IJSTR

International Journal of Scientific & Technology Research

Home About Us Scope Editorial Board Blog/Latest News Contact Us
0.2
2019CiteScore
 
10th percentile
Powered by  Scopus
Scopus coverage:
Nov 2018 to May 2020

CALL FOR PAPERS
AUTHORS
DOWNLOADS
CONTACT

IJSTR >> Volume 11 - Issue 01, January 2022 Edition



International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616



A Review On The Fundamental Concepts Of Quantum Elements, Efficient Quantum Algorithms And Quantum Error Correcting Codes

[Full Text]

 

AUTHOR(S)

C. H. Ugwuishiwu , U. E. Orji, O.Ukwueze , P. O. Ogbobe

 

KEYWORDS

Quantum elements; quantum algorithm; error correcting codes; quantum physics.

 

ABSTRACT

Quantum Elements, Efficient Quantum Algorithms and Quantum Error Correcting Codes are some of the fundamental concepts of quantum computing. In this paper, the authors aim to introduce readers and potential researchers to the subject areas to help them appreciate the intrigues and ideas behind quantum computing. The authors introduced the basic concepts of quantum physics which is the foundation for quantum computing. Related literature such as books, journals, conference proceedings, lecture notes and webpages on this field of study were sourced and reviewed from top databases like IEEE Xplore, JSTOR, ScienceDirect etc.

 

REFERENCES

[1] J.A. Smolin, G. Smith, and A. Vargo, “Pretending to factor large numbers on a quantum computer.” 2013. arXiv preprint arXiv:1301.7007.
[2] M. Xu, D.A. Tieri, and M.J. Holland, “Simulating open quantum systems by applying SU (4) to quantum master equations.” Physical Review A, 2013. 87(6), p.062101.
[3] A. Broadbent, and C. Schaffner, “Quantum cryptography beyond quantum key distribution. Designs, Codes and Cryptography” 2016. Vol. 78(1), pp.351-382.
[4] J.W. Harrington, “Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes” Doctoral dissertation, California Institute of Technology. 2004.
[5] Monroe, C. Quantum information processing with atoms and photons. Nature 416, 238–246 (2002). https://doi.org/10.1038/416238a
[6] https://www.ibm.com/quantum-computing/what-is-quantum-computing/
[7] C. Sparrow, "Quantum interference in universal linear optical devices for quantum computation and simulation." (2017). https://doi.org/10.25560/67638
[8] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning.” Nature, 2017. Vol. 549(7671), pp.195-202.
[9] P. W. Shor, "Why haven't more quantum algorithms been found?." Journal of the ACM (JACM) Vol. 50, no. 1 (2003): pp. 87-90.
[10] D.P. DiVincenzo, “The physical implementation of quantum computation. Fortschritte der Physik: Progress of Physics.” 2000. Vol. 48(9‐11), pp.771-783.
[11] J. Stolze, and D. Suter, “Quantum computing.” Wiley-VCH, Weinheim, 2004. Vol. 29, pp.30-31.
[12] L. Dellantonio, A.S. Sørensen, and D. Bacco, “High-dimensional measurement-device-independent quantum key distribution on two-dimensional subspaces.” Physical Review A, 2018. 98(6), p.062301.
[13] X. Qiang, X. Zhou, J. Wang, C.M. Wilkes, T. Loke, S. O’Gara, L. Kling, G.D. Marshall, R. Santagati, T.C. Ralph, and J.B. Wang, “Large-scale silicon quantum photonics implementing arbitrary two-qubit processing.” Nature photonics, 2018. Vol. 12(9), pp.534-539.
[14] Jaeger, Gregg. "Classical and quantum computing. Quantum Information: An Overview.” (2007): 203-217.
[15] Yu I. Bogdanov, N. A. Bogdanova, D. V. Fastovets, and V. F. Lukichev. "On the Relationship between Boolean Algebra and Quantum Informatics." Russian Microelectronics 49, no. 1 (2020): 1-15.
[16] N. Raoof, “Difference between Classical Computing and Quantum Computing” Available online at: https://medium.com/faun/classical-computing-c1a126a7bd73, Accessed on: Mar. 23, 2021.
[17] A. Galindo, and M. A. Martin-Delgado. "Information and computation: Classical and quantum aspects." Reviews of Modern Physics 74, no. 2 (2002): 347.
[18] K Valiev, "Quantum computers and quantum computations." Physics-Uspekhi 48, no. 1 (2005): 1
[19] Wie, Chu-Ryang. "Bloch sphere model for two-qubit pure states." arXiv preprint arXiv:1403.8069 (2014).
[20] H.R. Bolhasani, A.M. Rahmani, and F. Kheiri, “An Introduction to Quantum Computers Architecture.” Available online at: https://www.researchgate.net/publication/337144719_An_Introduction_to_Quantum_Computers_Architecture, Accessed on: Mar. 23, 2021.
[21] Richard Versluis "Here’s a Blueprint for a Practical Quantum Computer" Available online at: https://spectrum.ieee.org/computing/hardware/heres-a-blueprint-for-a-practical-quantum-computer Accessed on: May. 23, 2021.
[22] Surya Teja Marella and Hemanth Sai Kumar Parisa, "Introduction to Quantum Computing." Available online at: https://www.intechopen.com/online-first/introduction-to-quantum-computing Accessed on: May. 23, 2021.
[23] R. Omnes, “The interpretation of quantum mechanics.” Princeton University Press, 2018.
[24] D. Tong, "The Unquantum Quantum." Scientific American 307, no. 6 (2012): 46-49.
[25] I. Pitowsky, "Quantum mechanics as a theory of probability." In Physical theory and its interpretation, pp. 213-240. 2006. Springer, Dordrecht.
[26] M. Schlosshauer, "Decoherence, the measurement problem, and interpretations of quantum mechanics." Reviews of Modern physics 76, no. 4 (2005): 1267.
[27] D. Aerts, and S. Massimiliano "The extended Bloch representation of quantum mechanics and the hidden-measurement solution to the measurement problem." Annals of Physics 351 (2014): 975-1025.
[28] W. Bertrand, “Quantum Entanglement.” International Journal of Automatic Control System. 2019; 5(2): 1–7p.
[29] X.S. Geng, L.L. Ji, B.F. Shen, et al. “Quantum reflection above the classical radiation-reaction barrier in the quantum electro-dynamics regime.” Commun Phys 2, 66 (2019). https://doi.org/10.1038/s42005-019-0164-2
[30] Bolhasani, Hamidreza, and Amir Masoud Rahmani. "AN INTRODUCTION TO QUANTUM COMPUTERS." Available online at: https://www.researchgate.net/profile/Hamidreza-Bolhasani/publication/337144719_An_Introduction_to_Quantum_Computers_Architecture/links/5f4c8a97299bf13c5062f83f/An-Introduction-to-Quantum-Computers-Architecture.pdf , Accessed on: Mar. 23, 2021.
[31] Č. Brukner, and Z. Anton, "Information and fundamental elements of the structure of quantum theory." In Time, quantum and information, pp. 323-354. Springer, Berlin, Heidelberg, 2003.
[32] S. Akama, “Elements of Quantum Computing: History, Theories and Engineering Applications” Springer International Publishing Switzerland (2015). Available at http://mmrc.amss.cas.cn/tlb/201702/W020170224608149203392.pdf
[33] E. G. Rieffel, "An Overview of Quantum Computing for Technology Managers." arXiv preprint arXiv:0804.2264 (2008).
[34] P. Shor, “Algorithms for quantum computation: Discrete logarithms and factoring.” In:Proc. of the 35th Annual Symposium on Foundations of Computer Science, pp. 124–134(1994)
[35] R. Rivest, A. Shamir, L. Adleman, “A method for obtaining digital signatures and public-key cryptosystems.” Communications of the ACM 21, 120–126 (1978)
[36] C. H. Ugwuishiwu, U. E. Orji, C. I. Ugwu, and C. N. Asogwa. "An overview of Quantum Cryptography and Shor’s Algorithm." International Journal 9, no. 5 (2020). https://doi.org/10.30534/ijatcse/2020/214952020
[37] D. Simon, “On the power of quantum computation.” In: Proc. of the 35th Annual Symposium on Foundations of Computer Science, pp. 116–123 (1994)
[38] "Grover’s Algorithm + Quantum Zeno Effect + Vaidman Bomb," Available online at: https://people.eecs.berkeley.edu/~vazirani/f04quantum/notes/lec10/lec11.pdf Accessed on: Mar. 23, 2021.
[39] A. Montanaro, “Quantum algorithms: an overview. npj Quantum Inf 2, 15023 (2016). https://doi.org/10.1038/npjqi.2015.23
[40] B. Jean-François, and S. Fang, "Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields." In Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms, pp. 893-902. Society for Industrial and Applied Mathematics, 2016.
[41] W. C. Huffman, and P. Vera “Fundamentals of error-correcting codes.” Cambridge university press, 2010.
[42] R. Alrifai, "Error detection and correction using hamming code." Journal of Computing Sciences in Colleges 35, no. 6 (2020): 121-121.
[43] "An Introduction to Error-Correcting Codes - Part 1" available at: https://www.section.io/engineering-education/understanding-error-correcting-codes-part-1/ Accessed on: Mar. 23, 2021.
[44] M. Rudelson and R. Vershynin, "Geometric approach to error-correcting codes and reconstruction of signals," in International Mathematics Research Notices, vol. 2005, no. 64, pp. 4019-4041, 2005, doi: 10.1155/IMRN.2005.4019.
[45] J.L. Massey, O.N. García, “Error-Correcting Codes in Computer Arithmetic.” In: Tou J.T. (eds) Advances in Information Systems Science. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-9053-8_5 (1972)
[46] N. Wolchover, “How Space and Time Could Be a Quantum Error-Correcting Code” Available online at: https://www.quantamagazine.org/how-space-and-time-could-be-a-quantum-error-correcting-code-20190103/ Accessed on: Mar. 23, 2021.
[47] M. Grassl, "Algorithmic aspects of quantum error-correcting codes." Mathematics of Quantum Computation (2002): 223-252.
[48] K. Guenda, S. Jitman, & T.A. Gulliver, “Constructions of good entanglement-assisted quantum error correcting codes.” Des. Codes Cryptogr. 86, 121–136 (2018). https://doi.org/10.1007/s10623-017-0330-z
[49] D. Gottesman, "An introduction to quantum error correction." In Proceedings of Symposia in Applied Mathematics, vol. 58, pp. 221-236. 2002.