Structure optimization for parameterized quantum circuits

Mateusz Ostaszewski1,2, Edward Grant2,3, and Marcello Benedetti2,4

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

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

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

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

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

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

[4] 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).

[5] 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.

[6] Maria Schuld, Ryan Sweke, and Johannes Jakob Meyer, "The effect of data encoding on the expressive power of variational quantum machine learning models", arXiv:2008.08605.

[7] 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).

[8] 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.

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

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

[11] 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 (NISQ) algorithms", arXiv:2101.08448.

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

[13] Xin Wang, Zhixin Song, and Youle Wang, "Variational Quantum Singular Value Decomposition", arXiv:2006.02336.

[14] 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).

[15] Bálint Koczor and Simon C. Benjamin, "Quantum Analytic Descent", arXiv:2008.13774.

[16] Tatiana A. Bespalova and Oleksandr Kyriienko, "Hamiltonian operator approximation for energy measurement and ground state preparation", arXiv:2009.03351.

[17] Fergus Barratt, James Dborin, Matthias Bal, Vid Stojevic, Frank Pollmann, and Andrew G. Green, "Parallel Quantum Simulation of Large Systems on Small Quantum Computers", arXiv:2003.12087.

[18] 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).

[19] Sukin Sim, Jonathan Romero, Jerome F. Gonthier, and Alexander A. Kunitsa, "Adaptive pruning-based optimization of parameterized quantum circuits", arXiv:2010.00629.

[20] Shi-Xin Zhang, Chang-Yu Hsieh, Shengyu Zhang, and Hong Yao, "Differentiable Quantum Architecture Search", arXiv:2010.08561.

[21] 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.

[22] Marcello Benedetti, Mattia Fiorentini, and Michael Lubasch, "Hardware-efficient variational quantum algorithms for time evolution", arXiv:2009.12361.

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

[24] 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.

[25] 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).

[26] 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).

[27] Mohammad Pirhooshyaran and Tamas Terlaky, "Quantum Circuit Design Search", arXiv:2012.04046.

[28] Soumik Adhikary, "Entanglement assisted training algorithm for supervised quantum classifiers", arXiv:2006.13302.

[29] Stefano Mangini, Francesco Tacchino, Dario Gerace, Daniele Bajoni, and Chiara Macchiavello, "Quantum computing models for artificial neural networks", arXiv:2102.03879.

[30] Brian Coyle, Mina Doosti, Elham Kashefi, and Niraj Kumar, "Variational Quantum Cloning: Improving Practicality for Quantum Cryptanalysis", arXiv:2012.11424.

[31] Shu Kanno, "Optimization of chemical reaction path via molecular geometry generation using quantum circuits", arXiv:2009.06803.

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

[33] Zhide Lu, Pei-Xin Shen, and Dong-Ling Deng, "Markovian Quantum Neuroevolution for Machine Learning", arXiv:2012.15131.

[34] 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 Quantum Chemistry Calculations", arXiv:2102.01544.

The above citations are from SAO/NASA ADS (last updated successfully 2021-03-04 06:07:17). 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 2021-03-04 06:07:16).