Implementing Quantum Fourier Transform in a Digital Quantum Coprocessor

2019;
: pp. 6 - 13
Authors:
1
Lviv Polytechnic National University, Department of Electronic Computing Machines

In this paper, the digital quantum coprocessor has been checked for the possibility of quantum Fourier transform, which is the main quantum operation of the Shor's algorithm. To do this, the model of the 4-qubit coprocessor has been created, its work has been simulated and it has been implemented in FPGA.

[1] Valeriy Hlukhov. “Kvantovyy kompyuter kak veroyatnostnyy kompyuter”. Shosta mizhnarodna naukova konferencija «Modeljuvannja-2018». September 12-14, 2018 Kyiv, Ukraine. Zbirka pracj konferenciji, p. 111 – 114.

[2] Valerii Hlukhov, Bohdan Havano. FPGA-based Digital Quantum Coprocessor. Advances in Cyber-Physical Systems. Volume 3. Number 2. Lviv Polytechnic National University. 2018. pp. 12 - 31.

[3] Peter W. Shor. Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, Santa Fe, NM, Nov. 20–22, 1994, IEEE Computer Society Press, pp. 124–134.

[4] Shor's algorithm. https: //en.wikipedia.org/wiki/Shor%27s_algorithm 08.02.2019.

[5] Applying Moore’s Law to Quantum Qubits https://quantumcomputingreport.com/our-take/applyingmoores-law-to-quantu... Copyright © 2019 Quantum Computing Report, All rights reserved 19.02.2019

[6] Quantum computing. https://en.wikipedia.org/wiki/Quantum_computing 08.02.2019.

[7] Qubit. https://en.wikipedia.org/wiki/Qubit. 08.02.2019.

[8] Introduction to Quantum Computing. https://blogs.msdn.microsoft.com/uk_faculty_connection/2018/02/06/introd... 08.02.2019.

[9] Quantum logic gate. https://en.wikipedia.org/wiki/Quantum_logic_gate 08.02.2019.

[10] Quantum Fourier transform. https://en.wikipedia.org/wiki/Quantum_Fourier_transform 08.02.2019.

[11] National Academies of Sciences, Engineering, and Medicine. 2019. Quantum Computing: Progress and Prospects. The National Academies Press, Washington, DC. doi: https://doi.org/10.17226/25196.

[12] Welcome to the Microsoft Quantum Development Kit Preview. https://docs.microsoft.com/ruru/quantum/?view=qsharp-preview 08.02.2019

[13] M. Khalil-Hani, Y. H. Lee, M. N. Marsono. An Accurate FPGA-Based Hardware Emulation on Quantum Fourier Transform. Proceedings of the 13th Australasian Symposium on Parallel and Distributed Computing (AusPDC 2015), Sydney, Australia, 27 - 30 January 2015. Pp. 23 – 30.

[14] CPLD. https://www.xilinx.com/products/silicondevices/cpld/cpld.html 16.02.2019

[15] Gushanskiy S. M., Pereverzev V. A. Simulation of Quantum Computing using Hardware Cores. Nauchnyy zhurnal KubGAU, №123(09), 2016. pp. http://ej.kubagro.ru/2016/09/pdf/37.pdf

[16] LFSR-Random number generator:: Overview. https://opencores.org/projects/lfsr_randgen 14.02.2019.

[17] Pseudo Random Number Generators as synthesizable VHDL code. https://github.com/jorisvr/vhdl_prng 14.02.2019

[18] Popov B.A.. Tesler G.S. Vychisleniye funktsiy na EVM. Spravochnik. Kiyev: Nauk. Dumka, 1984. 59 p. (In Russian).

[19] V. V. Aristov. Integro-algoritmicheskiye vychisleniya. "Nauk. Dumka", 1980. 189 p. (In Russian).

[20] Jonathan Hui. QC — Quantum Fourier Transform. https://medium.com/@jonathan_hui/qc-quantum-fouriertransform-45436f90a43 2019.07.07 01:17

[21] Spartan-6 Family Overview. DS160 (v2.0) October 25, 2011. Product Specification. https://www.xilinx.com/support/documentation/data_sheets/ds160.pdf 14.02.2019

[22] Valeriy Hlukhov, Bohdan Havano. Principles of Digital Quantum Coprocessor Based on a FPGA, which Operates under the Control of a Classical Compute. Advanced Computer Information Technologies Acit 2019. June 5 - 7, 2019. International Conference. Ceske Budejovice, Czech Republic. Conference Proceedings, pp.