Edward Grant, "Machine learning logical gates for quantum error correction", arXiv:1912.10063, (2019).

[109] Kerstin Beer and Gabriel Müller, "Dissipative quantum generative adversarial networks", arXiv:2112.06088, (2021).

[110] Soumik Adhikary, "Entanglement assisted training algorithm for supervised quantum classifiers", Quantum Information Processing 20 8, 254 (2021).

[111] Mina Doosti, "Unclonability and Quantum Cryptanalysis: From Foundations to Applications", arXiv:2210.17545, (2022).

[112] Waheeda Saib, Petros Wallden, and Ismail Akhalwaya, "The Effect of Noise on the Performance of Variational Algorithms for Quantum Chemistry", arXiv:2108.12388, (2021).

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