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On the Quantum Computation and Quantum Information

Year 2022, Volume: 5 Issue: 2, 76 - 86, 31.12.2022

Abstract

Quantum mechanics is considered to be the most important achievement and mysterious scientific theory in mid-1900. Then it was successfully applied to understand a wide variety of physical phenomena including fundamental forces of nature, nuclear physics, superconductors, etc. Toward the end of 1900, people began to ask whether a quantum system can actually be designed instead of looking at them just a phenomena found in nature. Some of the question of interests are: what are the fundamental physical limitation son space and time required to construct a quantum state? What makes quantum systems difficult to simulate by conventional classical means?
In this study, we present the basic concepts of quantum bits and quantum calculators and compare them with their classical counterparts. We also address the main challenges faced when aiming to simulate a quantum system. Frequently used quantum gates are presented.

References

  • [1] Wootters, W. K., & Zurek, W. H. (2009). The no-cloning theorem. Physics Today, 62(2), 76-77.
  • [2] Einstein, A. (1905). On the Electrodynamics of Moving Bodies Annalen der Physik. Vol. 17,322 (10).
  • [3] Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete?. Physical review,47(10), 777.
  • [4] Zhou, Y., Stoudenmire, E. M., & Waintal, X. (2020). What limits the simulation of quantum computers?. Physical Review X, 10(4), 041038.
  • [5] Nielsen, M. A., & Chuang, I. L. (2001). Quantum computation and quantum information.Phys. Today,54, 60-2.
  • [6] Feynman R. P , (1982). Simulating physics with computers”, International Journal of Theoretical Physics 21:6/7, s.467-488.
  • [7] Nielsen, M. A., & Chuang, I. (2002). Quantum computation and quantum information.
  • [8] Shannon, C. E. (1948). A mathematical theory of communication. Bell system technical journal, 27(3), 379-423.
  • [9] Benioff, P. A. (1982). Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Application to Turing machines. International Journal of Theoretical Physics, 21(3-4), 177-201.
  • [10] Deutsch, D. (1985). Quantum theory, the Church–Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 400(1818), 97-117.
  • [11] Bernstein, E., & Vazirani, U. (1997). Quantum complexity theory. SIAM Journal on computing, 26(5), 1411-1473.
  • [12] Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th annual symposium on foundations of computer science, p. 20-22.
  • [13] Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (pp. 212-219).
  • [14] Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical review A,52(4), p. 2493-2496.
  • [15] Preskill, J. (1998). Robust solutions to hard problems. Nature, 391(6668), 631-632.
  • [16] Ulucan, H. (2017). Süperilerken Kubitli Kuantum Bilgisayarlar ve Kuantum Hesaplama, yüksek lisans tezi, İstanbul Gelişim Üniversitesi Fen Bilimleri Enstitüsü
  • [17] Gisin, N., & Bechmann-Pasquinucci, H. (1998). Bell inequality, Bell states and maximally entangled states for n qubits. Physics Letters A, 246(1-2), 1-6.
  • [18] Collins, D., Kim, K. W., & Holton, W. C. (1998). Deutsch-Jozsa algorithm as a test of quantum computation. Physical Review A, 58(3), R1633.
  • [19] Grover, L. K. (1997). Quantum mechanics helps in searching for a needle in a haystack. Physical review letters, 79(2), 325.
  • [20] Shor, P. W. (1999). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review, 41(2), 303-332.

Kuantum Hesaplama ve Kuantum Bilgisi Hakkında

Year 2022, Volume: 5 Issue: 2, 76 - 86, 31.12.2022

Abstract

Kuantum mekaniği, 1900'lerin ortalarında en önemli başarı ve en gizemli bilimsel teori olarak kabul edilir. Daha sonra, doğanın temel kuvvetleri, nükleer fizik, süper iletkenler vb. dahil olmak üzere çok çeşitli fiziksel fenomenleri anlamak için başarıyla uygulandı. 1900’lerin sonlarına doğru, insanlar sadece doğada bulunan bir kuantum olaylarını incelemek yerine gerçek kuantum sisteminin tasarlanıp tasarlanamayacağını sormaya başladılar. Bununla ilgili olarak ele alınan bazı sorular şunlardır: Bir kuantum durum oluşturmak için gereken uzay ve zaman üzerindeki temel fiziksel sınırlamalar nelerdir? Kuantum sistemlerinin geleneksel klasik yöntemlerle simüle edilmesini zorlaştıran nedir?
Bu çalışmada kuantum biti ve kuantum hesaplayıcılar ile ilgili temel kavramları sunuyoruz ve klasik eşlenikleri ile karşılaştırıyoruz. Ayrıca bir kuantum sisteminin simüle edilmesi hedeflendiğinde karşılaşılan temel zorluklara değiniyoruz.

References

  • [1] Wootters, W. K., & Zurek, W. H. (2009). The no-cloning theorem. Physics Today, 62(2), 76-77.
  • [2] Einstein, A. (1905). On the Electrodynamics of Moving Bodies Annalen der Physik. Vol. 17,322 (10).
  • [3] Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete?. Physical review,47(10), 777.
  • [4] Zhou, Y., Stoudenmire, E. M., & Waintal, X. (2020). What limits the simulation of quantum computers?. Physical Review X, 10(4), 041038.
  • [5] Nielsen, M. A., & Chuang, I. L. (2001). Quantum computation and quantum information.Phys. Today,54, 60-2.
  • [6] Feynman R. P , (1982). Simulating physics with computers”, International Journal of Theoretical Physics 21:6/7, s.467-488.
  • [7] Nielsen, M. A., & Chuang, I. (2002). Quantum computation and quantum information.
  • [8] Shannon, C. E. (1948). A mathematical theory of communication. Bell system technical journal, 27(3), 379-423.
  • [9] Benioff, P. A. (1982). Quantum mechanical Hamiltonian models of discrete processes that erase their own histories: Application to Turing machines. International Journal of Theoretical Physics, 21(3-4), 177-201.
  • [10] Deutsch, D. (1985). Quantum theory, the Church–Turing principle and the universal quantum computer. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 400(1818), 97-117.
  • [11] Bernstein, E., & Vazirani, U. (1997). Quantum complexity theory. SIAM Journal on computing, 26(5), 1411-1473.
  • [12] Shor, P. W. (1994). Algorithms for quantum computation: discrete logarithms and factoring. In Proceedings 35th annual symposium on foundations of computer science, p. 20-22.
  • [13] Grover, L. K. (1996). A fast quantum mechanical algorithm for database search. In Proceedings of the twenty-eighth annual ACM symposium on Theory of computing (pp. 212-219).
  • [14] Shor, P. W. (1995). Scheme for reducing decoherence in quantum computer memory. Physical review A,52(4), p. 2493-2496.
  • [15] Preskill, J. (1998). Robust solutions to hard problems. Nature, 391(6668), 631-632.
  • [16] Ulucan, H. (2017). Süperilerken Kubitli Kuantum Bilgisayarlar ve Kuantum Hesaplama, yüksek lisans tezi, İstanbul Gelişim Üniversitesi Fen Bilimleri Enstitüsü
  • [17] Gisin, N., & Bechmann-Pasquinucci, H. (1998). Bell inequality, Bell states and maximally entangled states for n qubits. Physics Letters A, 246(1-2), 1-6.
  • [18] Collins, D., Kim, K. W., & Holton, W. C. (1998). Deutsch-Jozsa algorithm as a test of quantum computation. Physical Review A, 58(3), R1633.
  • [19] Grover, L. K. (1997). Quantum mechanics helps in searching for a needle in a haystack. Physical review letters, 79(2), 325.
  • [20] Shor, P. W. (1999). Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM review, 41(2), 303-332.
There are 20 citations in total.

Details

Primary Language Turkish
Journal Section Research Papers
Authors

Selim Kaya 0000-0001-7477-3522

Necati Çelik 0000-0002-8270-9288

Mustafa Nuri Ural 0000-0001-7011-401X

Publication Date December 31, 2022
Submission Date September 26, 2022
Acceptance Date November 9, 2022
Published in Issue Year 2022 Volume: 5 Issue: 2

Cite

APA Kaya, S., Çelik, N., & Ural, M. N. (2022). Kuantum Hesaplama ve Kuantum Bilgisi Hakkında. Journal of Investigations on Engineering and Technology, 5(2), 76-86.