Abstract
We propose a genetic-algorithm-based method to find the unitary transformations for any desired quantum computation. We formulate a simple genetic algorithm by introducing the “genetic parameter vector” of the unitary transformations to be found. In the genetic algorithm process, all components of the genetic parameter vectors are supposed to evolve to the solution parameters of the unitary transformations. We apply our method to find the optimal unitary transformations and to generalize the corresponding quantum algorithms for a realistic problem, the one-bit oracle decision problem, or the often-called Deutsch problem. By numerical simulations, we can faithfully find the appropriate unitary transformations to solve the problem by using our method. We analyze the quantum algorithms identified by the found unitary transformations and generalize the variant models of the original Deutsch’s algorithm.
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References
M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000).
A. Bisio, G. Chiribella, G. M. D’Ariano, S. Facchini and P. Perinotti, Phys. Rev. A 81, 032324 (2010).
J. Bang, J. Lim, S. Yoo, M. S. Kim and J. Lee, [arXiv:0803.2976] (2008).
J. Bang, J. Ryu, S. Yoo, M. Pawłowski and J. Lee, New J. Phys. 16, 073017 (2014).
J. Audretsch, Entangled Systems, New Directions in Quantum Physics (Wiley, Weinheim, 2007).
J. H. Holland, Adaptation in Natural and Artificial Systems (The University of Michigan Press, Ann Arbor, 1975).
S. Forrest, Science 261, 872 (1993).
C. R. Houck, J. A. Joines and M. G. Kay, Technical Report NCSU-IE-TR-95-09, North Carolina State University, Raleigh, NC (1995).
M. Mohammadi and M. Eshghi, Quantum Information Processing 7, 175 (2008).
A. SaiToh, R. Rahimi and M. Nakahara, Quantum Information Processing 13, 737 (2014).
R. S. Judson and H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992).
A. Assion, T. Baumert, M. Bergt, T. Brixner, B. Kiefer, V. Seyfried, M. Strehle and G. Gerber, Science 282, 919 (1998).
J. C. Navarro-Muñoz, H. C. Rosu and R. López-Sandoval, Phys. Rev. A 74, 052308 (2006).
V. S. Manu and A. Kumar, Phys. Rev. A 86, 022324 (2012).
G. Quiroz and D. A. Lidar, Phys. Rev. A 88, 052306 (2013).
J. Bang, S-W. Lee, H. Jeong and J. Lee, Phys. Rev. A 86, 062317 (2012).
R. B. McDonald and H. G. Katzgraber, Phys. Rev. B 87, 054414 (2013).
R. Biswas et al., Phys. Rev. D 88, 062003 (2013).
D. Deutsch, Proc. R. Soc. London A 400, 97 (1985).
D. Deutsch and R. Jozsa, Proc. R. Soc. London A 439, 553 (1992).
G. Cybenko, Comput. Sci. Eng. 3, 27 (2001).
A. Daskin and S. Kais, J. Chem. Phys. 134, 144112 (2011).
F. Rothlauf, Representations for Genetic and Evolutionary Algorithms (Springer, Berlin, 2006).
H. Aytug and G. Koehler, ORSA J. Comput. 8, 183 (1996).
D. Whitley, Stat. and Comput. 4, 65 (1994).
F. T. Hioe and J. H. Eberly, Phys. Rev. Lett. 47, 838 (1981).
W. Son, J. Lee and M. S. Kim, J. Phys. A 37, 11897 (2004).
M. Reck, A. Zeilinger, H. J. Bernstein and P. Bertani, Phys. Rev. Lett. 73, 58 (1994).
J. Kim, J. Lee and S. Lee, Phys. Rev. A 61, 032312 (2000).
E. Kashefi, A. Kent, V. Vedral and K. Banaszek, Phys. Rev. A 65, 050304 (2002).
R. Storn and K. Price, J. Global Optim. 11, 341 (1997).
M. Tian, Z. W. Barber, J. A. Fischer and W. R. Babbitt, Phys. Rev. A 69, 050301 (2004).
F. van den Bergh and A. P. Engelbrecht, IEEE Trans. on Evolutionary Comput. 8, 225 (2004).
W. Chu, X. Gao and S. Sorooshian, Information Science 181, 4909 (2011).
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Bang, J., Yoo, S. A genetic-algorithm-based method to find unitary transformations for any desired quantum computation and application to a one-bit oracle decision problem. Journal of the Korean Physical Society 65, 2001–2008 (2014). https://doi.org/10.3938/jkps.65.2001
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DOI: https://doi.org/10.3938/jkps.65.2001