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Editor-in-Chief
Nikiforov
Vladimir O.
D.Sc., Prof.
Partners
doi: 10.17586/2226-1494-2019-19-3-394-401
MODELING OF INTEGRATED OPTICAL QUANTUM SEARCH ALGORITHM
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Abstract
Samsonov E.O., Kiselev F.D.,Chivilikhin S.A., Egorov V.I., Kirichenko D.N., Adam Yu.A., Kabiev R.A., Gleim A.V. Modeling of integrated optical quantum search algorithm. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2019, vol. 19, no. 3, pp. 394-401 (in Russian).
doi: 10.17586/2226-1494-2019-19-3-394-401
Abstract
Subject of Research. The paper presents a quantum search algorithm model, suitable for integration into a linear optical chip. Error impact caused by two-qubit operator implementation and directional coupler manufacture imperfection on the algorithm output is studied. Method. Analytical calculation of the algorithm scheme was performed to assess error impact caused by two-qubit operator optical implementation. Numerical simulation of the algorithm was executed for taking into account distortions caused by directional coupler imperfections. The simulation was completed using Qutip library on Python programming language. Main Results. Two well-known implementations of the algorithm scheme main component, a two-qubit CZ gate, are compared in order to select the most optimal chip architecture. It was shown that one of two-qubit gate implementations introduces an error critical for the algorithm work. Another implementation based on projection measurements does not introduce an error, but has a lower efficiency. We have performed simulation of the proposed scheme, taking into account the imperfections of its components in the framework of unitary dynamics. We have shown that the algorithm error probability does not exceed 0.011. Two-qubit Grover’s algorithm оptical implementation with regard to directional coupler imperfections has a low error rate, but it is limited by the low two-qubit operator efficiency. Practical Relevance. The study carried out can be useful for the physical implementation of the algorithm. Creation of an integrated optical scheme that implements Grover’s algorithm will make it possible to build a quantum router for the optimal route search in quantum networks with complex topology.
Keywords: Quantum computing, Grover’s algorithm, optical chip, linear optical quantum computing
References
References
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3. Gard B.T., Motes K.R., Olson J.P., Rohde P.P., Dowling J.P. An introduction to boson-sampling. In From Atomic to Mesoscale: The Role of Quantum Coherence in Systems of Various Complexities. World Scientific Publ., 2015, 272 p. doi: 10.1142/9613
4. Harris N.C., Bunandar D., Pant M., Steinbrecher G.R., Mower J., Prabhu M., Baehr-Jones T., Hochberg M., Englund D. Large - scale quantum photonic circuits in silicon. Nanophotonics, 2016, vol. 5, no. 3. doi: 10.1515/nanoph-2015-0146
5. Gavrilov M.I., Gortinskaya L.V., Pestov A.A. et al. Quantum computer elements based on coupled quantum waveguides. Physics of Particles and Nuclei Letters, 2007, vol. 4, no. 2, pp. 137–140. doi: 10.1134/S1547477107020082
6. Carolan J., Harrold C., Sparrow C., Mart´ın-L´opez E., Russell N., Silverstone J., Shadbolt P.J., Matsuda N., Oguma M., Itoh M., Marshall G.D., Thompson M.G., Matthews J.C., Hashimoto T., O’Brien J.L., Laing A. Universal linear optics. Science, 2015, vol. 349, no. 6249, pp. 711–716. doi: 10.1126/science.aab3642
7. Dodd J.L., Ralph T.S., Milburn G.J. Experimental requirements for Grover’s algorithm in optical quantum computation. Physical Review A, 2003, vol. 68, no. 4. doi: 10.1103/PhysRevA.68.042328
8. Nielsen M.A., Chuang L.I. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, 2000.
9. Kok P., Munro W.J., Nemoto K., Ralph T.C., Dowling J.P., Milburn G.J. Linear optical quantum computing with photonic qubits. Reviews of Modern Physics, 2007, vol. 79, pp. 135–174.
10. Miroshnichenko G.P. Linear optical quantum computing. Nanosystems: Physics, Chemistry, Mathematics, 2012, vol. 3, no. 4, pp. 36–53. (in Russian)
11. Knill E., Laflamme R., Milburn G.J. A scheme for efficient quantum computation with linear optics. Nature, 2001, vol. 409, no. 6816, pp. 46–52. doi: 10.1038/35051009
12. Ralph T.C., Langford N.K., Bell T.B., White A.G. Linear optical controlled-NOT gate in the coincidence basis. Physical Review A, 2002, vol. 65, no. 6. doi: 10.1103/PhysRevA.65.062324
13. Okamoto R., O’Brien J.L., Hofmann H.F., Takeuchi S. Realization of a Knill-Laflamme-Milburn controlled-NOT photonic quantum circuit combining effective optical nonlinearities. PNAS, 2011, vol. 108, no. 25, pp. 10067–10071. doi: 10.1073/pnas.1018839108
14. O’Brien J.L., Pryde G.J., White A.G., Ralph T.C., Branning D. Demonstration of an all-optical quantum controlled-NOT gate. Nature, 2003, vol. 426, no. 6964, pp. 264–267. doi: 10.1038/nature02054
15. Grover L.K. Quantum mechanics helps in searching for a needle in a haystack. Physical Review Letters, 1996, vol. 79, no. 2, pp. 325–328. doi: 10.1103/PhysRevLett.79.325
16. Politi A., Matthews J., Thompson M.J., O’Brien J.L. Integrated quantum photonics. IEEE Journal of Selected Topics in Quantum Electronics, 2009, vol. 15, no. 6, pp. 1673–1684. doi: 10.1109/JSTQE.2009.2026060
17. Vasilev A., Kozubov A., Gaidash A., Chivilikhin S. On-chip realization of quantum circuits by using waveguides on Si3N4. Journal of Physics: Conference Series, 2016, vol. 741. doi: 10.1088/1742-6596/741/1/012104
18. Johansson J.R., Nation P.D., Nori F. QuTiP 2: A Python framework for the dynamics of open quantum systems. Computer Physics Communications, 2013, vol. 184, no. 4, pp. 1234–1240. doi: 10.1016/j.cpc.2012.11.019