DOI QR코드

DOI QR Code

Metaheuristic optimization scheme for quantum kernel classifiers using entanglement-directed graphs

  • Yozef Tjandra (Calvin Institute of Technology) ;
  • Hendrik Santoso Sugiarto (Calvin Institute of Technology)
  • 투고 : 2024.04.03
  • 심사 : 2024.08.13
  • 발행 : 2024.10.10

초록

Entanglement is crucial for achieving quantum advantages. However, in the context of quantum machine learning, existing optimization strategies for generating quantum classifier circuits often result in unentangled circuits, indicating an underutilization of the entanglement effect needed to learn complex patterns. In this study, we proposed a novel metaheuristic approach-genetic algorithm-for designing a quantum kernel classifier that incorporates expressive entanglement. This classifier utilizes a loopless entanglement-directed graph, where each directed edge represents the entanglement between the target and control qubits. The proposed method consistently outperforms classical and quantum baselines across various artificial and actual datasets, achieving improvements up to 32.4% and 17.5%, respectively, compared with the best model among all other baselines. Moreover, this method successfully reconstructs the hidden entanglement structures underlying artificial datasets. The results also demonstrate that the optimized circuits exhibit diverse entanglement variations across different datasets, indicating the versatility of the proposed approach.

키워드

과제정보

This work was funded by PT Lancs Arche Consumma (MOU.003/CIT/XI/2022) and PT Astra International TBK - TSO (MOU.002/CIT/XI/2022).

참고문헌

  1. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2 (2018), 79. https://doi.org/10.22331/q-2018-08-06-79
  2. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, and B. Burkett, Quantum supremacy using a programmable superconducting processor, Nature 574 (2019), no. 7779, 505-510. https://doi.org/10.1038/s41586-019-1666-5
  3. S. Bravyi, D. Gosset, R. Konig, and M. Tomamichel, Quantum advantage with noisy shallow circuits, Nature Phys. 16 (2020), no. 10, 1040-1045. https://doi.org/10.1038/s41567-020-0948-z
  4. M. R. Perelshtein, A. I. Pakhomchik, A. A. Melnikov, M. Podobrii, A. Termanova, I. Kreidich, B. Nuriev, S. Iudin, C. W. Mansell, and V. M. Vinokur, NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization, Quantum 7 (2023), 1186. https://doi.org/10.22331/q-2023-11-21-1186
  5. Y. Wang and J. Liu, Quantum machine learning: from NISQ to fault tolerance, arXiv preprint, 2024. https://doi.org/10.48550/arXiv.2401.11351
  6. Y. Zhang and Q. Ni, Recent advances in quantum machine learning, Quantum Eng. 2 (2020), no. 1, e34.
  7. I. Cong, S. Choi, and M. D. Lukin, Quantum convolutional neural networks, Nat. Phys. 15 (2019), no. 12, 1273-1278.
  8. Y. Dang, N. Jiang, H. Hu, Z. Ji, and W. Zhang, Image classification based on quantum k-nearest-neighbor algorithm, Quantum Inf. Process. 17 (2018), 1-18.
  9. M. J. Bremner, A. Montanaro, and D. J. Shepherd, Achieving quantum supremacy with sparse and noisy commuting quantum computations, Quantum 1 (2017), 8.
  10. K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Phys. Rev. A 98 (2018), no. 3, 32309.
  11. M. Schuld, A. Bocharov, K. M. Svore, and N. Wiebe, Circuitcentric quantum classifiers, Phys. Rev. A 101 (2020), no. 3, 32308.
  12. C. Cortes and V. N. Vapnik, Support-vector networks, Mach. Learn. 20 (2004), 273-297.
  13. S. Theodoridis and K. Koutroumbas, Pattern recognition, Elsevier, 2006.
  14. V. Havlicek, A. D. Corcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Supervised learning with quantum-enhanced feature spaces, Nature 567 (2019), no. 7747, 209-212.
  15. M. Schuld and N. Killoran, Quantum machine learning in feature Hilbert spaces, Phys. Rev. Lett. 122 (2019), no. 4, 40504.
  16. S. Jerbi, L. J. Fiderer, H. Poulsen Nautrup, J. M. Kubler, H. J. Briegel, and V. Dunjko, Quantum machine learning beyond kernel methods, Nature Commun. 14 (2023), no. 1, 517. https://doi.org/10.1038/s41467-023-36159-y
  17. M. Schuld, Supervised quantum machine learning models are kernel methods, arXiv preprint, 2021. https://doi.org/10.48550/arXiv.2101.11020
  18. S. Altares-Lopez, J. J. Garcia-Ripoll, and A. Ribeiro, AutoQML: Automatic generation and training of robust quantum-inspired classifiers by using genetic algorithms on grayscale images, arXiv preprint, 2022. https://doi.org/10.48550/arXiv.2208.13246
  19. Y. Tjandra and H. Sugiarto, An evolutionary algorithm design for Pauli-based quantum kernel classification, (Joint Workshops 49th Int. Conf. Very Large Data Bases - Int. Workshop Quantum Data Sci. Manag., Cancouver, Canada), 2023.
  20. L. Davis, Handbook of genetic algorithms, 1991.
  21. H. Chiroma, S. Abdulkareem, A. Abubakar, and T. Herawan, Neural networks optimization through genetic algorithm searches: a review, Appl. Math. Inf. Sci 11 (2017), no. 6, 1543-1564.
  22. J. Kratica, V. Kovacevic-Vujcic, and M. Cangalovic, Computing the metric dimension of graphs by genetic algorithms, Computat. Optim. Applicat. 44 (2009), no. 2, 343-361.
  23. T. Hubregtsen, J. Pichlmeier, P. Stecher, and K. Bertels, Evaluation of parameterized quantum circuits: on the relation between classification accuracy, expressibility, and entangling capability, Quantum Mach. Intell. 3 (2021), no. 1, 9. https://doi.org/10.1007/s42484-021-00038-w
  24. S. Sim, P. D. Johnson, and A. Aspuru-Guzik, Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, Adv. Quantum Technol. 2 (2019), no. 12, 1900070. https://doi.org/10.1002/qute.201900070
  25. S. Altares-Lopez, A. Ribeiro, and J. J. Garcia-Ripoll, Automatic design of quantum feature maps, Quantum Sci. Technol. 6 (2021), no. 4, 45015.
  26. B.-S. Chen and J.-L. Chern, Genetically auto-generated quantum feature maps, arXiv preprint, 2022.
  27. N. Nguyen and K.-C. Chen, Quantum embedding search for quantum machine learning, IEEE Access 10 (2022), 41444-41456.
  28. E. Torabian and R. V. Krems, Compositional optimization of quantum circuits for quantum kernels of support vector machines, Phys. Rev. Res. 5 (2023), no. 1, 13211.
  29. M. Incudini, F. Martini, and A. Di Pierro, Structure learning of quantum embeddings, arXiv preprint, 2022. https://doi.org/10.48550/arXiv.2209.11144
  30. L. Bai, L. Cui, Y. Wang, M. Li, J. Li, S. Y. Philip, and E. R. Hancock, HAQJSK: hierarchical-aligned quantum Jensen-Shannon kernels for graph classification, IEEE Trans. Knowl. Data Eng. (2024).
  31. L. Cui, M. Li, L. Bai, Y. Wang, J. Li, Y. Wang, Z. Li, Y. Chen, and E. R. Hancock, QBER: quantum-based entropic representations for un-attributed graphs, Pattern Recogn. 145 (2024), 109877. https://doi.org/10.1016/j.patcog.2023.109877
  32. Q. Meng, J. Zhang, Z. Li, M. Li, and L. Cui, Entangled quantum neural network, inQuantum computing: a shift from bits to qubits, Springer, 2023, pp. 245-262.
  33. Y. Suzuki, H. Yano, Q. Gao, S. Uno, T. Tanaka, M. Akiyama, and N. Yamamoto, Analysis and synthesis of feature map for kernel-based quantum classifier, Quantum Mach. Intell. 2 (2020), 1-9.
  34. M. Grossi, N. Ibrahim, V. Radescu, R. Loredo, K. Voigt, C. Von Altrock, and A. Rudnik, Mixed quantum-classical method for fraud detection with quantum feature selection, IEEE Trans. Quantum Eng. 3 (2022), 1-12.
  35. J. Mancilla and C. Pere, A preprocessing perspective for quantum machine learning classification advantage in finance using nisq algorithms, Entropy 24 (2022), no. 11, 1656.
  36. M. Feurer, J. N. Van Rijn, A. Kadra, P. Gijsbers, N. Mallik, S. Ravi, A. Muller, J. Vanschoren, and F. Hutter, Openml-python: an extensible python api for openml, J. Mach. Learn. Res. 22 (2021), no. 1, 4573-4577.
  37. R. A. Fisher, The use of multiple measurements in taxonomic problems, Ann. Eugen. 7 (1936), no. 2, 179-188.
  38. I.-C. Yeh, K.-J. Yang, and T.-M. Ting, Knowledge discovery on rfm model using Bernoulli sequence, Expert Syst. Appl. 36 (2009), no. 3, 5866-5871.
  39. V. Greaney and T. Kellaghan, Equality of opportunity in irish schools: a longitudinal study of 500 students, Educational Company, 1984.
  40. J. D. Kalbfleisch and R. L. Prentice, The statistical analysis of failure time data, John Wiley & Sons, 2011.
  41. B. V. Ramana, M. S. P. Babu, and N. B. Venkateswarlu, A critical comparative study of liver patients from USA and India: an exploratory analysis, Int. J. Comput. Sci. Issues 9 (2012), no. 3, 506-516.
  42. R. K. Bock, A. Chilingarian, M. Gaug, F. Hakl, T. Hengstebeck, M. Jirina, J. Klaschka, E. Kotrc, P. Savicky, S. Towers, and A. Vaiciulis, Methods for multidimensional event classification: a case study using images from a Cherenkov gamma-ray telescope, Nucl. Instrum. Methods Phys. Res. Sect. A: Accelerators, Spectrometers, Detectors and Assoc. Equip. 516 (2004), no. 2-3, 511-528.
  43. Qiskit contributors, Qiskit: an open-source framework for quantum computing, 2023.
  44. D. Sharma, P. Singh, and A. Kumar, The role of entanglement for enhancing the efficiency of quantum kernels towards classification, Phys. A: Stat. Mechan. Applicat. 625 (2023), 128938. https://doi.org/10.1016/j.physa.2023.128938
  45. D. A. Shoieb, A. Younes, S. M. Youssef, and K. M. Fathalla, HQMC-CPC: a hybrid quantum multiclass cardiac pathologies classification integrating a modified hardware efficient ansatz, IEEE Access 12 (2024), 18295-18314.
  46. Z. Li, P. Liu, P. Zhao, Z. Mi, H. Xu, X. Liang, T. Su, W. Sun, G. Xue, J. N. Zhang, and W. Liu, Error per single-qubit gate below 10-4 in a superconducting qubit, npj Quantum Inform. 9 (2023), no. 1, 111. https://doi.org/10.1038/s41534-023-00781-x
  47. Suppressing quantum errors by scaling a surface code logical qubit, Nature 614 (2023), no. 7949, 676-681.
  48. S. Brandhofer, S. Devitt, T. Wellens, and I. Polian, Special session: noisy intermediate-scale quantum (NISQ) computers-how they work, how they fail, how to test them? 2021 IEEE 39th VLSI Test Symposium (VTS), San Diego, CA, USA, 2021, pp. 1-10. https://doi.org/10.1109/VTS50974.2021.9441047
  49. G. Gonzalez-Garcia, R. Trivedi, and J. I. Cirac, Error propagation in NISQ devices for solving classical optimization problems, PRX Quantum 3 (2022), no. 4, 40326. https://doi.org/10.1103/PRXQuantum.3.040326
  50. F. Leymann and J. Barzen, The bitter truth about gate-based quantum algorithms in the NISQ era, Quantum Sci. Technol. 5 (2020), no. 4, 44007. https://doi.org/10.1088/2058-9565/abae7d