Quantum cluster algorithm for data classification
Tóm tắt
We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of
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A. J. Arko, J. J. Joyce, A. B. Andrews, J. D. Thompson, J. L. Smith, D. Mandrus, M. F. Hundley, A. L. Cornelius, E. Moshopoulou, Z. Fisk, et al., Strongly correlated electron systems: Photoemission and the single-impurity model. Phys. Rev. B.56(12), R7041 (1997).
J. M. Arrazola, T. R. Bromley, J. Izaac, C. R. Myers, K. Brádler, N. Killoran, Machine learning method for state preparation and gate synthesis on photonic quantum computers. Quantum Sci. Technol.4(2), 024004 (2019).
L. -F. Arsenault, A. Lopez-Bezanilla, O. A. von Lilienfeld, A. J. Millis, Machine learning for many-body physics: The case of the anderson impurity model. Phys. Rev. B. 90(15), 155136 (2014).
F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., Quantum supremacy using a programmable superconductingprocessor. Nature. 574(7779), 505–510 (2019).
J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, S. Lloyd, Quantum machine learning. Nature. 549(7671), 195 (2017).
V. Botu, R. Ramprasad, Adaptive machine learning framework to accelerate ab initio molecular dynamics. Int. J. Quantum Chem.115(16), 1074–1083 (2015).
F. Brockherde, L. Vogt, L. Li, M. E. Tuckerman, K. Burke, K. -R. Müller, Bypassing the kohn-sham equations with machine learning. Nat. Commun.8(1), 1–10 (2017).
P. Broecker, J. Carrasquilla, R. G. Melko, S. Trebst, Machine learning quantum phases of matter beyond the fermion sign problem. Sci. Rep.7(1), 1–10 (2017).
X. -D. Cai, D. Wu, Z. -E. Su, M. -C. Chen, X. -L. Wang, L. Li, N. -L. Liu, C. -Y. Lu, J. -W. Pan, Entanglement-based machine learning on a quantum computer. Phys. Rev. Lett.114(11), 110504 (2015).
J. Cao, Y. Fang, Q. Liu, A. Liu, in 2016 5th International Conference on Computer Science and Network Technology (ICCSNT). Combined prediction model of quantum genetic grey prediction model and support vector machine (IEEE, 2016), pp. 247–251.
Y. Chen, S. Zhang, F. Ke, C. Ko, S. Lee, K. Liu, B. Chen, J. W. Ager, R. Jeanloz, V. Eyert, et al., Pressure–temperature phase diagram of vanadium dioxide. Nano Lett.17(4), 2512–2516 (2017).
K. Ch’Ng, J. Carrasquilla, R. G. Melko, E. Khatami, Machine learning phases of strongly correlated fermions. Phys. Rev. X. 7(3), 031038 (2017).
J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett.23(15), 880 (1969).
E. Dagotto, Complexity in strongly correlated electronic systems. Science. 309(5732), 257–262 (2005).
P. De Luna, J. Wei, Y. Bengio, A. Aspuru-Guzik, E. Sargent, Use machine learning to find energy materials (Nature Publishing Group, 2017).
S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman, K. Wright, C. Monroe, Demonstration of a small programmable quantum computer with atomic qubits. Nature. 536(7614), 63 (2016).
V. Dixit, R. Selvarajan, T. Aldwairi, Y. Koshka, M. A. Novotny, T. S. Humble, M. A. Alam, S. Kais, Training a quantum annealing based restricted boltzmann machine on cybersecurity data. IEEE Trans. Emerg. Top. Comput. Intell. (2021). IEEE.
R. O. Duda, P. E. Hart, et al., Pattern classification and scene analysis, vol. 3 (Wiley, New York, 1973).
E. Farhi, H. Neven, Classification with quantum neural networks on near term processors. arXiv preprint arXiv:1802.06002 (2018).
J. Gao, L. -F. Qiao, Z. -Q. Jiao, Y. -C. Ma, C. -Q. Hu, R. -J. Ren, A. -L. Yang, H. Tang, M. -H. Yung, X. -M. Jin, Experimental machine learning of quantum states. Phys. Rev. Lett.120(24), 240501 (2018).
F. Häse, C. Kreisbeck, A. Aspuru-Guzik, Machine learning for quantum dynamics: deep learning of excitation energy transfer properties. Chem. Sci.8(12), 8419–8426 (2017).
V. Havlíček, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, J. M. Gambetta, Supervised learning with quantum-enhanced feature spaces. Nature. 567(7747), 209 (2019).
Z. Hu, R. Xia, S. Kais, A quantum algorithm for evolving open quantum dynamics on quantum computing devices. Sci. Rep.10(1), 1–9 (2020).
J. Jeong, N. Aetukuri, T. Graf, T. D. Schladt, M. G. Samant, S. S. Parkin, Suppression of metal-insulator transition in vo2 by electric field–induced oxygen vacancy formation. Science. 339(6126), 1402–1405 (2013).
M. Karra, K. Sharma, B. Friedrich, S. Kais, D. Herschbach, Prospects for quantum computing with an array of ultracold polar paramagnetic molecules. J. Chem. Phys.144(9), 094301 (2016).
A. G. Kusne, T. Gao, A. Mehta, L. Ke, M. C. Nguyen, K. -M. Ho, V. Antropov, C. -Z. Wang, M. J. Kramer, C. Long, et al., On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets. Sci. Rep.4(1), 1–7 (2014).
D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, et al., Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature. 422(6930), 412 (2003).
J. Li, Z. Hu, S. Kais, A practical quantum encryption protocol with varying encryption configurations. arXiv preprint arXiv:2101.09314 (2021).
Z. Li, X. Liu, N. Xu, J. Du, Experimental realization of a quantum support vector machine. Phys. Rev. Lett.114(14), 140504 (2015).
D. J. C. MacKay, D. J. C. Mac Kay, Information theory, inference and learning algorithms (Cambridge university press, 2003).
K. Mitarai, M. Negoro, M. Kitagawa, K. Fujii, Quantum circuit learning. Phys. Rev. A. 98(3), 032309 (2018).
T. Mitchell, B. Buchanan, G. DeJong, T. Dietterich, P. Rosenbloom, A. Waibel, Machine learning. Ann. Rev. Comput. Sci.4(1), 417–433 (1990).
G. Montavon, M. Rupp, V. Gobre, A. Vazquez-Mayagoitia, K. Hansen, A. Tkatchenko, K. -R. Müller, O. A. Von Lilienfeld, Machine learning of molecular electronic properties in chemical compound space. New J. Phys.15(9), 095003 (2013).
W. E. Perreault, N. Mukherjee, R. N. Zare, Cold quantum-controlled rotationally inelastic scattering of hd with h 2 and d 2 reveals collisional partner reorientation. Nat. Chem.10(5), 561 (2018).
M. M. Qazilbash, M. Brehm, B. -G. Chae, P. -C. Ho, G. O. Andreev, B. -J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, et al., Mott transition in vo2 revealed by infrared spectroscopy and nano-imaging. Science. 318(5857), 1750–1753 (2007).
P. Rebentrost, T. R. Bromley, C. Weedbrook, S. Lloyd, Quantum hopfield neural network. Phys. Rev. A.98(4), 042308 (2018).
S. Roy, Z. Hu, S. Kais, P. Bermel, Enhancement of Photovoltaic Current through Dark States in Donor-Acceptor Pairs of Tungsten-Based Transition Metal Di-Chalcogenides. Adv. Funct. Mater.31(23), 2100387 (2021).
M. Sajjan, S. H. Sureshbabu, S. Kais, Quantum machine-learning for eigenstate filtration in two-dimensional materials. arXiv preprint arXiv:2105.09488 (2021).
M. Schuld, N. Killoran, Quantum machine learning in feature hilbert spaces. Phys. Rev. Lett.122(4), 040504 (2019).
Z. W. Ulissi, A. J. Medford, T. Bligaard, J. K. Nørskov, To address surface reaction network complexity using scaling relations machine learning and dft calculations. Nat. Commun.8(1), 1–7 (2017).
E. P. L. Van Nieuwenburg, Y. -H. Liu, S. D. Huber, Learning phase transitions by confusion. Nat. Phys.13(5), 435–439 (2017).
L. Wang, Discovering phase transitions with unsupervised learning. Phys. Rev. B.94(19), 195105 (2016).
J. N. Wei, D. Duvenaud, A. Aspuru-Guzik, Neural networks for the prediction of organic chemistry reactions. ACS Cent. Sci.2(10), 725–732 (2016).
N. Wiebe, A. Kapoor, K. Svore, Quantum algorithms for nearest-neighbor methods for supervised and unsupervised learning. arXiv preprint arXiv:1401.2142 (2014).
R. Xia, T. Bian, S. Kais, Electronic structure calculations and the ising hamiltonian. J. Phys. Chem. B.122(13), 3384–3395 (2017).
R. Xia, S. Kais, Quantum machine learning for electronic structure calculations. Nat. Commun.9(1), 1–6 (2018).
Y. Xia, W. Li, Q. Zhuang, Z. Zhang, Quantum-enhanced data classification with a variational entangled sensor network. Phys. Rev. X. 11(2), 021047 (2021).