On The Practical Usefulness Of The Hardware Efficient Ansatz

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Lorenzo Leone^1,2,3, Salvatore F.E. Oliviero^1,2,3, Lukasz Cincio¹, and M. Cerezo⁴

¹Theoretical Division (T-4), Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
³Physics Department, University of Massachusetts Boston, Boston, Massachusetts 02125, USA
⁴Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA

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Abstract

Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) models train a parametrized quantum circuit to solve a given learning task. The success of these algorithms greatly hinges on appropriately choosing an ansatz for the quantum circuit. Perhaps one of the most famous ansatzes is the one-dimensional layered Hardware Efficient Ansatz (HEA), which seeks to minimize the effect of hardware noise by using native gates and connectives. The use of this HEA has generated a certain ambivalence arising from the fact that while it suffers from barren plateaus at long depths, it can also avoid them at shallow ones. In this work, we attempt to determine whether one should, or should not, use a HEA. We rigorously identify scenarios where shallow HEAs should likely be avoided (e.g., VQA or QML tasks with data satisfying a volume law of entanglement). More importantly, we identify a Goldilocks scenario where shallow HEAs could achieve a quantum speedup: QML tasks with data satisfying an area law of entanglement. We provide examples for such scenario (such as Gaussian diagonal ensemble random Hamiltonian discrimination), and we show that in these cases a shallow HEA is always trainable and that there exists an anti-concentration of loss function values. Our work highlights the crucial role that input states play in the trainability of a parametrized quantum circuit, a phenomenon that is verified in our numerics.

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Featured image: Our results show that QML tasks using Hardware-Efficient Ansatz (HEA) with input data sets composed of states possessing an area law of entanglement are trainable, whereas tasks with data sets composed of states possessing a volume law of entanglement are untrainable.

Popular summary

In this work, we provide a novel framework for determining the suitability of Hardware-Efficient Ansatzes (HEAs) in Variational Quantum Algorithms (VQAs) and Quantum Machine Learning (QML) tasks. Leveraging tools from entanglement theory, we demonstrate that HEAs are untrainable for QML tasks with input data following a volume law of entanglement due to the presence of barren plateaus. Conversely, we show that HEAs can be effectively used for QML tasks with input data following an area law of entanglement, and avoiding barren plateaus. Our research not only identifies when HEAs should be used but also introduces a new source of untrainability linked to the entanglement of input states. These insights provide essential guidelines for the effective and trainability-aware application of HEAs, emphasizing the critical role of input data entanglement in the success of quantum models.

► BibTeX data

@article{Leone2024practicalusefulness, doi = {10.22331/q-2024-07-03-1395}, url = {https://doi.org/10.22331/q-2024-07-03-1395}, title = {On the practical usefulness of the {H}ardware {E}fficient {A}nsatz}, author = {Leone, Lorenzo and Oliviero, Salvatore F.E. and Cincio, Lukasz and Cerezo, M.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1395}, month = jul, year = {2024} }

► References

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

[2] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, et al. “Quantum supremacy using a programmable superconducting processor”. Nature 574, 505–510 (2019).
https://doi.org/10.1038/s41586-019-1666-5

[3] Yulin Wu, Wan-Su Bao, Sirui Cao, Fusheng Chen, et al. “Strong Quantum Computational Advantage Using a Superconducting Quantum Processor”. Physical Review Letters 127, 180501 (2021).
https://doi.org/10.1103/PhysRevLett.127.180501

[4] Lars S Madsen, Fabian Laudenbach, Mohsen Falamarzi Askarani, Fabien Rortais, Trevor Vincent, Jacob FF Bulmer, Filippo M Miatto, Leonhard Neuhaus, Lukas G Helt, Matthew J Collins, et al. “Quantum computational advantage with a programmable photonic processor”. Nature 606, 75–81 (2022).
https://doi.org/10.1038/s41586-022-04725-x

[5] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles. “Variational quantum algorithms”. Nature Reviews Physics 3, 625–644 (2021).
https://doi.org/10.1038/s42254-021-00348-9

[6] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S Kottmann, Tim Menke, et al. “Noisy intermediate-scale quantum algorithms”. Reviews of Modern Physics 94, 015004 (2022).
https://doi.org/10.1103/RevModPhys.94.015004

[7] Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien. “A variational eigenvalue solver on a photonic quantum processor”. Nature Communications 5, 1–7 (2014).
https://doi.org/10.1038/ncomms5213

[8] 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

[9] Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. “A quantum approximate optimization algorithm” (2014). url: https://arxiv.org/abs/1411.4028.
arXiv:1411.4028

[10] Matthew P. Harrigan, Kevin J. Sung, Matthew Neeley, Kevin J. Satzinger, et al. “Quantum approximate optimization of non-planar graph problems on a planar superconducting processor”. Nature Physics 17, 332–336 (2021).
https://doi.org/10.1038/s41567-020-01105-y

[11] Carlos Bravo-Prieto, Ryan LaRose, Marco Cerezo, Yigit Subasi, Lukasz Cincio, and Patrick J Coles. “Variational quantum linear solver”. Quantum 7, 1188 (2023).
https://doi.org/10.22331/q-2023-11-22-1188

[12] Hsin-Yuan Huang, Kishor Bharti, and Patrick Rebentrost. “Near-term quantum algorithms for linear systems of equations with regression loss functions”. New Journal of Physics 23, 113021 (2021).
https://doi.org/10.1088/1367-2630/ac325f

[13] Xiaosi Xu, Jinzhao Sun, Suguru Endo, Ying Li, et al. “Variational algorithms for linear algebra”. Science Bulletin 66, 2181–2188 (2021).
https://doi.org/10.1016/j.scib.2021.06.023

[14] 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

[15] Maria Schuld and Francesco Petruccione. “Machine Learning with Quantum Computers”. Springer International Publishing. Cham, Switzerland (2021).
https://doi.org/10.1007/978-3-030-83098-4

[16] 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

[17] Louis Schatzki, Andrew Arrasmith, Patrick J. Coles, and M. Cerezo. “Entangled datasets for quantum machine learning” (2021). url: https://arxiv.org/abs/2109.03400.
arXiv:2109.03400

[18] J. S. Otterbach, R. Manenti, N. Alidoust, A. Bestwick, et al. “Unsupervised machine learning on a hybrid quantum computer” (2017). url: https://arxiv.org/abs/1712.05771.
arXiv:1712.05771

[19] Sofiene Jerbi, Casper Gyurik, Simon Marshall, Hans Briegel, et al. “Parametrized Quantum Policies for Reinforcement Learning”. Advances in Neural Information Processing Systems 34, 28362–28375 (2021). url: https://proceedings.neurips.cc/paper/2021/hash/eec96a7f788e88184c0e713456026f3f-Abstract.html.
https://proceedings.neurips.cc/paper/2021/hash/eec96a7f788e88184c0e713456026f3f-Abstract.html

[20] Adrián Pérez-Salinas, Alba Cervera-Lierta, Elies Gil-Fuster, and José I Latorre. “Data re-uploading for a universal quantum classifier”. Quantum 4, 226 (2020).
https://doi.org/10.22331/q-2020-02-06-226

[21] Iris Cong, Soonwon Choi, and Mikhail D Lukin. “Quantum convolutional neural networks”. Nature Physics 15, 1273–1278 (2019).
https://doi.org/10.1038/s41567-019-0648-8

[22] Matthias C Caro, Hsin-Yuan Huang, Marco Cerezo, Kunal Sharma, Andrew Sornborger, Lukasz Cincio, and Patrick J Coles. “Generalization in quantum machine learning from few training data”. Nature Communications 13 (2022).
https://doi.org/10.1038/s41467-022-32550-3

[23] Hsin-Yuan Huang, Richard Kueng, Giacomo Torlai, Victor V. Albert, and John Preskill. “Provably efficient machine learning for quantum many-body problems”. Science 377, eabk3333 (2022).
https://doi.org/10.1126/science.abk3333

[24] M Cerezo, Guillaume Verdon, Hsin-Yuan Huang, Lukasz Cincio, and Patrick J Coles. “Challenges and opportunities in quantum machine learning”. Nature Computational Science (2022).
https://doi.org/10.1038/s43588-022-00311-3

[25] Linghua Zhu, Ho Lun Tang, George S Barron, Nicholas J Mayhall, Edwin Barnes, and Sophia E Economou. “An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer” (2020). url: https://arxiv.org/abs/2005.10258.
arXiv:2005.10258

[26] Ho Lun Tang, VO Shkolnikov, George S Barron, Harper R Grimsley, Nicholas J Mayhall, Edwin Barnes, and Sophia E Economou. “qubit-adapt-vqe: An adaptive algorithm for constructing hardware-efficient ansätze on a quantum processor”. PRX Quantum 2, 020310 (2021).
https://doi.org/10.1103/PRXQuantum.2.020310

[27] Zi-Jian Zhang, Thi Ha Kyaw, Jakob S. Kottmann, Matthias Degroote, and Alán Aspuru-Guzik. “Mutual information-assisted adaptive variational quantum eigensolver”. Quantum Science and Technology 6, 035001 (2021).
https://doi.org/10.1088/2058-9565/abdca4

[28] Matias Bilkis, Marco Cerezo, Guillaume Verdon, Patrick J Coles, and Lukasz Cincio. “A semi-agnostic ansatz with variable structure for variational quantum algorithms”. Quantum Machine Intelligence 5, 43 (2023).
https://doi.org/10.1007/s42484-023-00132-1

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

[30] Stuart Hadfield, Zhihui Wang, Bryan O’Gorman, Eleanor G Rieffel, Davide Venturelli, and Rupak Biswas. “From the quantum approximate optimization algorithm to a quantum alternating operator ansatz”. Algorithms 12, 34 (2019).
https://doi.org/10.3390/a12020034

[31] Roeland Wiersema, Cunlu Zhou, Yvette de Sereville, Juan Felipe Carrasquilla, Yong Baek Kim, and Henry Yuen. “Exploring entanglement and optimization within the hamiltonian variational ansatz”. PRX Quantum 1, 020319 (2020).
https://doi.org/10.1103/PRXQuantum.1.020319

[32] Juneseo Lee, Alicia B Magann, Herschel A Rabitz, and Christian Arenz. “Progress toward favorable landscapes in quantum combinatorial optimization”. Physical Review A 104, 032401 (2021).
https://doi.org/10.1103/PhysRevA.104.032401

[33] Guillaume Verdon, Trevor McCourt, Enxhell Luzhnica, Vikash Singh, Stefan Leichenauer, and Jack Hidary. “Quantum graph neural networks” (2019). url: https://arxiv.org/abs/1909.12264.
arXiv:1909.12264

[34] Johannes Bausch. “Recurrent quantum neural networks”. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems. Volume 33, pages 1368–1379. Curran Associates, Inc. (2020). url: https://proceedings.neurips.cc/paper/2020/file/0ec96be397dd6d3cf2fecb4a2d627c1c-Paper.pdf.
https://proceedings.neurips.cc/paper/2020/file/0ec96be397dd6d3cf2fecb4a2d627c1c-Paper.pdf

[35] Martín Larocca, Frédéric Sauvage, Faris M. Sbahi, Guillaume Verdon, Patrick J. Coles, and M. Cerezo. “Group-invariant quantum machine learning”. PRX Quantum 3, 030341 (2022).
https://doi.org/10.1103/PRXQuantum.3.030341

[36] 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”. PRX Quantum 4, 010328 (2023).
https://doi.org/10.1103/PRXQuantum.4.010328

[37] Andrea Skolik, Michele Cattelan, Sheir Yarkoni, Thomas Bäck, and Vedran Dunjko. “Equivariant quantum circuits for learning on weighted graphs” (2022). url: https://arxiv.org/abs/2205.06109.
arXiv:2205.06109

[38] Frederic Sauvage, Martin Larocca, Patrick J Coles, and Marco Cerezo. “Building spatial symmetries into parameterized quantum circuits for faster training”. Quantum Science and Technology 9, 015029 (2024).
https://doi.org/10.1088/2058-9565/ad152e

[39] Michael Ragone, Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Martin Larocca, Frederic Sauvage, Patrick J. Coles, and M. Cerezo. “Representation theory for geometric quantum machine learning” (2022). url: https://arxiv.org/abs/2210.07980.
arXiv:2210.07980

[40] Quynh T. Nguyen, Louis Schatzki, Paolo Braccia, Michael Ragone, Patrick J. Coles, Frédéric Sauvage, Martín Larocca, and M. Cerezo. “Theory for equivariant quantum neural networks”. PRX Quantum 5, 020328 (2024).
https://doi.org/10.1103/PRXQuantum.5.020328

[41] Louis Schatzki, Martín Larocca, Quynh T. Nguyen, Frédéric Sauvage, and M. Cerezo. “Theoretical guarantees for permutation-equivariant quantum neural networks”. npj Quantum Information 10 (2024).
https://doi.org/10.1038/s41534-024-00804-1

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

[43] M Cerezo, Akira Sone, Tyler Volkoff, Lukasz Cincio, and Patrick J Coles. “Cost function dependent barren plateaus in shallow parametrized quantum circuits”. Nature Communications 12, 1–12 (2021).
https://doi.org/10.1038/s41467-021-21728-w

[44] Kunal Sharma, Marco Cerezo, Lukasz Cincio, and Patrick J Coles. “Trainability of dissipative perceptron-based quantum neural networks”. Physical Review Letters 128, 180505 (2022).
https://doi.org/10.1103/PhysRevLett.128.180505

[45] Supanut Thanasilp, Samson Wang, Nhat A. Nghiem, Patrick J. Coles, and M. Cerezo. “Subtleties in the trainability of quantum machine learning models”. Quantum Machine Intelligence 5, 21 (2023).
https://doi.org/10.1007/s42484-023-00103-6

[46] Zoë Holmes, Kunal Sharma, M. Cerezo, and Patrick J Coles. “Connecting ansatz expressibility to gradient magnitudes and barren plateaus”. PRX Quantum 3, 010313 (2022).
https://doi.org/10.1103/PRXQuantum.3.010313

[47] Andrew Arrasmith, Zoë Holmes, Marco Cerezo, and Patrick J Coles. “Equivalence of quantum barren plateaus to cost concentration and narrow gorges”. Quantum Science and Technology 7, 045015 (2022).
https://doi.org/10.1088/2058-9565/ac7d06

[48] Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T Sornborger, and Patrick J Coles. “Absence of barren plateaus in quantum convolutional neural networks”. Physical Review X 11, 041011 (2021).
https://doi.org/10.1103/PhysRevX.11.041011

[49] AV Uvarov and Jacob D Biamonte. “On barren plateaus and cost function locality in variational quantum algorithms”. Journal of Physics A: Mathematical and Theoretical 54, 245301 (2021).
https://doi.org/10.1088/1751-8121/abfac7

[50] Carlos Ortiz Marrero, Mária Kieferová, and Nathan Wiebe. “Entanglement-induced barren plateaus”. PRX Quantum 2, 040316 (2021).
https://doi.org/10.1103/PRXQuantum.2.040316

[51] Taylor L Patti, Khadijeh Najafi, Xun Gao, and Susanne F Yelin. “Entanglement devised barren plateau mitigation”. Physical Review Research 3, 033090 (2021).
https://doi.org/10.1103/PhysRevResearch.3.033090

[52] Sumeet Khatri, Ryan LaRose, Alexander Poremba, Lukasz Cincio, Andrew T Sornborger, and Patrick J Coles. “Quantum-assisted quantum compiling”. Quantum 3, 140 (2019).
https://doi.org/10.22331/q-2019-05-13-140

[53] David H Wolpert and William G Macready. “No free lunch theorems for optimization”. IEEE transactions on evolutionary computation 1, 67–82 (1997).
https://doi.org/10.1109/4235.585893

[54] 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 Science and Technology 4, 014008 (2018).
https://doi.org/10.1088/2058-9565/aad3e4

[55] 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

[56] “IBM Q 16 Rueschlikon backend specification” (2018).

[57] Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, and Patrick J Coles. “Noise-induced barren plateaus in variational quantum algorithms”. Nature Communications 12, 1–11 (2021).
https://doi.org/10.1038/s41467-021-27045-6

[58] Daniel Stilck França and Raul Garcia-Patron. “Limitations of optimization algorithms on noisy quantum devices”. Nature Physics 17, 1221–1227 (2021).
https://doi.org/10.1038/s41567-021-01356-3

[59] Fernando GSL Brandao, Aram W Harrow, and Michał Horodecki. “Local random quantum circuits are approximate polynomial-designs”. Communications in Mathematical Physics 346, 397–434 (2016).
https://doi.org/10.1007/s00220-016-2706-8

[60] Aram W Harrow and Saeed Mehraban. “Approximate unitary t-designs by short random quantum circuits using nearest-neighbor and long-range gates”. Communications in Mathematical Physics 401, 1531–1626 (2023).
https://doi.org/10.1007/s00220-023-04675-z

[61] Valerie Coffman, Joydip Kundu, and William K Wootters. “Distributed entanglement”. Physical Review A 61, 052306 (2000).
https://doi.org/10.1103/PhysRevA.61.052306

[62] Dmitry A. Abanin and Eugene Demler. “Measuring entanglement entropy of a generic many-body system with a quantum switch”. Physical Review Letters 109, 020504 (2012).
https://doi.org/10.1103/PhysRevLett.109.020504

[63] Steph Foulds, Viv Kendon, and Tim Spiller. “The controlled SWAP test for determining quantum entanglement”. Quantum Science and Technology 6, 035002 (2021).
https://doi.org/10.1088/2058-9565/abe458

[64] Jacob L. Beckey, N. Gigena, Patrick J. Coles, and M. Cerezo. “Computable and operationally meaningful multipartite entanglement measures”. Phys. Rev. Lett. 127, 140501 (2021).
https://doi.org/10.1103/PhysRevLett.127.140501

[65] Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma. “Stabilizer Rényi entropy”. Physical Review Letters 128, 050402 (2022).
https://doi.org/10.1103/PhysRevLett.128.050402

[66] Salvatore F. E. Oliviero, Lorenzo Leone, Alioscia Hamma, and Seth Lloyd. “Measuring magic on a quantum processor”. npj Quantum Inf 8, 1–8 (2022).
https://doi.org/10.1038/s41534-022-00666-5

[67] Tobias Haug and MS Kim. “Scalable measures of magic resource for quantum computers”. PRX Quantum 4, 010301 (2023).
https://doi.org/10.1103/PRXQuantum.4.010301

[68] Min-Sung Kang, Jino Heo, Seong-Gon Choi, Sung Moon, and Sang-Wook Han. “Implementation of swap test for two unknown states in photons via cross-kerr nonlinearities under decoherence effect”. Scientific reports 9, 1–14 (2019).
https://doi.org/10.1038/s41598-019-42662-4

[69] Román Orús. “A practical introduction to tensor networks: Matrix product states and projected entangled pair states”. Annals of Physics 349, 117–158 (2014).
https://doi.org/10.1016/j.aop.2014.06.013

[70] Ulrich Schollwöck. “The density-matrix renormalization group in the age of matrix product states”. Annals of Physics 326, 96–192 (2011).
https://doi.org/10.1016/j.aop.2010.09.012

[71] Frank Verstraete, Valentin Murg, and J Ignacio Cirac. “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems”. Advances in physics 57, 143–224 (2008).
https://doi.org/10.1080/14789940801912366

[72] Norbert Schuch, Michael M Wolf, Frank Verstraete, and J Ignacio Cirac. “Entropy scaling and simulability by matrix product states”. Physical review letters 100, 030504 (2008).
https://doi.org/10.1103/PhysRevLett.100.030504

[73] Frank Verstraete and J Ignacio Cirac. “Renormalization algorithms for quantum-many body systems in two and higher dimensions” (2004). url: https://arxiv.org/abs/cond-mat/0407066.
https://arxiv.org/abs/cond-mat/0407066

[74] Jakob S. Kottmann and Alán Aspuru-Guzik. “Optimized low-depth quantum circuits for molecular electronic structure using a separable-pair approximation”. Physical Review A 105, 032449 (2022).
https://doi.org/10.1103/PhysRevA.105.032449

[75] Román Orús. “A practical introduction to tensor networks: Matrix product states and projected entangled pair states”. Annals of Physics 349, 117–158 (2014).
https://doi.org/10.1016/j.aop.2014.06.013

[76] Yimin Ge and Jens Eisert. “Area laws and efficient descriptions of quantum many-body states”. New Journal of Physics 18, 083026 (2016).
https://doi.org/10.1088/1367-2630/18/8/083026

[77] Salvatore F. E. Oliviero, Lorenzo Leone, Francesco Caravelli, and Alioscia Hamma. “Random Matrix Theory of the Isospectral twirling”. SciPost Physics 10, 76 (2021).
https://doi.org/10.21468/SciPostPhys.10.3.076

[78] Lorenzo Leone, Salvatore F. E. Oliviero, and Alioscia Hamma. “Isospectral twirling and quantum chaos”. Entropy 23 (2021).
https://doi.org/10.3390/e23081073

[79] Sandu Popescu, Anthony J. Short, and Andreas Winter. “Entanglement and the foundations of statistical mechanics”. Nature Physics 2, 754–758 (2006).
https://doi.org/10.1038/nphys444

[80] Aram W Harrow. “The church of the symmetric subspace” (2013). url: https://arxiv.org/abs/1308.6595.
arXiv:1308.6595

[81] Kosuke Mitarai, Makoto Negoro, Masahiro Kitagawa, and Keisuke Fujii. “Quantum circuit learning”. Physical Review A 98, 032309 (2018).
https://doi.org/10.1103/PhysRevA.98.032309

[82] Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. “Evaluating analytic gradients on quantum hardware”. Physical Review A 99, 032331 (2019).
https://doi.org/10.1103/PhysRevA.99.032331

[83] Don Weingarten. “Asymptotic behavior of group integrals in the limit of infinite rank”. Journal of Mathematical Physics 19, 999–1001 (1978). arXiv:https://doi.org/10.1063/1.523807.
https://doi.org/10.1063/1.523807
arXiv:https://doi.org/10.1063/1.523807

[84] Benoı̂t Collins. “Moments and cumulants of polynomial random variables on unitary groups, the Itzykson-Zuber integral, and free probability”. International Mathematics Research Notices 2003, 953–982 (2003).
https://doi.org/10.1155/S107379280320917X

[85] Benoı̂t Collins and Piotr Śniady. “Integration with respect to the haar measure on unitary, orthogonal and symplectic group”. Communications in Mathematical Physics 264, 773–795 (2006).
https://doi.org/10.1007/s00220-006-1554-3

[86] Patrick J Coles, M Cerezo, and Lukasz Cincio. “Strong bound between trace distance and hilbert-schmidt distance for low-rank states”. Physical Review A 100, 022103 (2019).
https://doi.org/10.1103/PhysRevA.100.022103

[87] Pavan Hosur, Xiao-Liang Qi, Daniel A. Roberts, and Beni Yoshida. “Chaos in quantum channels”. Journal of High Energy Physics 2016, 4 (2016).
https://doi.org/10.1007/JHEP02(2016)004

[88] Lorenzo Leone, Salvatore F. E. Oliviero, You Zhou, and Alioscia Hamma. “Quantum Chaos is Quantum”. Quantum 5, 453 (2021).
https://doi.org/10.22331/q-2021-05-04-453

[89] Salvatore F.E. Oliviero, Lorenzo Leone, and Alioscia Hamma. “Transitions in entanglement complexity in random quantum circuits by measurements”. Physics Letters A 418, 127721 (2021).
https://doi.org/10.1016/j.physleta.2021.127721

[90] Dawei Ding, Patrick Hayden, and Michael Walter. “Conditional mutual information of bipartite unitaries and scrambling”. Journal of High Energy Physics 2016, 145 (2016).
https://doi.org/10.1007/JHEP12(2016)145

[91] Zi-Wen Liu, Seth Lloyd, Elton Zhu, and Huangjun Zhu. “Entanglement, quantum randomness, and complexity beyond scrambling”. Journal of High Energy Physics 2018, 41 (2018).
https://doi.org/10.1007/JHEP07(2018)041

[92] Jordan Cotler, Nicholas Hunter-Jones, Junyu Liu, and Beni Yoshida. “Chaos, complexity, and random matrices”. Journal of High Energy Physics 2017, 48 (2017).
https://doi.org/10.1007/JHEP11(2017)048

[93] Zbigniew Puchala and Jaroslaw Adam Miszczak. “Symbolic integration with respect to the haar measure on the unitary groups”. Bulletin of the Polish Academy of Sciences Technical Sciences 65, 21–27 (2017). url: http://journals.pan.pl/dlibra/publication/121307/edition/105697/content.
http://journals.pan.pl/dlibra/publication/121307/edition/105697/content

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[1] 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 simulability? Or, why we need to rethink variational quantum computing”, arXiv:2312.09121, (2023).

[2] Christo Meriwether Keller, Stephan Eidenbenz, Andreas Bärtschi, Daniel O’Malley, John Golden, and Satyajayant Misra, “Hierarchical Multigrid Ansatz for Variational Quantum Algorithms”, arXiv:2312.15048, (2023).

[3] Martin Larocca, Supanut Thanasilp, Samson Wang, Kunal Sharma, Jacob Biamonte, Patrick J. Coles, Lukasz Cincio, Jarrod R. McClean, Zoë Holmes, and M. Cerezo, “A Review of Barren Plateaus in Variational Quantum Computing”, arXiv:2405.00781, (2024).

[4] Nicolas PD Sawaya, Daniel Marti-Dafcik, Yang Ho, Daniel P Tabor, David E Bernal Neira, Alicia B Magann, Shavindra Premaratne, Pradeep Dubey, Anne Matsuura, Nathan Bishop, Wibe A de Jong, Simon Benjamin, Ojas D Parekh, Norm Tubman, Katherine Klymko, and Daan Camps, “HamLib: A library of Hamiltonians for benchmarking quantum algorithms and hardware”, arXiv:2306.13126, (2023).

[5] Guilherme Ilário Correr, Ivan Medina, Pedro C. Azado, Alexandre Drinko, and Diogo O. Soares-Pinto, “Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement”, arXiv:2405.02265, (2024).

[6] Lukas Mouton, Florentin Reiter, Ying Chen, and Patrick Rebentrost, “Deep learning-based quantum algorithms for solving nonlinear partial differential equations”, arXiv:2305.02019, (2023).

[7] Filip B. Maciejewski, Stuart Hadfield, Benjamin Hall, Mark Hodson, Maxime Dupont, Bram Evert, James Sud, M. Sohaib Alam, Zhihui Wang, Stephen Jeffrey, Bhuvanesh Sundar, P. Aaron Lott, Shon Grabbe, Eleanor G. Rieffel, Matthew J. Reagor, and Davide Venturelli, “Design and execution of quantum circuits using tens of superconducting qubits and thousands of gates for dense Ising optimization problems”, arXiv:2308.12423, (2023).

[8] Manuel S. Rudolph, Sacha Lerch, Supanut Thanasilp, Oriel Kiss, Sofia Vallecorsa, Michele Grossi, and Zoë Holmes, “Trainability barriers and opportunities in quantum generative modeling”, arXiv:2305.02881, (2023).

[9] Lorenzo Leone, Salvatore F. E. Oliviero, Stefano Piemontese, Sarah True, and Alioscia Hamma, “Retrieving information from a black hole using quantum machine learning”, Physical Review A 106 6, 062434 (2022).

[10] Paolo Braccia, Pablo Bermejo, Lukasz Cincio, and M. Cerezo, “Computing exact moments of local random quantum circuits via tensor networks”, arXiv:2403.01706, (2024).

[11] Xin Wang, Bo Qi, Yabo Wang, and Daoyi Dong, “Entanglement-variational hardware-efficient ansatz for eigensolvers”, Physical Review Applied 21 3, 034059 (2024).

[12] Alistair Letcher, Stefan Woerner, and Christa Zoufal, “Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits”, arXiv:2309.12681, (2023).

[13] Xinjian Yan, Xinwei Lee, Ningyi Xie, Yoshiyuki Saito, Leo Kurosawa, Nobuyoshi Asai, Dongsheng Cai, and HoongChuin Lau, “Light Cone Cancellation for Variational Quantum Eigensolver Ansatz”, arXiv:2404.19497, (2024).

[14] Chae-Yeun Park, Minhyeok Kang, and Joonsuk Huh, “Hardware-efficient ansatz without barren plateaus in any depth”, arXiv:2403.04844, (2024).

[15] Lucas T. Brady and Stuart Hadfield, “Iterative Quantum Algorithms for Maximum Independent Set: A Tale of Low-Depth Quantum Algorithms”, arXiv:2309.13110, (2023).

[16] Guilherme Ilário Correr, Pedro C. Azado, Diogo O. Soares-Pinto, and Gabriel Carlo, “Optimal complexity of parameterized quantum circuits”, arXiv:2405.19537, (2024).

[17] Azar C. Nakhl, Thomas Quella, and Muhammad Usman, “Calibrating the role of entanglement in variational quantum circuits”, Physical Review A 109 3, 032413 (2024).

[18] Akash Kundu, “Reinforcement learning-assisted quantum architecture search for variational quantum algorithms”, arXiv:2402.13754, (2024).

[19] Su Yeon Chang, Supanut Thanasilp, Bertrand Le Saux, Sofia Vallecorsa, and Michele Grossi, “Latent Style-based Quantum GAN for high-quality Image Generation”, arXiv:2406.02668, (2024).

[20] Lento Nagano, Alexander Miessen, Tamiya Onodera, Ivano Tavernelli, Francesco Tacchino, and Koji Terashi, “Quantum data learning for quantum simulations in high-energy physics”, Physical Review Research 5 4, 043250 (2023).

[21] Yudai Suzuki and Muyuan Li, “Effect of alternating layered ansatzes on trainability of projected quantum kernel”, arXiv:2310.00361, (2023).

[22] Ben Jaderberg, Antonio A. Gentile, Atiyo Ghosh, Vincent E. Elfving, Caitlin Jones, Davide Vodola, John Manobianco, and Horst Weiss, “Potential of quantum scientific machine learning applied to weather modelling”, arXiv:2404.08737, (2024).

[23] Yudai Suzuki, Rei Sakuma, and Hideaki Kawaguchi, “Light-cone feature selection for quantum machine learning”, arXiv:2403.18733, (2024).

[24] Tamojit Ghosh, Arijit Mandal, Shreya Banerjee, and Prasanta K. Panighrahi, “Lower bound of the expressibility of ansatzes for Variational Quantum Algorithms”, arXiv:2311.01330, (2023).

[25] Elijah Pelofske, Andreas Bärtschi, and Stephan Eidenbenz, “Short-depth QAOA circuits and quantum annealing on higher-order ising models”, npj Quantum Information 10, 30 (2024).

[26] Michael Kölle, Timo Witter, Tobias Rohe, Gerhard Stenzel, Philipp Altmann, and Thomas Gabor, “A Study on Optimization Techniques for Variational Quantum Circuits in Reinforcement Learning”, arXiv:2405.12354, (2024).

[27] Michelle Gelman, “A Survey of Methods for Mitigating Barren Plateaus for Parameterized Quantum Circuits”, arXiv:2406.14285, (2024).

[28] André Sequeira, Luis Paulo Santos, and Luis Soares Barbosa, “Trainability issues in quantum policy gradients”, arXiv:2406.09614, (2024).

[29] Zhihui Song, Xin Zhou, Jinchen Xu, Xiaodong Ding, and Zheng Shan, “Recurrent quantum embedding neural network and its application in vulnerability detection”, Scientific Reports 14 1, 13642 (2024).

[30] Baptiste Chevalier, Wojciech Roga, and Masahiro Takeoka, “Compressed sensing enhanced by quantum approximate optimization algorithm”, arXiv:2403.17399, (2024).

[31] Afrad Basheer, Yuan Feng, Christopher Ferrie, and Sanjiang Li, “Ansatz-Agnostic Exponential Resource Saving in Variational Quantum Algorithms Using Shallow Shadows”, arXiv:2309.04754, (2023).

The above citations are from SAO/NASA ADS (last updated successfully 2024-07-03 21:13:44). The list may be incomplete as not all publishers provide suitable and complete citation data.

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This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.