Basic quantum circuits for classification and approximation tasks

• Autorzy: Wiśniewska Joanna , Sawerwain Marek , Obuchowicz Andrzej

Identyfikatory

DOI

10.34768/amcs-2020-0054

• Języki publikacji: EN

Abstrakty

EN

We discuss a quantum circuit construction designed for classification. The circuit is built of regularly placed elementary quantum gates, which implies the simplicity of the presented solution. The realization of the classification task is possible after the procedure of supervised learning which constitutes parameter optimization of Pauli gates. The process of learning can be performed by a physical quantum machine but also by simulation of quantum computation on a classical computer. The parameters of Pauli gates are selected by calculating changes in the gradient for different sets of these parameters. The proposed solution was successfully tested in binary classification and estimation of basic non-linear function values, e.g., the sine, the cosine, and the tangent. In both the cases, the circuit construction uses one or more identical unitary operations, and contains only two qubits and three quantum gates. This simplicity is a great advantage because it enables the practical implementation on quantum machines easily accessible in the nearest future.

Słowa kluczowe

EN

quantum circuits; data classification; supervised learning; qubits; qudits

PL

układ kwantowy; klasyfikacja danych; uczenie nadzorowane; kubit

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2020
• Tom: Vol. 30, no. 4
• Strony: 733--744
• Opis fizyczny: Bibliogr. 26 poz., rys., tab., wykr.

Twórcy

autor

Wiśniewska Joanna

• Institute of Information Systems, Military University of Technology, ul. Gen. S. Kaliskiego 2, 00-908 Warsaw, Poland

autor

Sawerwain Marek

• Institute of Control and Computation Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516 Zielona Góra, Poland

autor

Obuchowicz Andrzej

• Institute of Control and Computation Engineering, University of Zielona Góra, ul. Szafrana 2, 65-516 Zielona Góra, Poland

Bibliografia

• [1] Augusto, L.M. (2017). Many-Valued Logics: A Mathematical and Computational Introduction, College Publications, London.
• [2] Bertlmann, R. and Krammer, P. (2008). Bloch vectors for qudits, Journal of Physics A: Mathematical and Theoretical 41(23): 235303, DOI: 10.1088/1751-8113/41/23/235303.
• [3] Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N. and Lloyd, S. (2017). Quantum machine learning, Nature 549(7671): 195–202, DOI: 10.1038/nature23474.
• [4] Gibney, E. (2019). Hello quantum world! Google publishes landmark quantum supremacy claim, Nature 574(7779): 461–462, DOI: 10.1038/d41586-019-03213-z.
• [5] IBM (2019). Q Experience, https://quantum-computing.ibm.com/.
• [6] Kołaczek, D., Spisak, B.J. and Wołoszyn, M. (2019). The phase-space approach to time evolution of quantum states in confined systems: The spectral split-operator method, International Journal of Applied Mathematics and Computer Science 29(3): 439–451, DOI: 10.2478/amcs-2019-0032.
• [7] Li, J., Yang, X., Peng, X. and Sun, C. (2017). Hybrid quantum-classical approach to quantum optimal control, Physical Review Letters 118(15): 150503, DOI: 10.1103/PhysRevLett.118.150503.
• [8] Li, Z. and Li, P. (2015). Clustering algorithm of quantum self-organization network, Open Journal of Applied Sciences 05(6): 270–278, DOI: 10.4236/ojapps.2015.56028.
• [9] MacMahon, D. (2007). Quantum Computing Explained, John Wiley, Hoboken, NJ.
• [10] Mitarai, K., Negoro, M., Kitagawa, M. and Fujii, K. (2018). Quantum circuit learning, Physical Review Letters 98(3): 032309, DOI: 10.1103/PhysRevA.98.032309.
• [11] Narayanan, A. and Menneer, T. (2000). Quantum artificial neural network architectures and components, Information Sciences 128(3–4): 231–255, DOI: 10.1016/S0020-0255(00)00055-4.
• [12] Nielsen, M. and Chuang, I. (2010). Quantum Computation and Quantum Information, 10th Anniversary Edition, Cambridge University Press, Cambridge.
• [13] Ortigoso, J. (2018). Twelve years before the quantum no-cloning theorem, American Journal of Physics 86(3): 201–205, DOI: 10.1119/1.5021356.
• [14] Park, J. (1970). The concept of transition in quantum mechanics, Foundations of Physics 1(1): 23–33, DOI: 10.1007/BF00708652.
• [15] Pati, A.K. and Braunstein, S.L. (2000). Impossibility of deleting an unknown quantum state, Nature 404(6774): 164–165, DOI: 10.1038/35004532.
• [16] Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. and Duchesnay, E. (2011). Scikit-learn: Machine learning in Python, Journal of Machine Learning Research 12: 2825–2830, DOI: 10.5555/1953048.2078195.
• [17] Pérez-Salinas, A., Cervera-Lierta, A., Gil-Fuster, E. and Latorre, J. (2020). Data re-uploading for a universal quantum classifier, Quantum 4: 226, DOI: 10.22331/q-2020-02-06-226.
• [18] Rigetti (2019). Quantum Computing Systems, https://www.rigetti.com/systems.
• [19] Schuld, M., Sinayskiy, I. and Petruccione, F. (2014). Quantum computing for pattern classification, in D.-N. Pham and S.-B. Park (Eds), PRICAI 2014: Trends in Artificial Intelligence, Springer, Cham, pp. 208–220, DOI: 10.1007/978-3-319-13560-1_17.
• [20] Schuld, M., Sinayskiy, I. and Petruccione, F. (2015). An introduction to quantum machine learning, Contemporary Physics 56(2): 172–185, DOI: 10.1080/00107514.2014.964942.
• [21] Veenman, C. and Reinders, M. (2005). The nearest sub-class classifier: a compromise between the nearest mean and nearest neighbor classifier, IEEE Transactions on Pattern Analysis and Machine Intelligence 27(9): 1417–1429, DOI: 10.1109/TPAMI.2005.187.
• [22] Weigang, L. (1998). A study of parallel self-organizing map, arXiv: quant-ph/9808025v3.
• [23] Wiebe, N., Kapoor, A. and Svore, M. (2015). Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning, Quantum Information and Computation 15(3–4): 316–356.
• [24] Wiśniewska, J. and Sawerwain, M. (2020). Simple quantum circuits for data classification, in N.T. Nguyen et al. (Eds), Intelligent Information and Database Systems, Springer, Cham, pp. 392–403, DOI: 0.1007/978-3-030-41964-6_34.
• [25] Wootters, W. and Zurek, W. (1982). A single quantum cannot be cloned, Nature 299(5886): 802–803, DOI: 10.1038/299802a0.
• [26] Zoufal, C., Lucchi, A. and Woerner, S. (2019). Quantum generative adversarial networks for learning and loading random distributions, Quantum Information 5(1): 103, DOI: 10.1038/s41534-019-0223-2.