Cavity control as a new quantum algorithms implementation treatment

Abstract

Based on recent experiments [Nature 449, 438 (2007) and Nature Physics 6, 777 (2010)], a new approach for realizing quantum gates for the design of quantum algorithms was developed. Accordingly, the operation times of such gates while functioning in algorithm applications depend on the number of photons present in their resonant cavities. Multi-qubit algorithms can be realized in systems in which the photon number is increased slightly over the qubit number. In addition, the time required for operation is considerably less than the dephasing and relaxation times of the systems. The contextual use of the photon number as a main control in the realization of any algorithm was demonstrated. The results indicate the possibility of a full integration into the realization of multi-qubit multiphoton states and its application in algorithm designs. Furthermore, this approach will lead to a successful implementation of these designs in future experiments.

Keywords

quantum computation / quantum algorithms implementation / cavity control

References

[1] A. M.Turing, On computable numbers, with an application to the Entscheidungsproblem, Proc. Lond. Math. Soc. s2–42(1), 230 (1937)

[2] R. P.Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21(6–7), 467(1982)

[3] P.Benioff, Quantum mechanical models of Turing machines that dissipate no energy, Phys. Rev. Lett. 48(23), 1581(1982)

[4] D.Deutsch, Quantum theory, the Church-Turing Principle and the universal quantum computer, Proc. R. Soc. Lond. A400(1818), 97(1985)

[5] D.Deutsch, Quantum computational networks, Proc. R. Soc. Lond. A425(1868), 73(1989)

[6] D. P.DiVincenzo, Quantum computation, Science270(5234), 255(1995)

[7] D. P.DiVincenzo, The physical implementation of quantum computation, Fortschr. Phys. 48(9–11), 771(2000)

[8] M.Nakahara, S.Kanemitsu, M. M.Salomaa, and S.Takagi(Eds.), Physical Realization of Quantum Computing: Are the DiVincenzo Criteria Fulfilled in 2004? Singapore: World Scientific, 2006

[9] L. M. K.Vandersypenand I. L.Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76(4), 1037(2005)

[10] E. L.Raab, M.Prentiss, A.Cable, S.Chu, and D. E.Pritchard, Trapping of neutral sodium atoms with radiation pressure, Phys. Rev. Lett. 59(23), 2631(1987)

[11] G.Wendinand V. S.Shumeiko, Superconducting quantum circuits, qubits and computing, arXiv: condmat/ 0508729 (2005)

[12] B. D.Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1(7), 251(1962)

[13] B. D.Josephson, The discovery of tunnelling supercurrents, Rev. Mod. Phys. 46(2), 251(1974)

[14] U.Meirav, M. A.Kastner, and S. J.Wind, Singleelectron charging and periodic conductance resonances in GaAs nanostructures, Phys. Rev. Lett.65(6), 771(1990)

[15] O.Gamel, H.Chan, G.Fleming, and K. B.Whaley, Fully quantum analysis of photosynthetic coherent energy absorption and transfer, Bull. Am. Phys. Soc. 62, 4 (2017)

[16] B.Schumacher, Quantum coding, Phys. Rev. A51(4), 2738(1995)

[17] J. M.Martinis, Superconducting phase qubits, Quant. Inf. Proc. 8(2–3), 81(2009)

[18] H.Eleuch, Entanglement and autocorrelation function in semiconductor microcavities, Int. J. Mod. Phys. B24(29), 5653(2010)

[19] H.Eleuch, Autocorrelation function of microcavityemitting field in the linear regime, EPJD48(1), 139(2008)

[20] E. A.Sete, A. A.Svidzinsky, H.Eleuch, Z.Yang, R. D.Nevels, and M. O.Scully, Correlated spontaneous emission on the Danube, J. Mod. Opt. 57(14–15), 1311(2010)

[21] E. A.Sete, A. A.Svidzinsky, Y. V.Rostovtsev, H.Eleuch, P. K.Jha, S.Suckewer, and M. O.Scully, Using quantum coherence to generate gain in the XUV and X-ray: Gain-Swept superradiance and lasing without inversion, IEEE J. Sel. Top. Quantum Electron. 18(1), 541(2012)

[22] H.Eleuchand R.Bennaceur, An optical soliton pair among absorbingthree-level atoms, J. Opt. A5(5), 528(2003)

[23] M.Tinkham, Introduction to Superconductivity, 2nd Ed., New York: McGraw Hill, 1996

[24] R. W.Simmonds, K.Lang, D.Hite, S.Nam, D.Pappas, and J.Martinis, Decoherence in Josephson Phase Qubits from Junction Resonators, Phys. Rev. Lett. 93(7), 077003(2004)

[25] M. A.Sillanpää, J. I.Park, and R. W.Simmonds, Coherent quantum state storage and transfer between two phase qubits via a resonant cavity, Nature449, 438(2007)

[26] F.Altomare, J. I.Park, K.Cicak, M. A.Sillanpää, M. S.Allman, D.Li, A.Sirois, J. A.Strong, J. D.Whittaker, and R. W.Simmonds, Tripartite interactions between two phase qubits and a resonant cavity, Nat. Phys. 6(10), 777(2010)

[27] O.Gameland D. F. V.James, Time-averaged quantum dynamics and the validity of the effective Hamiltonian model, Phys. Rev. A82, 052106(2010)

[28] M. A.Nielsenand I. L.Chuang, Quantum Computation and Quantum Information, Cambridge: Cambridge University Press, Ch. 4 and 6 (2000)

[29] H. F.Wang, X. Q.Shao, Y. F.Zhao, S.Zhang, and K. H.Yeon, Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED, J. Phys. At. Mol. Opt. Phys. 43(6), 065503(2010)

[30] H. F.Wang, J. J.Wen, A. D.Zhu, S.Zhang, and K. H.Yeon, Deterministic CNOT gate and entanglement swapping for photonic qubits using a quantum-dot spin in a double-sided optical microcavity, New J. Phys. 13, 013021(2011)

[31] H. F.Wang, X. X.Jiang, S.Zhang, and K. H.Yeon, Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits, J. Phys. At. Mol. Opt. Phys. 44(11), 115502(2011)

[32] A. S. F.Obada, H. A.Hessian, A. B. A.Mohamed, and A. H.Homid, Efficient protocol of NN-bit discrete quantum Fourier transform via transmon qubits coupled to a resonator, Quant. Inf. Proc. 13(2), 475(2014)

[33] A. H.Homid, A.Abdel-Aty, M.Abdel-Aty, A.Badawi, and A. S. F.Obada, Efficient realization of quantum search algorithm using quantum annealing processor with dissipation, J. Opt. Soc. Am. B32(9), 2025(2015)

[34] D.Deutschand R.Jozsa, Rapid solution of problems by quantum computation, Proc. R. Soc. Lond. A439(1907), 553(1992)

[35] D. R.Simon,On the power of quantum computation, Proc. 35th IEEE Symp. Found. Comp. Sci., Santa Fe, NM116–123 (1994)

[36] D. R.Simon, On the power of quantum computation, SIAM J. Comput. 26(5), 1474(1997)

[37] B. C.Sandersand G. J.Milburn, Optimal quantum measurements for phase estimation, Phys. Rev. Lett. 75(16), 2944(1995)

[38] P.Shor, Discrete logarithms and factoring, Proc. 35th Ann. Symp. Found.Comp. Sci. 124(1994)

[39] P.Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26(5), 1484(1997)

[40] O.Manasreh, Semiconductor Heterojunctions and Nanostructures, New York: McGraw-Hill Profes-sional, 2005

[41] R. D.Levine, Quantum Mechanics of Molecular Rate Processes, New York: Dover Publications, 1999

[42] N.Fromanand P. O.Froman, JWKB Approximation, Amsterdam: North-Holland, Amsterdam, 1965

[43] H.Eleuch, Y. V.Rostovtsev, and M. O.Scully, New analytic solution of Schrödinger’s equation, EPL(Europhys. Lett.)89(5), 50004(2010)

[44] J. Q.You and F.Nori, Superconducting circuits and quantum information, Phys. Today58(11), 42 (2005)

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