Layerwise learning for quantum neural networks

Andrea Skolik1, Jarrod R. McClean2, Masoud Mohseni2, Patrick van der Smagt3, Martin Leib1
1Volkswagen Data:Lab, Ungererstraße 69, 80805, Munich, Germany
2Google Research, 340 Main Street, Venice, CA, 90291, USA
3Volkswagen Group Machine Learning Research Lab, Munich, Germany

Tóm tắt

AbstractWith the increased focus on quantum circuit learning for near-term applications on quantum devices, in conjunction with unique challenges presented by cost function landscapes of parametrized quantum circuits, strategies for effective training are becoming increasingly important. In order to ameliorate some of these challenges, we investigate a layerwise learning strategy for parametrized quantum circuits. The circuit depth is incrementally grown during optimization, and only subsets of parameters are updated in each training step. We show that when considering sampling noise, this strategy can help avoid the problem of barren plateaus of the error surface due to the low depth of circuits, low number of parameters trained in one step, and larger magnitude of gradients compared to training the full circuit. These properties make our algorithm preferable for execution on noisy intermediate-scale quantum devices. We demonstrate our approach on an image-classification task on handwritten digits, and show that layerwise learning attains an 8% lower generalization error on average in comparison to standard learning schemes for training quantum circuits of the same size. Additionally, the percentage of runs that reach lower test errors is up to 40% larger compared to training the full circuit, which is susceptible to creeping onto a plateau during training.

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Tài liệu tham khảo

Arute F, Arya K, Babbush R, Bacon D, Bardin JC, Barends R, Biswas R, Boixo S, Brandao Fernando GSL, Buell DA et al (2019) Nature 574(7779):505–510

Benedetti M, Garcia-Pintos D, Perdomo O, Leyton-Ortega V, Nam Y, Perdomo-Ortiz A (2019a) npj Quantum Inf 5(1):45. https://doi.org/10.1038/s41534-019-0157-8, http://www.nature.com/articles/s41534-019-0157-8

Benedetti M, Grant E, Wossnig L, Severini S (2019b) New J Phys 21(4):043023. https://doi.org/10.1088/1367-2630/ab14b5, http://stacks.iop.org/1367-2630/21/i=4/a=043023?key=crossref.0b5ab94ed3e2ea2943830f1d0073c780

Bengio Y, Bengio Y, Lamblin P, Popovici D, Larochelle H (2007) Greedy layer-wise training of deep networks. Advances in Neural Information Processing. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.2022

Boixo S, Isakov S V, Smelyanskiy VN, Babbush R, Ding N, Jiang Z, Bremner MJ, Martinis JM, Neven H (2018) Nat Phys 14(6):595–600. https://doi.org/10.1038/s41567-018-0124-x, http://www.nature.com/articles/s41567-018-0124-x

Broughton M, Verdon G, McCourt T, Martinez AJ, Yoo JH, Isakov SV, Massey P, Niu MY, Halavati R, Peters E et al (2020) arXiv:2003.02989

Carolan J, Mohseni M, Olson JP, Prabhu M, Chen C, Bunandar D, Niu MY, Harris NC, Wong Franco NC, Hochberg M et al (2020) Nat Phys 16(3):322–327

Cerezo M, Sone A, Volkoff T, Cincio L, Coles PJ (2020) arXiv:2001.00550

Chen H, Wossnig L, Severini S, Neven H, Mohseni M (2018) arXiv:1805.08654

Colless JI, Ramasesh VV, Dahlen D, Blok MS, Kimchi-Schwartz ME, McClean JR, Carter J, de Jong WA, Siddiqi I (2018) Phys Rev X 8:011021. https://doi.org/10.1103/PhysRevX.8.011021

Cong I, Choi S, Lukin MD (2019) Nat Phys 15(12):1273–1278

Fahlman S E, Lebiere C (1990) Adv Neural Inf Process 2:524–532. https://doi.org/10.1.1.125.6421

Farhi E, Goldstone J, Gutmann S (2014) A quantum approximate optimization algorithm. Preprint at arXiv:1411.4028

Grant E, Benedetti M, Cao S, Hallam A, Lockhart J, Stojevic V, Green A G, Severini S (2018) npj Quantum Inf 4(1):65. https://doi.org/10.1038/s41534-018-0116-9, http://www.nature.com/articles/s41534-018-0116-9

Grant E, Wossnig L, Ostaszewski M, Benedetti M (2019) Quantum 3:214

Hadfield S, Wang Z, O’Gorman B, Rieffel E, Venturelli D, Biswas R, Hadfield S, Wang Z, O’Gorman B, Rieffel E G, Venturelli D, Biswas R (2019) Algorithms 12(2):34. https://doi.org/10.3390/a12020034, http://www.mdpi.com/1999-4893/12/2/34

Harrow AW, Low RA (2009) Commun Math Phys 291(1):257–302. https://doi.org/10.1007/s00220-009-0873-6

Havlíček V, Córcoles AD, Temme K, Harrow AW, Kandala A, Chow JM, Gambetta JM (2019) Nature 567(7747):209–212

Hempel C, Maier C, Romero J, McClean J, Monz T, Shen H, Jurcevic P, Lanyon BP, Love P, Babbush R, Aspuru-Guzik A, Blatt R, Roos C F (2018) Phys Rev X 8:031022. https://doi.org/10.1103/PhysRevX.8.031022

Hettinger C, Christensen T, Ehlert B, Humpherys J, Jarvis T, Wade S (2017) In: 31st Conference on Neural Information Processing Systems. 1706.02480

Hinton GE, Osindero S, Teh Y-W (2006) Neural Comput 18(7):1527–1554. https://doi.org/10.1162/neco.2006.18.7.1527

Kandala A, Mezzacapo A, Temme K, Takita M, Brink M, Chow JM, Gambetta JM (2017) Nature 549(7671):242–246

Kiani BT, Lloyd S, Maity R (2020) arXiv:2001.11897

Kingma DP, Ba J (2015) In: International Conference on Learning Representations. https://www.semanticscholar.org/paper/Adam%3A-A-Method-for-Stochastic-Optimization-Kingma-Ba/272216c1f097706721096669d85b2843c23fa77d

Knill E, Ortiz G, Somma RD (2007) Phys Rev A 75(1):012328. https://doi.org/10.1103/PhysRevA.75.012328

Liu J-G, Wang L (2018) Phys Rev A 98(6):062324. https://doi.org/10.1103/PhysRevA.98.062324

Lyu C, Montenegro V, Bayat A (2020) Quantum 4:324

McClean JR, Boixo S, Smelyanskiy VN, Babbush R, Neven H (2018) Nat Commun 9(1):4812. https://doi.org/10.1038/s41467-018-07090-4, http://www.nature.com/articles/s41467-018-07090-4

McClean JR, Jiang Z, Rubin NC, Babbush R, Neven H (2020) Nat Commun 11(1):1–9

McClean JR, Romero J, Babbush R, Aspuru-Guzik A (2016) New J Phys 18(2):023023. https://doi.org/10.1088/1367-2630/18/2/023023

Mitarai K, Negoro M, Kitagawa M, Fujii K (2018) Phys Rev A 98(3):032309

Nakanishi KM, Fujii K, Todo S (2020) Phys Rev Res 2(4):043158

Nannicini G (2019) Phys Rev E 99(1):013304. https://doi.org/10.1103/PhysRevE.99.013304

O’Malley PJJ, Babbush R, Kivlichan ID, Romero J, McClean JR, Barends R, Kelly J, Roushan P, Tranter A, Ding N et al (2016). Physical Review X 6(3):031007. https://doi.org/10.1103/PhysRevX.6.031007

Peruzzo A, McClean J, Shadbolt P, Yung M-H, Zhou X-Q, Love PJ, Aspuru-Guzik A, O’brien JL (2014) Nat Commun 5:4213. https://www.nature.com/articles/ncomms5213

Romero J, Olson JP, Aspuru-Guzik A (2017) Quantum Sci Technol 2(4):045001. https://doi.org/10.1088/2058-9565/aa8072/meta

Rubin NC, Babbush R, McClean J (2018) New J Phys 20(5):053020. https://doi.org/10.1088/1367-2630/aab919

Rumelhart DE, Hinton GE, Williams RJ (1986) Nature 323(6088):533–536. https://doi.org/10.1038/323533a0, http://www.nature.com/articles/323533a0

Santagati R, Wang J, Gentile AA, Paesani S, Wiebe N, McClean JR, Morley-Short S, Shadbolt PJ, Bonneau D, Silverstone JW, Tew DP, Zhou X, O’Brien JL, Thompson MG (2018) Sci Adv 4:1. http://advances.sciencemag.org/content/4/1/eaap9646

Schuld M, Bergholm V, Gogolin C, Izaac J, Killoran N (2019) Phys Rev A 99(3):032331. https://doi.org/10.1103/PhysRevA.99.032331

Streif M, Leib M (2020) Quantum Sci Technol 5(3):034008

Sung KJ, Yao J, Harrigan M, Rubin N, Jiang Z, Lin L, Babbush R, McClean J (2020) Quantum Science and Technology

Verdon G, Broughton M, McClean JR, Sung KJ, Babbush R, Jiang Z, Neven H, Mohseni M (2019) Learning to learn with quantum neural networks via classical neural networks

Volkoff T, Coles PJ (2020) arXiv:2005.12200

Wang Z, Hadfield S, Jiang Z, Rieffel E G (2018) Phys Rev A 97(2):022304. https://doi.org/10.1103/PhysRevA.97.022304

Wecker D, Hastings M B, Troyer M (2015) Phys Rev A 92 (4):042303. https://doi.org/10.1103/PhysRevA.92.042303

Yung M-H, Casanova J, Mezzacapo A, McClean J, Lamata L, Aspuru-Guzik A, Solano E (2014) Sci Rep 4(3589):1–7. https://www.nature.com/articles/srep03589

Zhou L, Wang S-T, Choi S, Pichler H, Lukin MD (2018) arXiv:1812.01041