IMPLEMENTATION OF A PROBABLE DEEP NEURAL NETWORK DECODER FOR STABILIZER CODES
Keywords:
Modeling, quantum algorithm, qubit, model of a quantum computer, entanglement, superposition, quantum operator
Abstract
Recently, there has been a rapid increase in interest in quantum computers. Their work is
based on the use of quantum-mechanical phenomena such as superposition and entanglement for
computing to transform input data into outputs that can actually provide effective performance
3–4 orders of magnitude higher than any modern computing devices, which will allow solving the
above and other tasks in real and accelerated time scale. This work is a study of the influence of
the environment on a quantum system of qubits and the results of its implementation. A probabilistic
deep neural network decoder for stabilizer codes has been developed. The issues of error correction
for a three-bit code without state decoding are analyzed and considered. The relevance of
these studies lies in mathematical and software modeling and implementation of correction codes
for correcting several types of quantum errors in the development and implementation of quantum
algorithms for solving classes of problems of a classical nature. The scientific novelty of this direction
is expressed in the elimination of one of the disadvantages of the quantum computational
process. The scientific novelty of this area is primarily expressed in the constant updating and
supplementation of the field of quantum research in a number of areas.
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Quantum Gates, Springer, 2011, pp. 51-122.
21. Potapov V., Gushanskiy S., Guzik V., Polenov M. The Computational Structure of the Quantum
Computer Simulator and Its Performance Evaluation, In: Software Engineering Perspectives
and Application in Intelligent Systems. Advances in Intelligent Systems and Computing.
Springer, 2019, Vol. 763, pp. 198-207.
22. 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.
23. 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).
24. Hallgren H.S. An improved quantum Fourier transform algorithm and applications, In: Proceedings
of the 41st Annual Symposium on Foundations of Computer Science, Redondo Beach,
CA. IEEE, 2000, pp. 515.
25. Boneh D., Zhandry M. Quantum-secure message authentication codes, In: Proceedings of
Eurocrypt, 2013, pp. 592-608.
26. Potapov V., Gushansky S., Guzik V., Polenov M. Architecture and Software Implementation of
a Quantum Computer Model // In: Advances in Intelligent Systems and Computing. Springer,
2016, Vol. 465, pp. 59-68.
Vol. 54, pp. 1098-1106.
2. Linke N.M., Gutierrez M., Landsman K.A., et al. Fault-tolerant quantum error detection, Science
Advances, 2017, 3 (10): e1701074. Available from: https://doi.org/10.1126/
sciadv.1701074.
3. Vuillot C. Is error detection helpful on IBM 5q chips?, Quantum Information and Computation,
2018, Vol. 18, No. 11-12, pp. 0949-0964.
4. Harper R., Flammia S.T. Fault-tolerant logical gates in the IBM quantum experience, Phys Rev
Lett., 2019. 122:080504. Available from: https://link.aps.org/doi/10.1103/
PhysRevLett.122.080504.
5. Wootton J.R., Loss D. Repetition code of 15 qubits, Physical Review A, 2018, Vol. 97 (5).
Available from: https://doi.org/10.1103/physreva.97.052313.
6. Aspuru-Guzik A., Dutoi A.D., Love P.J., et al. Simulated quantum computation of molecular
energies, Science, 2005, Vol. 309 (5741), pp. 1704-1707. Available from: https://science.
sciencemag.org/content/309/5741/1704.
7. Knill M., Laflamme R., and Zurek W. Threshold accuracy for quantum computation.
quantph/9610011, 15 Oct 1996.
8. 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.
9. 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. 6 (191), pp. 223-233.
10. Guzik V.F., Gushanskiy S.M., Potapov V.S. Kolichestvennye kharakteristiki stepeni
zaputannosti [Quantitative characteristics of the degree of entanglement], Izvestiya YuFU.
Tekhnicheskie nauki [Izvestiya SFedU. Engineering Sciences], 2016, No. 3 (176), pp. 76-86.
11. Kleppner D., Kolenkow R. An Introduction to Mechanics (Second ed.). Cambridge: Cambridge
University Press, 2014, 49 p.
12. 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, postgraduates
and students of ITSAiU-2016]. Rostov-on-Don: Izd-vo YuFU, 2016, Vol. 3, pp. 123-129.
13. Gushansky S., Pykhovskiy V., Kozlovskiy A., Potapov V. Development of a scheme of a hardware
accelerator of quantum computing for correction quantum types of errors, The 4-th Computational
Methods in Systems and Software 2020, Czech Republic, pp. 64-73.
14. 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.
15. Guzik V., Gushanskiy S., Polenov M., Potapov V. Complexity Estimation of Quantum Algorithms
Using Entanglement Properties, 16th International Multidisciplinary Scientific
GeoConference, Bulgaria, 2016, pp. 20-26;
16. Guzik V., Gushanskiy S., Polenov M., Potapov V. Models of a quantum computer, their characteristics
and analysis, 9th International Conference on Application of Information and Communication
Technologies (AICT). Institute of Electrical and Electronics Engineers, 2015,
pp. 583-587.
17. Collier D. The Comparative Method. In: Finifter A.W. (ed.) Political Sciences: The State of
the Discipline II. pp. 105-119: American Science Association. Washington, DC, 1993.
18. Olukotun K. Chip Multiprocessor Architecture – Techniques to Improve Throughput and Latency.
Morgan and Claypool Publishers, San Rafael, 2007.
19. 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, 2007, Vol. 176, pp. 121-136.
20. Williams C.P. Explorations in Quantum Computing. Texts in Computer Science, Chapter 2.
Quantum Gates, Springer, 2011, pp. 51-122.
21. Potapov V., Gushanskiy S., Guzik V., Polenov M. The Computational Structure of the Quantum
Computer Simulator and Its Performance Evaluation, In: Software Engineering Perspectives
and Application in Intelligent Systems. Advances in Intelligent Systems and Computing.
Springer, 2019, Vol. 763, pp. 198-207.
22. 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.
23. 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).
24. Hallgren H.S. An improved quantum Fourier transform algorithm and applications, In: Proceedings
of the 41st Annual Symposium on Foundations of Computer Science, Redondo Beach,
CA. IEEE, 2000, pp. 515.
25. Boneh D., Zhandry M. Quantum-secure message authentication codes, In: Proceedings of
Eurocrypt, 2013, pp. 592-608.
26. Potapov V., Gushansky S., Guzik V., Polenov M. Architecture and Software Implementation of
a Quantum Computer Model // In: Advances in Intelligent Systems and Computing. Springer,
2016, Vol. 465, pp. 59-68.
Published
2021-12-24
Issue
Section
SECTION II. INFORMATION PROCESSING ALGORITHMS
