Keywords
quantum simulation
quantum algorithms
How to Cite
Abstract
In this paper, we examine a simple algorithm for loading initial data into the quantum register. In order to perform the algorithm standard two input gates are used. The algorithm is tested for the Gaussian and sine wave states. In the Appendix full PyQuil code of the algorithm is attached.
References
Feynman, R., Internat. J. Theor. Phys., Vol. 21, 1982, pp. 467-488.
Shor, P. W., Proc 35th Ann. Symp. Found. Comp. Sci., IEEE Comp.Soc. Pr., Vol. 124, 1994.
Grover, L. K., From Schrodinger equation to the quantum search algorithm, Am. J. Phys., Vol. 69, 2001, pp. 769-777.
Lloyd, S., Universal Quantum Simulators, Science, Vol. 273, 1996, pp. 5278.
Schaetz, T., Monroe, C. R., and Esslinger, T., Focus on quantum simulation, New Journal of Physics, Vol. 15, 2013, pp. 085009.
Lanyon, B. P., Universal digital quantum simulation with tapped ions, 2011, http://xxx.lanl.gov//arXiv:1109.1512v2.
Childs, A. M., Maslov, D., Nam, Y., Ross, N. J., and Su, Y., Toward the first quantum simulation with quantum speedup, PNAS, Vol. 115, No. 38, 2018.
Wecker, D., Solving strongly correlated electron models on a quantum com- puter, Phys Rev A, Vol. 92, 2015, pp. 062318.
Kokail, C., Maier, C., and van Bijnen, R., Self-verifying variational quantum simulation of lattice models, Nature, Vol. 569, 2019.
Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B., and Troyer, M., Gate count estimates for performing quantum chemistry on small quantum com- puters, Phys Rev A, Vol. 90, 2014, pp. 022305.
Hempel, C., Maier, C., and Romero, J., Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator, Phys. Rev. X, Vol. 8, 2018, pp. 031022.
Jordan, S. P., Lee, K. S. M., and Preskill, J., Quantum algorithms for quantum field theories, Science, Vol. 336, 2012, pp. 1130-1133.
Ostrowski, M., Simulation of the Schrödinger particle nonelastic scatter- ing with emission of photon in the quantum register, Bull. Pol. Ac.: Tech., Vol. 68, No. 5, 2020.
Ostrowski, M., Simulation of diffusion of a single Schrödinger particle in the quantum register, Acta Phys. Polon. A, Vol. 137, No. 6, 2020, pp. 1182-1186.
Ventura, D., Learning quantum operators, In: Proceedings of the Joint Con- ference on Information Sciences, 2000, pp. 750–752.
Nielsen, M. A. and Chuang, I. L., Quantum Computation and Quantum In- formation, Cambridge University Press, 2000.
Faber, J., Thess, R. N., and Giraldi, G., Lerning linear operators by generic algorithms, 2003.
Rubinstein, B. I. P., Evolving quantum circuits using generic programming, In: Generic Algorithms and Generic Programming at Stanford 2000, Stanford Bookstore, Stanford, California, 94305-3079 USA, 2000, pp. 325–334.
Williams, C. P. and Gray, A., Automated Design of Quantum Circuits, Lec- ture Notes in Computer Science, Springer-Verlag New York, Inc., Vol. 1509, 1999.
Siedlecka-Lamach, O., A minimization algorithm of 1-way quantum finite automata, Metody Informatyki Stosowanej, Polska Akademia Nauk Oddzial w Gdansku, Komisja Informatyki, , No. 4, 2010, pp. 73-79.
Agaian, S. S. and Klappenecker, A., Quantum Computing and a Unitary Ap- proach to Fast Unitary Transforms, Image Processing: Algorithms and Sys- tems, 2002.
Hoyer, P., Efficient Quantum Transforms, http://arXiv:quant-ph/9702028, 1997.
Pang, C.-Y. and Zhou, R.-G., Signal and image compression using quantum discrete cosine transform, Information Sciences, Vol. 473, 2019, pp. 121– 141.
Preskill, J., http://www.theory.caltech.edu/∼preskill/ph229.