STUDY OF A QUANTUM COMPUTING SYSTEM AND IMPLEMENTATION OF A QUANTUM CORE ON FPGA
Abstract
The quantum core method is one of the most important methods in quantum machine learning.
However, the number of features used for quantum nuclei is limited to a few dozen features.
The block product state structure is used as a quantum feature map and the implementation of
programmable gate matrices is demonstrated. The relevance of these studies lies in the mathematical
and software modeling and implementation of a quantum computing system as part of the
development of the implementation of a quantum core on FPGA for solving classes of problems of
a classical nature. The scientific novelty of this research area is the development of a hybrid simulator
of the quantum cores of a central processing unit (CPU) and a programmable logic integrated
circuit (FPGA) several orders of magnitude faster than a conventional quantum computing
simulator. This joint development of the implemented quantum core and its efficient FPGA implementation allowed numerical simulation of the quantum core based on gates in terms of input
features, up to 780-dimensional features using 4000 samples. We applied the quantum kernel to
image classification problems using the Fashion-MNIST dataset and showed that the quantum
kernel is comparable to Gaussian kernels with optimized throughput. The analysis of the work in
this field has shown that a new qualitative level has now been reached, opening up promising opportunities
for the implementation of multi-qubit quantum computing. The prospects for implementation
and development are connected not only with technological capabilities, but also with solving
the issues of building effective quantum systems for solving actual mathematical problems,
cryptography problems and control (optimization) problems.
References
05.11.2022. Available at: http://ru.wikipedia.org/?oldid=82377595 (accessed 05 November 2022).
2. Trubitsyn A.A. Raschet traektorii dvizheniya material'noy tochki v dvumernom
(osesimmetrichnom) konservativnom pole [Calculation of the trajectory of a material point in a
two-dimensional (axisymmetric) conservative field], Zhurnal vychislitel'noy matematiki i
matematematicheskoy fiziki [Journal of Computational Mathematics and Mathematical Physics],
1990, Vol. 30, No. 7, pp. 1113-1115; U.S.S.R. Comput. Math. Math. Phys., 1990, 30:4,
pp. 107-109.
3. Arthur Trew (ed.), Greg Wilson (ed.). Past, Present, Parallel: A Survey of Available Parallel
Computer Systems. Springer, 1991, 392 p. ISBN 9783540196648.
4. Quantum phase estimation algorithm (2022, Nov 03). In Wikipedia, The Free Encyclopedia.
Retrieved. 05:15, Nov 3, 2022, from https://en.wikipedia.org/w/index.php?Title=Quantum_
phase_estimation_algorithm&oldid=731732789.
5. Richard G. Milner. A Short History of Spin, Contribution to the XVth International Workshop
on Polarized Sources, Targets, and Polarimetry. Charlottesville, Virginia, USA, September
9-13, 2013. arXiv:1311.5016.
6. Gushanskiy S.M., Potapov V.S. Metodika razrabotki i postroeniya kvantovykh algoritmov
[Methodology of development and construction of quantum algorithms], Informatizatsiya i
svyaz' [Informatization and communication], 2017, No. 3, pp. 101-104.
7. Gushanskiy S.M. Polenov M.Yu., Potapov V.S. Realizatsiya komp'yuternogo modelirovaniya
sistemy s chastitsey v odnomernom i dvukhmernom prostranstve na kvantovom urovne [Implementation
of computer simulation of a system with a particle in one-dimensional and twodimensional
space at the quantum level], Izvestiya YuFU. Tekhnicheskie nauki [Izvestiya
SFedU. Engineering Sciences], 2017, No. 3 (188), pp. 223-233.
8. Hales S. Hallgren. An improved quantum Fourier transform algorithm and applications, Proceedings
of the 41st Annual Symposium on Foundations of Computer Science. November
12–14, 2000, pp. 515.
9. Potapov V., Gushanskiy S., Polenov M. The Methodology of Implementation and Simulation
of Quantum Algorithms and Processes, 2017 11th International Conference on Application of
Information and Communication Technologies (AICT). Institute of Electrical and Electronics
Engineers, 2017, pp. 437-441.
10. Lukin M.D. Attractive photons in a quantum nonlinear medium, Ofer Firstenberg, Nature.
October 2013, Vol. 502.
11. Nil'sen M., Chang I. Kvantovye vychisleniya i kvantovaya informatsiya = Quantum Computation
and Quantum Information [Quantum computing and quantum information = Quantum
Compu-tation and Quantum Information]. Moscow: Mir, 2006.
12. Quantum mechanics. In Wikipedia, The Free Encyclopedia. Retrieved 15:50, March 30, 2022.
Available at: https://en.wikipedia.org/w/index. php?title=Quantum_mechanics&oldid=772744105.
13. Boneh D., Zhandry M. Quantum-secure message authentication codes, Proceedings of
Eurocrypt, 2013, pp. 592-608.
14. Chris Ferrie. Quantum Physics for Babies, Sourcebooks Jabberwocky. Brdbk edition,
2017-05-02, pp. 23-24.
15. Tomas Kh. Kormen, Charl'z I. Leyzerson, Ronal'd L. Rivest, Klifford SHtayn. Algoritmy:
postroenie i analiz = Introduction to Algorithms [Algorithms: Construction and analysis = Introduction
to Algorithms]. 2nd ed. Moscow: Vil'yams, 2006, 1296 p. ISBN 0-07-013151-1.
16. Bennett С.H., Shor P.W., Smolin J.A., Thapliyal A.V. Entanglement-assisted Capacity of a
Quantum Channel and the Reverse Shannon Theorem, IEEE Transactions on Information
Theory, 2002, Vol. 48, pp. 2637-2655.
17. Kleppner D., Kolenkow R. An Introduction to Mechanics (Second ed.). Cambridge: Cambridge
University Press, 2014, 49 p.
18. Potapov V.S., Gushanskiy S.M. Kvantovye tipy oshibok i metody ikh ustraneniya, zavisimost'
oshibki ot mery i chistoty zaputannosti [Quantum types of errors and methods of their elimination,
the dependence of error on the measure and purity of entanglement], Sb. trudov XIV Vserossiyskoy
nauchnoy konferentsii molodykh uchenykh, aspirantov i studentov ITSAiU-2016 [Proceedings of the
XIV All-Russian Scientific Conference of Young Scientists, graduate Students and students of
ITSAiU-2016]. Rostov-on-Don: Izd-vo YuFU, 2016, Vol. 3, pp. 123-129.
19. Olukotun K. Chip Multiprocessor Architecture – Techniques to Improve Throughput and Latency.
Morgan and Claypool Publishers, San Rafael, 2007.
20. Raedt K.D., Michielsen K., De Raedt H., Trieu B., Arnold G., Marcus Richter, Th Lip-pert,
Watanabe H., and Ito, N. Massively parallel quantum computer simulator, Computer Physics
Communications, Vol. 176, pp. 121-136.
21. Williams C.P. Explorations in Quantum Computing, Texts in Computer Science. Chapter 2.
Quantum Gates, pp. 51-122. Springer, 2011.
22. Potapov V., Gushanskiy S., Guzik V., Polenov M. The Computational Structure of the Quantum
Computer Simulator and Its Performance Evaluation, Software Engineering Perspectives and
Application in Intelligent Systems. Advances in Intelligent Systems and Computing, Vol. 763,
pp. 198-207. Springer, 2019.
23. Potapov V.S., Gushanskiy S.M. Razrabotka i issledovanie metodiki postroeniya vychislitel'noy
kvantovoy sistemy s ispol'zovaniem apparatnykh sredstv optimizatsii [Development and research
of a methodology for constructing a computational quantum system using optimization
hardware], Informatsionnye tekhnologii i vychislitel'nye sistemy [Information technologies and
computing systems], 2022, No. 1, pp. 26-32.
24. Milner R.G. A Short History of Spin. In: Contribution to the XV International Workshop on
Polarized Sources, Targets, and Polarimetry. Charlottesville, Virginia, USA, September 9–13,
2013. arXiv:1311.5016, 2013.
25. Hallgren H.S. An improved quantum Fourier transform algorithm and applications, Proceedings
of the 41st Annual Symposium on Foundations of Computer Science, Redondo Beach, CA,
pp. 515. IEEE, 2000.
26. Boneh D., Zhandry M. Quantum-secure message authentication codes, Proceedings of
Eurocrypt, 2013, pp. 592-608.
