Top

Quantum Information Processing

Published in:

01-08-2023

A family of unitaries for the quantum period finding algorithm

Authors: John George Francis, Anil Shaji

Published in: Quantum Information Processing | Issue 8/2023

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We use differentiable programming and gradient descent to find unitary matrices that can be used in the period finding algorithm to extract period information from the state of a quantum computer post-application of the oracle. The standard procedure is to use the inverse quantum Fourier transform. Our findings suggest that this is not the only unitary matrix appropriate for the period finding algorithm. There exists a family of unitary matrices that can affect out the same transformation and they are related by a symmetry. An analysis of this symmetry is presented. These unitary matrices can be learned by an algorithm which reveals the underlying symmetry. We also find simple neural networks are able to learn this symmetry and differentiate such unitary matrices from randomly generated ones.

previous article The Feasible Hyper-encoding Measurement-device-independent Deterministic Secure Quantum Communication Protocol

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Available only for authorised users

Feynman, R.P.: Simulating physics with computers. Int. J. Theor. Phys. 21(6/7) (1982)

Deutsch, D., Jozsa, R.: Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. Ser. Math. Phys. Sci. 439, 553–558 (1992)ADSMathSciNetMATH

Simon, D.R.: On the power of quantum computation. SIAM J. Comput. 26(5), 1474–1483 (1997). https://doi.org/10.1137/S0097539796298637MathSciNetCrossRefMATH

Baydin, A.G., Pearlmutter, B.A., Radul, A.A., Siskind, J.M.: Automatic differentiation in machine learning: a survey. J. Mach. Learn. Res. 18(153), 1–43 (2018)MathSciNetMATH

Wengert, R.E.: A simple automatic derivative evaluation program. Commun. ACM 7(8), 463–464 (1964). https://doi.org/10.1145/355586.364791CrossRefMATH

Gepp, A., Stocks, P.: A review of procedures to evolve quantum algorithms. Genet. Program Evolvable Mach. 10(2), 181–228 (2009). https://doi.org/10.1007/s10710-009-9080-7CrossRef

Cincio, L., Subaşı, Y., Sornborger, A.T., Coles, P.J.: Learning the quantum algorithm for state overlap. New J. Phys. 20(11), 113022 (2018). https://doi.org/10.1088/1367-2630/aae94aADSCrossRef

Bang, J., Ryu, J., Yoo, S., Pawłowski, M., Lee, J.: A strategy for quantum algorithm design assisted by machine learning. New J. Phys. 16(7), 073017 (2014). https://doi.org/10.1088/1367-2630/16/7/073017ADSCrossRefMATH

Wan, K.H., Liu, F., Dahlsten, O., Kim, M.S.: Learning Simon’s Quantum Algorithm (2018)

10.

Morales, M.E.S., Tlyachev, T., Biamonte, J.: Variational learning of Grover’s quantum search algorithm. Phys. Rev. A 98, 062333 (2018). https://doi.org/10.1103/PhysRevA.98.062333ADSCrossRef

11.

Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing. STOC ’96, pp. 212–219. Association for Computing Machinery, New York (1996). https://doi.org/10.1145/237814.237866

12.

Gammelmark, S., Mølmer, K.: Quantum learning by measurement and feedback. New J. Phys. 11(3), 033017 (2009). https://doi.org/10.1088/1367-2630/11/3/033017ADSCrossRef

13.

Lomont, C.: The hidden subgroup problem-review and open problems. https://arxiv.org/abs/quant-ph/0411037 (2004)

14.

Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. In: Bengio, Y., LeCun, Y. (eds.) 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, 7–9 May, 2015, Conference Track Proceedings (2015). arXiv:1412.6980

15.

Ruder, S.: An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747 (2016)

16.

Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G.S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mané, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viégas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., Zheng, X.: TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems. Software available from tensorflow.org (2015). https://www.tensorflow.org/

17.

Jalabert, R.A., Pastawski, H.M.: Environment-independent decoherence rate in classically chaotic systems. Phys. Rev. Lett. 86, 2490–2493 (2001). https://doi.org/10.1103/PhysRevLett.86.2490ADSCrossRef

18.

Dreyfus, S.E.: Artificial neural networks, back propagation, and the Kelley-Bryson gradient procedure. J. Guid. Control. Dyn. 13(5), 926–928 (1990). https://doi.org/10.2514/3.25422ADSMathSciNetCrossRef

19.

Leshno, M., Lin, V.Y., Pinkus, A., Schocken, S.: Multilayer feedforward networks with a nonpolynomial activation function can approximate any function. Neural Netw. 6(6), 861–867 (1993). https://doi.org/10.1016/S0893-6080(05)80131-5CrossRef

20.

Nair, V., Hinton, G.E.: Rectified linear units improve restricted Boltzmann machines. In: Proceedings of the 27th International Conference on International Conference on Machine Learning. ICML’10, pp. 807–814. Omnipress, Madison (2010)

21.

Goodfellow, I.J., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., Bengio, Y.: Generative adversarial nets. In: Proceedings of the 27th International Conference on Neural Information Processing Systems—Volume 2. NIPS’14, pp. 2672–2680. MIT Press, Cambridge (2014)

22.

Mermin, N.D.: Period Finding and Continued Fractions. Quantum Computer Science, An Introduction, pp. 197–200. Cambridge University Press, Cambridge (2007)CrossRef

Title: A family of unitaries for the quantum period finding algorithm
Authors: John George Francis
Anil Shaji
Publication date: 01-08-2023
Publisher: Springer US
Published in: Quantum Information Processing / Issue 8/2023
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI: https://doi.org/10.1007/s11128-023-04079-x

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 8/2023

Renormalized Von Neumann entropy with application to entanglement in genuine infinite dimensional systems

Qudit surface codes and hypermap codes

Quantum error correction scheme for fully-correlated noise

An improved method for quantum matrix multiplication

Entanglement of two quantum dots with dipole–dipole interaction coupled to a cavity in plasmonic waveguide system

Anonymous quantum conference key agreement using the W state