{"type":"ScholarlyArticle","title":"Ansatz-Agnostic Exponential Resource Saving in Variational Quantum Algorithms Using Shallow Shadows","authors":[{"name":"Afrad Basheer","slug":"afrad-basheer","given":"Afrad","family":"Basheer","affiliation":"Centre for Quantum Software and Information , University of Technology Sydney , NSW 2007 , Australia"},{"name":"Yuan Feng","slug":"yuan-feng","given":"Yuan","family":"Feng","affiliation":"Department of Computer Science and Technology , Tsinghua University , Beijing 100084 , China"},{"name":"Christopher Ferrie","slug":"christopher-ferrie","given":"Christopher","family":"Ferrie","affiliation":"Centre for Quantum Software and Information , University of Technology Sydney , NSW 2007 , Australia"},{"name":"Sanjiang Li","slug":"sanjiang-li","given":"Sanjiang","family":"Li","affiliation":"Centre for Quantum Software and Information , University of Technology Sydney , NSW 2007 , Australia"}],"abstract":"Variational Quantum Algorithms (VQA) have been identified as a promising candidate for the demonstration of near-term quantum advantage in solving optimization tasks in chemical simulation, quantum information, and machine learning. The standard model of training requires a significant amount of quantum resources, which led researchers to use classical shadows to devise an alternative that consumes exponentially fewer quantum resources. However, the approach only works when the observables are local and the ansatz is the shallow Alternating Layered Ansatz (ALA), thus severely limiting its potential in solving problems such as quantum state preparation, where the ideal state might not be approximable with an ALA. In this work, we present a protocol based on shallow shadows that achieves similar levels of savings for almost any shallow ansatz studied in the literature, when combined with observables of low Frobenius norm. We show that two important applications in quantum information for which VQAs can be a powerful option, namely variational quantum state preparation and variational quantum circuit synthesis, are compatible with our protocol. We also experimentally demonstrate orders of magnitude improvement in comparison to the standard VQA model.","doi":"10.24963/ijcai.2024/410","url":"https://ijcai.org/proceedings/2024/410","pdf":"https://ijcai.org/proceedings/2024/0410.pdf","markdown":"https://ijcai.org/proceedings/2024/410.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/410","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Machine Learning","track":"Main Track","number":410,"pages":{"first":3706,"last":3714},"keywords":["Machine Learning: ML: Optimization","Machine Learning: ML: Other"],"videos":[],"references":[{"position":1,"raw":"[Ambainis et al., 2009] Andris Ambainis, Jan Bouda, and Andreas Winter. Nonmalleable encryption of quantum in- formation. Journal of Mathematical Physics, 50(4), apr 2009.","title":"Nonmalleable encryption of quantum information","authors":"Andris Ambainis, Jan Bouda, Andreas Winter","year":"2009","venue":"Journal of Mathematical Physics","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Arute et al., 2019] Frank Arute, Kunal Arya, Ryan Bab- bush, Dave Bacon, Joseph Bardin, Rami Barends, Ru- pak Biswas, Sergio Boixo, Fernando Brandao, David Buell, Brian Burkett, Yu Chen, Jimmy Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Michael Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger, Matthew Harrigan, Michael Hartmann, Alan Ho, Markus Rudolf Hoffmann, Trent Huang, Travis Humble, Sergei Isakov, Evan Jeffrey, Zhang Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Paul Klimov, Sergey Knysh, Alexander Korotkov, Fedor Kostritsa, Dave Landhuis, Mike Lindmark, Erik Lucero, Dmitry Lyakh, Salvatore Mandrà, Jarrod Ryan McClean, Matthew McEwen, Anthony Megrant, Xiao Mi, Kristel Michielsen, Masoud Mohseni, Josh Mutus, Ofer Naa- man, Matthew Neeley, Charles Neill, Murphy Yuezhen Niu, Eric Ostby, Andre Petukhov, John Platt, Chris Quin- tana, Eleanor G. Rieffel, Pedram Roushan, Nicholas Ru- bin, Daniel Sank, Kevin J. Satzinger, Vadim Smelyanskiy, Kevin Jeffery Sung, Matt Trevithick, Amit Vainsencher, Benjamin Villalonga, Ted White, Z. Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, and John Martinis. Quan- tum supremacy using a programmable superconducting processor. Nature, 574:505-510, 2019.","title":"Quantum supremacy using a programmable superconducting processor","authors":"Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando Brandao, David Buell, Brian Burkett, Yu Chen, Jimmy Chen, Ben Chiaro, Roberto Collins, William Courtney, Andrew Dunsworth, Edward Farhi, Brooks Foxen, Austin Fowler, Craig Michael Gidney, Marissa Giustina, Rob Graff, Keith Guerin, Steve Habegger, Matthew Harrigan, Michael Hartmann, Alan Ho, Markus Rudolf Hoffmann, Trent Huang, Travis Humble, Sergei Isakov, Evan Jeffrey, Zhang Jiang, Dvir Kafri, Kostyantyn Kechedzhi, Julian Kelly, Paul Klimov, Sergey Knysh, Alexander Korotkov, Fedor Kostritsa, Dave Landhuis, Mike Lindmark, Erik Lucero, Dmitry Lyakh, Salvatore Mandrà, Jarrod Ryan Mcclean, Matthew Mcewen, Anthony Megrant, Xiao Mi, Kristel Michielsen, Masoud Mohseni, Josh Mutus, Ofer Naaman, Matthew Neeley, Charles Neill, Murphy Yuezhen Niu, Eric Ostby, Andre Petukhov, John Platt, Chris Quintana, Eleanor G Rieffel, Pedram Roushan, Nicholas Rubin, Daniel Sank, Kevin J Satzinger, Vadim Smelyanskiy, Kevin Jeffery Sung, Matt Trevithick, Amit Vainsencher, Benjamin Villalonga, Ted White, Z Jamie Yao, Ping Yeh, Adam Zalcman, Hartmut Neven, John Martinis","year":"2019","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Basheer et al., 2023] Afrad Basheer, Yuan Feng, Christo- pher Ferrie, and Sanjiang Li. Alternating layered varia- tional quantum circuits can be classically optimized effi- ciently using classical shadows. Proceedings of the AAAI Conference on Artificial Intelligence, 37(6):6770-6778, Jun. 2023.","title":"Alternating layered variational quantum circuits can be classically optimized efficiently using classical shadows","authors":"Basheer","year":"2023","venue":"Proceedings of the AAAI Conference on Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bertoni et al., 2023] Christian Bertoni, Jonas Haferkamp, Marcel Hinsche, Marios Ioannou, Jens Eisert, and Hakop Pashayan. Shallow shadows: Expectation estimation us- ing low-depth random clifford circuits. arXiv:2209.12924, 2023.","title":"Shallow shadows: Expectation estimation using low-depth random clifford circuits","authors":"Bertoni","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Boyd and Koczor, 2022] Gregory Boyd and Bálint Koc- zor. Training variational quantum circuits with co- var: covariance root finding with classical shadows. arXiv:2204.08494, 2022.","title":"Training variational quantum circuits with covar: covariance root finding with classical shadows","authors":"Gregory Boyd, Bálint Koczor","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Bridgeman et al., 2015] Jacob C. Bridgeman, Aroon O'Brien, Stephen D. Bartlett, and Andrew C. Doherty. Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality. Phys. Rev. B, 91:165129, Apr 2015.","title":"Multiscale entanglement renormalization ansatz for spin chains with continuously varying criticality","authors":"Jacob C Bridgeman, O' Aroon, Stephen D Brien, Andrew C Bartlett, Doherty","year":"2015","venue":"Phys. Rev. B","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Cerezo et al., 2021] M. Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J. Coles. Cost function de- pendent barren plateaus in shallow parametrized quantum circuits. Nature Communications, 12(1), mar 2021.","title":"Cost function dependent barren plateaus in shallow parametrized quantum circuits","authors":"M Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, Patrick J Coles","year":"2021","venue":"Nature Communications","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Cerezo et al., 2023] M. Cerezo, Martin Larocca, Diego García-Martín, N. L. Diaz, Paolo Braccia, Enrico Fontana, Manuel S. Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R. Anschuetz, and Zoë Holmes. Does provable absence of barren plateaus imply classical sim- ulability? or, why we need to rethink variational quantum computing. arXiv:2312.09121, 2023.","title":"Does provable absence of barren plateaus imply classical simulability? or, why we need to rethink variational quantum computing","authors":"M Cerezo, Martin Larocca, Diego García-Martín, N L Diaz, Paolo Braccia, Enrico Fontana, Manuel S Rudolph, Pablo Bermejo, Aroosa Ijaz, Supanut Thanasilp, Eric R Anschuetz, Zoë Holmes","year":"2023","venue":null,"doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Dankert et al., 2009] Christoph Dankert, Richard Cleve, Joseph Emerson, and Etera Livine. Exact and approximate unitary 2-designs and their application to fidelity estima- tion. Phys. Rev. A, 80:012304, Jul 2009.","title":"Exact and approximate unitary 2-designs and their application to fidelity estimation","authors":"Christoph Dankert, Richard Cleve, Joseph Emerson, Etera Livine","year":"2009","venue":"Phys. Rev. A","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Farhi et al., 2014] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization al- gorithm. arXiv:1411.4028, 2014.","title":"A quantum approximate optimization algorithm","authors":"Edward Farhi, Jeffrey Goldstone, Sam Gutmann","year":"2014","venue":null,"doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Friedrich and Maziero, 2022] Lucas Friedrich and Jonas Maziero. Avoiding barren plateaus with classical deep neural networks. Physical Review A, 106(4), oct 2022.","title":"Avoiding barren plateaus with classical deep neural networks","authors":"Maziero Friedrich, Lucas Friedrich, Jonas Maziero","year":"2022","venue":"Physical Review A","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Grant et al., 2019] Edward Grant, Leonard Wossnig, Ma- teusz Ostaszewski, and Marcello Benedetti. An ini- tialization strategy for addressing barren plateaus in parametrized quantum circuits. Quantum, 3:214, dec 2019.","title":"An initialization strategy for addressing barren plateaus in parametrized quantum circuits","authors":"Edward Grant, Leonard Wossnig, Mateusz Ostaszewski, Marcello Benedetti","year":"2019","venue":"Quantum","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Grimsley et al., 2023a] Harper Grimsley, Nicholas May- hall, George Barron, Edwin Barnes, and Sophia Economou. Adaptive, problem-tailored variational quan- tum eigensolver mitigates rough parameter landscapes and barren plateaus. npj Quantum Information, 9, 03 2023.","title":"Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus","authors":"Grimsley","year":"2023","venue":"npj Quantum Information","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Grimsley et al., 2023b] Harper R. Grimsley, George S. Bar- ron, Edwin Barnes, Sophia E. Economou, and Nicholas J. Mayhall. Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and bar- ren plateaus. npj Quantum Information, 9(1), mar 2023.","title":"Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus","authors":"Grimsley","year":"2023","venue":"npj Quantum Information","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Harrow and Low, 2009] Aram W. Harrow and Richard A. Low. Random quantum circuits are approximate 2- designs. Communications in Mathematical Physics, 291(1):257-302, July 2009.","title":"Random quantum circuits are approximate 2designs","authors":"Aram W Harrow, Richard A Low","year":"2009","venue":"Communications in Mathematical Physics","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Havlíček et al., 2019] Vojtěch Havlíček, Antonio D. Córcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta. Super- vised learning with quantum-enhanced feature spaces. Nature, 567(7747):209-212, mar 2019.","title":"Supervised learning with quantum-enhanced feature spaces","authors":"Vojtěch Havlíček, Antonio D Córcoles, Kristan Temme, Aram W Harrow, Abhinav Kandala, Jerry M Chow, Jay M Gambetta","year":"2019","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Huang et al., 2020] Hsin-Yuan Huang, Richard Kueng, and John Preskill. Predicting many properties of a quantum system from very few measurements. Nature Physics, 16(10):1050-1057, jun 2020.","title":"Predicting many properties of a quantum system from very few measurements","authors":"Hsin-Yuan Huang, Richard Kueng, John Preskill","year":"2020","venue":"Nature Physics","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Huang et al., 2021] Hsin-Yuan Huang, Richard Kueng, Gi- acomo Torlai, Victor V. Albert, and John Preskill. Provably efficient machine learning for quantum many-body prob- lems. arXiv:2106.12627, 2021.","title":"Provably efficient machine learning for quantum many-body problems","authors":"Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, V Victor, John Albert, Preskill","year":"2021","venue":null,"doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Khatri et al., 2019] Sumeet Khatri, Ryan LaRose, Alexan- der Poremba, Lukasz Cincio, Andrew T. Sornborger, and Patrick J. Coles. Quantum-assisted quantum compiling. Quantum, 3:140, May 2019.","title":"Quantum-assisted quantum compiling","authors":"Sumeet Khatri, Ryan Larose, Alexander Poremba, Lukasz Cincio, Andrew T Sornborger, Patrick J Coles","year":"2019","venue":"Quantum","doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kulshrestha and Safro, 2022] Ankit Kulshrestha and Ilya Safro. Beinit: Avoiding barren plateaus in variational quantum algorithms. arXiv:2204.13751, 2022.","title":"Beinit: Avoiding barren plateaus in variational quantum algorithms","authors":"Ankit Kulshrestha, Ilya Safro","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Leone et al., 2022] Lorenzo Leone, Salvatore F. E. Oliviero, Lukasz Cincio, and M. Cerezo. On the practical usefulness of the hardware efficient ansatz. arXiv:2211.01477, 2022.","title":"On the practical usefulness of the hardware efficient ansatz","authors":"Lorenzo Leone, Salvatore F E Oliviero, Lukasz Cincio, M Cerezo","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Liu et al., 2022] Zidu Liu, Li-Wei Yu, L.-M. Duan, and Dong-Ling Deng. Presence and absence of barren plateaus in tensor-network based machine learning. Phys. Rev. Lett., 129:270501, Dec 2022.","title":"Presence and absence of barren plateaus in tensor-network based machine learning","authors":"Zidu Liu, Li-Wei Yu, L.-M Duan, Dong-Ling Deng","year":"2022","venue":"Phys. Rev. Lett","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Madsen et al., 2022] Lars Skovgaard Madsen, Fabian Lau- denbach, Mohsen Falamarzi Askarani, Fabien Rortais, Trevor Vincent, Jacob F F Bulmer, Filippo M. Miatto, Leonhard Neuhaus, Lukas G Helt, Matthew J Collins, Adriana E. Lita, Thomas Gerrits, Sae Woo Nam, Varun Vaidya, Matteo Menotti, Ish Dhand, Zachary Vernon, Nicolás Quesada, and Jonathan Lavoie. Quantum com- putational advantage with a programmable photonic pro- cessor. Nature, 606:75 -81, 2022.","title":"Quantum computational advantage with a programmable photonic processor","authors":"Madsen","year":"2022","venue":"Nature","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[McClean et al., 2016] Jarrod R McClean, Jonathan Romero, Ryan Babbush, and Alá n Aspuru-Guzik. The theory of variational hybrid quantum-classical algorithms. New Journal of Physics, 18(2):023023, feb 2016.","title":"The theory of variational hybrid quantum-classical algorithms","authors":"Jonathan Jarrod R Mcclean, Ryan Romero, Babbush, Alá N Aspuru-Guzik","year":"2016","venue":"New Journal of Physics","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Mele et al., 2022] Antonio A. Mele, Glen B. Mbeng, Giuseppe E. Santoro, Mario Collura, and Pietro Torta. Avoiding barren plateaus via transferability of smooth so- lutions in a hamiltonian variational ansatz. Physical Re- view A, 106(6), dec 2022.","title":"Avoiding barren plateaus via transferability of smooth solutions in a hamiltonian variational ansatz","authors":"Antonio A Mele, Glen B Mbeng, Giuseppe E Santoro, Mario Collura, Pietro Torta","year":"2022","venue":"Physical Review A","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Mitarai et al., 2018] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii. Quantum circuit learning. Phys. Rev. A, 98:032309, Sep 2018.","title":"Quantum circuit learning","authors":"K Mitarai, M Negoro, M Kitagawa, K Fujii","year":"2018","venue":"Phys. Rev. A","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Patti et al., 2021] Taylor L. Patti, Khadijeh Najafi, Xun Gao, and Susanne F. Yelin. Entanglement devised bar- ren plateau mitigation. Physical Review Research, 3(3), jul 2021.","title":"Entanglement devised barren plateau mitigation","authors":"Taylor L Patti, Khadijeh Najafi, Xun Gao, Susanne F Yelin","year":"2021","venue":"Physical Review Research","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Peruzzo et al., 2014] Alberto Peruzzo, Jarrod McClean, Pe- ter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J. Love, Alán Aspuru-Guzik, and Jeremy L. O'Brien. A vari- ational eigenvalue solver on a photonic quantum processor. Nature Communications, 5(1), jul 2014.","title":"A variational eigenvalue solver on a photonic quantum processor","authors":"Alberto Peruzzo, Jarrod Mcclean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, Jeremy L O'brien","year":"2014","venue":"Nature Communications","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Powell, 1964] M. J. D. Powell. An efficient method for find- ing the minimum of a function of several variables without calculating derivatives. The Computer Journal, 7(2):155- 162, 01 1964.","title":"An efficient method for finding the minimum of a function of several variables without calculating derivatives","authors":"M J D Powell","year":"1964","venue":"The Computer Journal","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Preskill, 2018] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, August 2018.","title":"Quantum Computing in the NISQ era and beyond","authors":"John Preskill","year":"2018","venue":"Quantum","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Rad et al., 2022] Ali Rad, Alireza Seif, and Norbert M. Linke. Surviving the barren plateau in variational quantum circuits with bayesian learning initialization. arXiv:2203.02464, 2022.","title":"Surviving the barren plateau in variational quantum circuits with bayesian learning initialization","authors":"Ali Rad, Alireza Seif, Norbert M Linke","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Romero et al., 2017] Jonathan Romero, Jonathan P Olson, and Alan Aspuru-Guzik. Quantum autoencoders for effi- cient compression of quantum data. Quantum Science and Technology, 2(4):045001, aug 2017.","title":"Quantum autoencoders for efficient compression of quantum data","authors":"Jonathan Romero, Jonathan P Olson, Alan Aspuru-Guzik","year":"2017","venue":"Quantum Science and Technology","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Schreiber et al., 2022] Franz J. Schreiber, Jens Eisert, and Johannes Jakob Meyer. Classical surrogates for quantum learning models. arXiv:2206.11740, 2022.","title":"Classical surrogates for quantum learning models","authors":"Franz J Schreiber, Jens Eisert, Johannes Jakob Meyer","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Scott, 2008] A J Scott. Optimizing quantum process tomog- raphy with unitary 2-designs. Journal of Physics A: Math- ematical and Theoretical, 41(5):055308, jan 2008.","title":"Optimizing quantum process tomography with unitary 2-designs","authors":"A J Scott","year":"2008","venue":"Journal of Physics A: Mathematical and Theoretical","doi":null,"url":null,"internal_url":null},{"position":35,"raw":"[Shi et al., 2006] Y.-Y. Shi, L.-M. Duan, and G. Vidal. Clas- sical simulation of quantum many-body systems with a tree tensor network. Phys. Rev. A, 74:022320, Aug 2006.","title":"Classical simulation of quantum many-body systems with a tree tensor network","authors":"Y.-Y Shi, L.-M Duan, G Vidal","year":"2006","venue":"Phys. Rev. A","doi":null,"url":null,"internal_url":null},{"position":36,"raw":"[Skolik et al., 2021] Andrea Skolik, Jarrod R. McClean, Ma- soud Mohseni, Patrick van der Smagt, and Martin Leib. Layerwise learning for quantum neural networks. Quan- tum Machine Intelligence, 3(1), jan 2021.","title":"Layerwise learning for quantum neural networks","authors":"Andrea Skolik, Jarrod R Mcclean, Masoud Mohseni, Martin Patrick Van Der Smagt, Leib","year":"2021","venue":"Quantum Machine Intelligence","doi":null,"url":null,"internal_url":null},{"position":37,"raw":"[Spall, 1992] J.C. Spall. Multivariate stochastic approxi- mation using a simultaneous perturbation gradient ap- proximation. IEEE Transactions on Automatic Control, 37(3):332-341, 1992.","title":"Multivariate stochastic approximation using a simultaneous perturbation gradient approximation","authors":"J C Spall","year":"1992","venue":"IEEE Transactions on Automatic Control","doi":null,"url":null,"internal_url":null},{"position":38,"raw":"[Stokes et al., 2020] James Stokes, Josh Izaac, Nathan Kil- loran, and Giuseppe Carleo. Quantum Natural Gradient. Quantum, 4:269, May 2020.","title":"Quantum Natural Gradient","authors":"James Stokes, Josh Izaac, Nathan Killoran, Giuseppe Carleo","year":"2020","venue":"Quantum","doi":null,"url":null,"internal_url":null},{"position":39,"raw":"[Verdon et al., 2019] Guillaume Verdon, Michael Broughton, Jarrod R. McClean, Kevin J. Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, and Masoud Mohseni. Learning to learn with quantum neural networks via classical neural networks. arXiv:1907.05415, 2019.","title":"Learning to learn with quantum neural networks via classical neural networks","authors":"Guillaume Verdon, Michael Broughton, Jarrod R Mcclean, Kevin J Sung, Ryan Babbush, Zhang Jiang, Hartmut Neven, Masoud Mohseni","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":40,"raw":"[Wierichs et al., 2020] David Wierichs, Christian Gogolin, and Michael Kastoryano. Avoiding local minima in varia- tional quantum eigensolvers with the natural gradient op- timizer. Phys. Rev. Research, 2:043246, Nov 2020.","title":"Avoiding local minima in variational quantum eigensolvers with the natural gradient optimizer","authors":"David Wierichs, Christian Gogolin, Michael Kastoryano","year":"2020","venue":"Phys. Rev. Research","doi":null,"url":null,"internal_url":null},{"position":41,"raw":"[Zhang et al., 2022] Kaining Zhang, Liu Liu, Min-Hsiu Hsieh, and Dacheng Tao. Escaping from the barren plateau via gaussian initializations in deep variational quantum cir- cuits. In S. Koyejo, S. Mohamed, A. Agarwal, D. Bel- grave, K. Cho, and A. Oh, editors, Advances in Neural In- formation Processing Systems, volume 35, pages 18612- 18627.","title":"Escaping from the barren plateau via gaussian initializations in deep variational quantum circuits","authors":"Kaining Zhang, Liu Liu, Min-Hsiu Hsieh, Dacheng Tao","year":null,"venue":"Advances in Neural Information Processing Systems","doi":null,"url":null,"internal_url":null},{"position":42,"raw":"Curran Associates, Inc., 2022.","title":null,"authors":"Curran Associates, Inc","year":"2022","venue":null,"doi":null,"url":null,"internal_url":null},{"position":43,"raw":"[Zhong et al., 2020] Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, Peng Hu, Xiao- Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan. Quan- tum computational advantage using photons. Science, 370(6523):1460-1463, 2020.","title":"Quantum computational advantage using photons","authors":"Han-Sen Zhong, Hui Wang, Yu-Hao Deng, Ming-Cheng Chen, Li-Chao Peng, Yi-Han Luo, Jian Qin, Dian Wu, Xing Ding, Yi Hu, Peng Hu, Xiao-Yan Yang, Wei-Jun Zhang, Hao Li, Yuxuan Li, Xiao Jiang, Lin Gan, Guangwen Yang, Lixing You, Zhen Wang, Li Li, Nai-Le Liu, Chao-Yang Lu, Jian-Wei Pan","year":"2020","venue":"Science","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}