Integer numeric multiplication using quantum Fourier transform. (English) Zbl 07899033
Summary: Quantum computing is a computation process that exploits the theory of quantum physics. Quantum algorithms have the power to perform tasks with fewer queries than classical computing. To realise the advantages of quantum algorithms, arithmetic operations are required. Among them, multiplication operation is a hot topic for research. In this paper, we have proposed a generic structure for the multiplication of any two integers using quantum Fourier transform. This approach of multiplication is applicable for different quantum applications. The generic pattern and the various merits of the proposed quantum circuits are explained and analysed.
MSC:
| 81-XX | Quantum theory |
References:
| [1] | Nielsen, M. A., Chuang, I. L.: Quantum computing and quantum information (2000) · Zbl 1049.81015 |
| [2] | Biswas, AK; Hasan, MM; Chowdhury, AR; Babu, HMH, Efficient approaches for designing reversible binary coded decimal adders, Microelectron. J., 39, 1693-1703 (2008) · doi:10.1016/j.mejo.2008.04.003 |
| [3] | Bruce, J., Thornton, M. A., Shivakumaraiah, L., Kokate, P., Li, X.: Efficient adder circuits based on a conservative reversible logic gate. In: Proceedings IEEE Computer Society Annual Symposium on VLSI. New Paradigms for VLSI Systems Design. ISVLSI 2002, IEEE, pp. 83-88 (2002) |
| [4] | Thapliyal, H., Mapping of subtractor and adder-subtractor circuits on reversible quantum gates, Transactions on Computational Science, 10-34 (2016), Berlin: Springer, Berlin · Zbl 1341.81019 |
| [5] | Takahashi, Y., Quantum arithmetic circuits: a survey, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., 92, 1276-1283 (2009) · doi:10.1587/transfun.E92.A.1276 |
| [6] | Tanaka, M.; Yamanashi, Y.; Kamiya, Y.; Akimoto, A.; Irie, N.; Park, H-J; Fujimaki, A.; Yoshikawa, N.; Terai, H.; Yorozu, S., A new design approach for high-throughput arithmetic circuits for single-flux-quantum microprocessors, IEEE Trans. Appl. Supercond., 17, 516-519 (2007) · doi:10.1109/TASC.2007.898714 |
| [7] | Hänninen, I.; Takala, J., Binary adders on quantum-dot cellular automata, J. Signal Process. Syst., 58, 87-103 (2010) · doi:10.1007/s11265-008-0284-5 |
| [8] | Gidney, C.: Windowed quantum arithmetic. arXiv:1905.07682 (arXiv preprint) (2019) |
| [9] | Pavlidis, A., Floratos, E.: Arithmetic circuits for multilevel qudits based on quantum fourier transform. arXiv:1707.08834 (arXiv preprint) (2017) |
| [10] | Thomsen, MK; Glück, R.; Axelsen, HB, Reversible arithmetic logic unit for quantum arithmetic, J. Phys. A Math. Theor., 43, 382002 (2010) · Zbl 1198.81070 · doi:10.1088/1751-8113/43/38/382002 |
| [11] | Oskin, M.; Chong, FT; Chuang, IL, A practical architecture for reliable quantum computers, Computer, 35, 79-87 (2002) · doi:10.1109/2.976922 |
| [12] | Waje, M.G., Dakhole, P., Design and implementation of 4-bit arithmetic logic unit using quantum dot cellular automata. In: 3rd IEEE International Advance Computing Conference (IACC). IEEE, 2013, 1022-1029 (2013) |
| [13] | Maynard, CM; Pius, E., A quantum multiply-accumulator, Quantum Inf. Process., 13, 1127-1138 (2014) · Zbl 1291.81105 · doi:10.1007/s11128-013-0715-5 |
| [14] | Weinstein, YS; Pravia, M.; Fortunato, E.; Lloyd, S.; Cory, DG, Implementation of the quantum Fourier transform, Phys. Rev. Lett., 86, 1889 (2001) · doi:10.1103/PhysRevLett.86.1889 |
| [15] | Şahin, E.: Quantum arithmetic operations based on quantum Fourier transform on signed integers. arXiv:2005.00443 (arXiv preprint) (2020) · Zbl 1457.81028 |
| [16] | Ruiz-Perez, L.; Garcia-Escartin, JC, Quantum arithmetic with the quantum Fourier transform, Quantum Inf. Process., 16, 152 (2017) · Zbl 1373.81150 · doi:10.1007/s11128-017-1603-1 |
| [17] | Shi, R-H; Mu, Y.; Zhong, H.; Cui, J.; Zhang, S., Secure multiparty quantum computation for summation and multiplication, Sci. Rep., 6, 1-9 (2016) · doi:10.1038/s41598-016-0001-8 |
| [18] | Shor, P. W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, IEEE, pp. 124-134 (1994) |
| [19] | Beauregard, S.: Circuit for Shor’s algorithm using 2n+ 3 qubits. arXiv:quant-ph/0205095 (arXiv preprint) (2002) · Zbl 1152.81676 |
| [20] | Draper, T. G.: Addition on a quantum computer. arXiv:quant-ph/0008033 (arXiv preprint) (2000) |
| [21] | Zhou, S.; Loke, T.; Izaac, JA; Wang, JB, Quantum Fourier transform in computational basis, Quantum Inf. Process., 16, 82 (2017) · Zbl 1373.81161 · doi:10.1007/s11128-017-1515-0 |
| [22] | Cleve, R., Watrous, J.: Fast parallel circuits for the quantum fourier transform. In: Proceedings 41st Annual Symposium on Foundations of Computer Science, IEEE, pp. 526-536 (2000) |
| [23] | Schönhage, A.; Strassen, V., Schnelle multiplikation grosser zahlen, Computing, 7, 281-292 (1971) · Zbl 0223.68007 · doi:10.1007/BF02242355 |
| [24] | Hales, L., Hallgren, S.: An improved quantum Fourier transform algorithm and applications. In: Proceedings 41st Annual Symposium on Foundations of Computer Science, IEEE, pp. 515-525 (2000) |
| [25] | Mosca, M.; Zalka, C., Exact quantum Fourier transforms and discrete logarithm algorithms, Int. J. Quantum Inf., 2, 91-100 (2004) · Zbl 1067.81017 · doi:10.1142/S0219749904000109 |
| [26] | Moore, C.; Rockmore, D.; Russell, A., Generic quantum Fourier transforms, ACM Trans. Algorithms (TALG), 2, 707-723 (2006) · Zbl 1321.81017 · doi:10.1145/1198513.1198525 |
| [27] | Sharpe, E., Notes on generalized global symmetries in qft, Fortschr. Phys., 63, 659-682 (2015) · Zbl 1338.81269 · doi:10.1002/prop.201500048 |
| [28] | Coppersmith, D.: An approximate Fourier transform useful in quantum factoring. arXiv:quant-ph/0201067 (arXiv preprint) (2002) |
| [29] | Ahokas, G., Cleve, R., Hales, L.: The complexity of quantum fourier transforms and integer multiplication. In: Proceedings of ERATO Conference on Quantum Information Science (EQIS2003), volume 1 (2003) |
| [30] | Mohammadi, M.; Eshghi, M., On figures of merit in reversible and quantum logic designs, Quantum Inf. Process., 8, 297-318 (2009) · Zbl 1181.81024 · doi:10.1007/s11128-009-0106-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
