Quantum Computing Concepts with Deutsch Jozsa Algorithm

Poornima Aradyamath - RYM Engineering College, Ballari, India
Naghabhushana N M - RYM Engineering College, Ballari, India
Rohitha Ujjinimatad - Proudhadevarya Institute of Technology, Hosapet, India

Citation Format:

DOI: http://dx.doi.org/10.30630/joiv.3.1.218


In this paper, we briefly review the basic concepts of quantum computation,  entanglement,  quantum cryptography and quantum fourier  transform.   Quantum algorithms like Deutsch Jozsa, Shor’s   factorization and Grover’s data search are developed using fourier  transform  and quantum computation concepts to build quantum computers.  Researchers are finding a way to build quantum computer that works more efficiently than classical computer.  Among the  standard well known  algorithms  in the field of quantum computation  and communication we  describe  mathematically Deutsch Jozsa algorithm  in detail for  2  and 3 qubits.  Calculation of balanced and unbalanced states is shown in the mathematical description of the algorithm.


quantum computer; quantum algorithms; qubit; quantum cryptography.

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Niklas Johansson, Jan-Åke Larsson Efficient classical simulation of the Deutsch– Jozsa and Simon’s algorithms, Quantum Inf Process (2017) 16:233, DOI 10.1007/s11128-017-1679-7

Nielsen M and Chuang I. Quantum computation and Quantum information. Cambridge Univ. press Cambridge, 2000.

Thaddeus D. Ladd, Fedor Jelezko, Raymond Laflamme, Yasunobu Nakamura, Christopher Monroe, Jeremy L. O'Brien, Quantum Computers, Nature 464, March 2010, PP 45-53

Nicolas Gisin, Gregoire Ribordy, Wolfgang Tittel, and Hugo Zbinden, Quantum cryptography, REVIEWS OF MODERN PHYSICS, 2002.

L. M. Duan and C. Monroe. “Quantum networks with trapped ionsâ€. In: REVIEWS OF MODERN PHYSICS 82.2 (Apr. 2010), pp. 1209–1224.

H J Kimble. “The quantum internetâ€. In: Nature 453 (June 2008), pp. 1023–1030. ISSN: 0028-0836.

J. Eisert, K. Jacobs, P. Papadopoulos, and M. B. Plenio, Optimal local implementation of nonlocal quantum gates, Physical Review A, vol. 62, no. 5, Nov. 2000.

Joseph F. Fitzsimons Naomi H. Nickerson and Simon C. Benjamin. “Freely Scalable Quantum Technologies Using Cells of 5-to-50 Qubits with Very Lossy and Noisy Photonic Linksâ€. In: PHYSICAL REVIEW X 4.4 (Dec. 2014).

Michael Ben-Or, Claude Crepeau, Daniel Gottesman, Avinatan Hassidim, and Adam Smith, Secure Multiparty Quantum Computation with (Only) a Strict Honest Majority, 47th IEEE Annual Symposium on Foundations of Computer Science (FOCS 2006), October 2006.

Michele Mosca Artur Ekert. “The Hidden Subgroup Problem and Eigenvalue, Estimation on a Quantum Computerâ€. In: Procceedings of 1st NASA International Conference on Quantum Computing and Quantum Communication, vol. 1509. Lecture Notes in Computer Science. 1999.

Cristian S. Calude and Elena Calude, The Road to Quantum Computational Supremacy, arXiv:1712.01356v1 [quant-ph] 4 Dec 2017

R P Poplavskii. “Quantum Computersâ€. In: 1975. Chap. Thermo dynamical models of information processing, pp. 465–501.

Paul Benioff. “The computer as a physical system: A microscopic quantum mechanical Hamiltonian model of computers as represented by turning machinesâ€. In: Journal of stastical physics (1980).

Vychislimoe Manin YU and I nevychislimoe. “Computable and Non computable (in Russian). Sov.Radio.†In: (Archived from the original on May 10,2013. Retrieved 2013-03-04.), pp. 13–15.

R P Feyman. “Simulating Physics with Computersâ€. In: International Journal of Theoretical Physics 21.6 (1982), pp. 467–488.

J. G. Hey. Feynman and Computation – Exploring the Limits of Computers. Perseus Books, 1999.

Bennet. C H. “Logical reversibility of computationâ€. In: IBM Journal of Research and Development (1973).

T. Toffoli. Reversible computing in Automata, Languages and Programming, Seventh Colloquium, Lecture Notes in Computer Science. Ed. By J. W. De Bakker and J. van Leeuwen. Vol. 84. Springer, 1980.

Yao. “Quantum circuit complexityâ€. In: Proceeding of the 34th IEEE Symposium on Foundations of Computer Science. 1993, pp. 352–361

D. Deutsch. “Quantum theory, the Church-Turing principle, and the universal quantum computerâ€. In: Royal Society London (1985).

D. Deutsch and R. Jozsa. “Rapid solution of problems by quantum computationâ€. In: Royal Society London (1992).

David Deutsch. “Quantum Theory as a Universal Physical Theoryâ€. In: International Journal of Theoretical Physics 24.1 (1985).

E. Bernstein and U. Vazirani. “Quantum complexity theoryâ€. In: Proceedings of 25th ACM Symposium on Theory of Computating. 1993, pp. 11–20.

D. Simon. “On the power of quantum computationâ€. In: 35th IEEE Symposium on the Foundations of Computer Science. 1994.

Natacha Portier Pascal Koiran Vincent Nesme. “A quantum lower bound for the query complexity of Simon’s problemâ€. In: Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg (Jan. 2005), pp. 1287–1298.

Richard Jozsa. “Quantum Factoring, Discrete Logarithms, and the Hidden Subgroup Problemâ€. In: Computing in Science and Engineering 3.2 (Mar. 2001), pp. 34–43.

P. W. Shor. “Algorithms for quantum computation: discrete logarithms and factoringâ€. In: Proceedings of 35th IEEE Symposium on Foundations of Computer Science. IEEE, Nov. 1994.

Wim van Dam and Sean Hallgren. “Efficient Quantum Algorithms for Shifted Quadratic Character Problemsâ€. In: quant-ph/0011067 (2001).

Michele Mosca, Artur Ekert. “The Hidden Subgroup Problem and Eigenvalue Estimation on a Quantum Computerâ€. In: Procceedings of 1st NASA International Conference on Quantum Computing and Quantum Communication, vol. 1509. Lecture Notes in Computer Science. 1999.

F. Magniez G. Ivanos and M. Santha. “Efficient quantum algorithms for some instances of the non-abelian hidden subgroup problemâ€. In: quant-ph/0102014 ().

S Hallgren. “Polynomial-time quantum algorithms for Pell’s equation and the principal ideal problem.†In: In Proceedings of the 34th ACM Symposium on the Theory of Computing (STOC). 2002, pp. 653–658.

John Watrous J Niel De Beaudrap Richard Cleve. “Sharp quantum versus classical query complexity separationsâ€. In: Algorithmica 34.4 (Jan. 2002), pp. 449–461.

Yu. Kitaev. “Quantum measurements and the Abelian Stabilizer Problemâ€. In: quant-ph/9511026 (2008).

Russell S. Hallgren and A. Ta-Shma. “Normal subgroup reconstruction and quantum computation using group representations.†In: In Proceendings of 32nd ACM Symposium on the Theory of Computing. 2000, pp. 627–635.

J. Watrous. “Quantum algorithms for solvable groupsâ€. In: In Proceedings of the. 33rd ACM Symposium on the Theory of Computing. 2001, pp. 60–67.

M. Grigni, L. Schulman, M. Vazirani, and U. Vazirani, “Quantum mechanical algorithms for the nonabelian hidden subgroup problem†In Proceedings of 33rd Annual ACM Symposium on Theory of Computing, 2001 pp. 68-74

L. Adleman R. L. Rivest A. Shamir. “A method for obtaining digital signatures and public-key cryptosystemsâ€. In: Communications of the ACM 21.2 (Feb. 1978), pp. 120–126

L. K. Grover. “A fast quantum mechanical algorithm for database searchâ€. In: In Proceedins of the 28th Annual ACM Symposium on the Theory of Computing, ACM, New York, 1996, pp. 212–219.

L. K. Grover. “Quantum mechanics helps in searching for a needle in a haystackâ€. In: Physical Review Letters 79.325 (July 1997).

Vandersypen L M, Steffen M, Breyta G, Yannoni CS, Sherwood MH, Chuang I L. “ Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance †Nature. 2001 Dec 20-27;414 (6866):883-7.

Pittman T. B, Fitch M. J., Jacobs B. C. and Franson, J. D. “Experimental controlled-not logic gate for single photons in the coincidence basis†Physical Reviews A, volume 68, number 032316, 2003.

Zhao, Zhi, Chen, Yu-Ao, Zhang, An-Ning, Yang, Tao, Briegel, Hans J, Pan, Jian-Wei. †Experimental demonstration of five-photon entanglement and open-destination teleportation †Nature, volume 430, no. 6995, pp 54-58, July 2004.

Rose H, and Hag J, “ Using a Cipher Key to Generate Dynamic S-Box in AES Cipher System †International Journal of Computer Science and Security, 6, pp 19-28, 2012.

Sekar A., Radhika, S. and Anand, K. “ Secure Communication Using 512 Bit Key †European Journal of Scientific Research, 52, pp 61-65, 2012