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Published in: Quantum Information Processing 2/2014

01-02-2014

Efficient protocol of \(N\)-bit discrete quantum Fourier transform via transmon qubits coupled to a resonator

Authors: A.-S. F. Obada, H. A. Hessian, A.-B. A. Mohamed, Ali H. Homid

Published in: Quantum Information Processing | Issue 2/2014

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Abstract

Based on the one- and two-qubit gates defined and generated via superconducting transmon qubits homogeneously coupled to a superconducting stripline resonator, we present a new physical protocol for implementing an \(N\)-bit discrete quantum Fourier transform. We propose and illustrate a detailed experimental feasibility for realizing the algorithm. The average fidelity is computed to prove the success of this algorithm. Estimated time for implementing the protocol using the proposed scheme is compared with previous schemes. Estimates show that the protocol can be successfully implemented within the present experimental limits.

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Literature
1.
go back to reference Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATH
3.
go back to reference Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)MathSciNetCrossRefMATH Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)MathSciNetCrossRefMATH
4.
go back to reference Lov K. Grover.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing (STOC), pp. 212–219 (1996) Lov K. Grover.: A fast quantum mechanical algorithm for database search. In: Proceedings of 28th Annual ACM Symposium on the Theory of Computing (STOC), pp. 212–219 (1996)
7.
go back to reference Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Goldwasser, S. (ed.) Foundations of Computer Science, IEEE Computer Society Press 35, pp. 124–134 (1994) Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Goldwasser, S. (ed.) Foundations of Computer Science, IEEE Computer Society Press 35, pp. 124–134 (1994)
8.
go back to reference Kitaev, AYu.: Quantum measurements and the abelian stabilizer problem. Electron. Colloquium Comput. Complex. 3, 1–22 (1996) Kitaev, AYu.: Quantum measurements and the abelian stabilizer problem. Electron. Colloquium Comput. Complex. 3, 1–22 (1996)
10.
go back to reference Boyer, M., Brassard, G., Hoyer, P., Tapp, A.: Tight bounds on quantum searching. Fortsch. Phys. 46, 493–505 (1998)CrossRefADS Boyer, M., Brassard, G., Hoyer, P., Tapp, A.: Tight bounds on quantum searching. Fortsch. Phys. 46, 493–505 (1998)CrossRefADS
11.
go back to reference Wang, H.F., Zhu, A.D., Zhang, S.: Physical optimization of quantum error correction circuits with spatially separated quantum dot spins. Opt. Express 21, 12484–12494 (2013)CrossRefADS Wang, H.F., Zhu, A.D., Zhang, S.: Physical optimization of quantum error correction circuits with spatially separated quantum dot spins. Opt. Express 21, 12484–12494 (2013)CrossRefADS
12.
go back to reference Obadaa, A.-S.F., Hessian, H.A., Mohamed, A.-B.A., Homid, Ali H.: Quantum logic gates generated by SC-charge qubits coupled to a resonator. J. Phys. A Math. Theor. 45, 485305 (2012)CrossRefMATHMathSciNet Obadaa, A.-S.F., Hessian, H.A., Mohamed, A.-B.A., Homid, Ali H.: Quantum logic gates generated by SC-charge qubits coupled to a resonator. J. Phys. A Math. Theor. 45, 485305 (2012)CrossRefMATHMathSciNet
13.
go back to reference Obadaa, A.-S.F., Hessian, H.A., Mohamed, A.-B.A., Homid, Ali H.: A proposal for the realization of universal quantum gates via superconducting qubits inside a cavity. Ann. Phys. 334, 47–57 (2013)CrossRefADSMATHMathSciNet Obadaa, A.-S.F., Hessian, H.A., Mohamed, A.-B.A., Homid, Ali H.: A proposal for the realization of universal quantum gates via superconducting qubits inside a cavity. Ann. Phys. 334, 47–57 (2013)CrossRefADSMATHMathSciNet
14.
go back to reference Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Optically controlled phase gate and teleportation of a controlled-not gate for spin qubits in a quantum-dot-microcavity coupled system. Phys. Rev. A 87, 062337 (2013)CrossRefADS Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Optically controlled phase gate and teleportation of a controlled-not gate for spin qubits in a quantum-dot-microcavity coupled system. Phys. Rev. A 87, 062337 (2013)CrossRefADS
15.
go back to reference Weinstein, Y.S., Pravia, M.A., Fortunato, E.M., Lloyd, S., Cory, D.G.: Implementation of the quantum Fourier transform. Phys. Rev. Lett. 86, 1889–1891 (2001)CrossRefADS Weinstein, Y.S., Pravia, M.A., Fortunato, E.M., Lloyd, S., Cory, D.G.: Implementation of the quantum Fourier transform. Phys. Rev. Lett. 86, 1889–1891 (2001)CrossRefADS
16.
go back to reference Scully, M.O., Zubairy, M.S.: Cavity QED implementation of the discrete quantum Fourier transform. Phys. Rev. A 65, 052324 (2002)CrossRefADS Scully, M.O., Zubairy, M.S.: Cavity QED implementation of the discrete quantum Fourier transform. Phys. Rev. A 65, 052324 (2002)CrossRefADS
17.
go back to reference Wang, H.F., Zhang, S., Yeon, K.H.: Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics. J. Korean Phys. Soc. 53, 1787–1790 (2008) Wang, H.F., Zhang, S., Yeon, K.H.: Implementing quantum discrete Fourier transform by using cavity quantum electrodynamics. J. Korean Phys. Soc. 53, 1787–1790 (2008)
18.
go back to reference Wang, H.F., Shao, X.Q., Zhao, Y.F., Zhang, S., Yeon, K.H.: Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED. J. Phys. B At. Mol. Opt. Phys. 43, 065503 (2010)CrossRefADS Wang, H.F., Shao, X.Q., Zhao, Y.F., Zhang, S., Yeon, K.H.: Protocol and quantum circuit for implementing the N-bit discrete quantum Fourier transform in cavity QED. J. Phys. B At. Mol. Opt. Phys. 43, 065503 (2010)CrossRefADS
19.
go back to reference Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics. New J. Phys. 13, 013021 (2011)CrossRefADS Wang, H.F., Zhu, A.D., Zhang, S., Yeon, K.H.: Simple implementation of discrete quantum Fourier transform via cavity quantum electrodynamics. New J. Phys. 13, 013021 (2011)CrossRefADS
20.
21.
go back to reference Imamoglu, A., Awschalom, D.D., Burkard, G., DiVincenzo, D.P., Loss, D., Sherwin, M., Small, A.: Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83, 4204–4207 (1999)CrossRefADS Imamoglu, A., Awschalom, D.D., Burkard, G., DiVincenzo, D.P., Loss, D., Sherwin, M., Small, A.: Quantum information processing using quantum dot spins and cavity QED. Phys. Rev. Lett. 83, 4204–4207 (1999)CrossRefADS
22.
go back to reference Wang, H.-F., Jiang, X.-X., Zhang, S., Yeon, K.-H.: Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits. J. Phys. B At. Mol. Opt. Phys. 44, 115502 (2011)CrossRefADS Wang, H.-F., Jiang, X.-X., Zhang, S., Yeon, K.-H.: Efficient quantum circuit for implementing discrete quantum Fourier transform in solid-state qubits. J. Phys. B At. Mol. Opt. Phys. 44, 115502 (2011)CrossRefADS
23.
go back to reference Wang, H.F., Zhang, S., Zhu, A.D., Yeon, K.H.: Fast and effective implementation of discrete quantum Fourier transform via virtual-photon-induced process in separate cavities. J. Opt. Soc. Am. B 29, 1078–1084 (2012)CrossRefADS Wang, H.F., Zhang, S., Zhu, A.D., Yeon, K.H.: Fast and effective implementation of discrete quantum Fourier transform via virtual-photon-induced process in separate cavities. J. Opt. Soc. Am. B 29, 1078–1084 (2012)CrossRefADS
24.
go back to reference Wendin, G., Shumeiko, V.S.: Quantum bits with Josephson junctions (Review Article). Low Temp. Phys. 33, 724 (2007)CrossRefADS Wendin, G., Shumeiko, V.S.: Quantum bits with Josephson junctions (Review Article). Low Temp. Phys. 33, 724 (2007)CrossRefADS
25.
go back to reference You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58, 42 (2005)CrossRef You, J.Q., Nori, F.: Superconducting circuits and quantum information. Phys. Today 58, 42 (2005)CrossRef
26.
go back to reference You, J.Q., Nori, F.: Quantum information processing with superconducting qubits in a microwave field. Phys. Rev. B 68, 064509 (2003)CrossRefADS You, J.Q., Nori, F.: Quantum information processing with superconducting qubits in a microwave field. Phys. Rev. B 68, 064509 (2003)CrossRefADS
27.
go back to reference Yang, C.P., Liu, Y.X., Nori, F.: Phase gate of one qubit simultaneously controlling \(n\) qubits in a cavity. Phys. Rev. A 81, 062323 (2010)CrossRefADS Yang, C.P., Liu, Y.X., Nori, F.: Phase gate of one qubit simultaneously controlling \(n\) qubits in a cavity. Phys. Rev. A 81, 062323 (2010)CrossRefADS
28.
go back to reference Devoret, M.H.: Quantum fluctuations in electrical circuits. In: Les Houches Session LXIII, Quantum Fluctuations, (1995) Devoret, M.H.: Quantum fluctuations in electrical circuits. In: Les Houches Session LXIII, Quantum Fluctuations, (1995)
29.
go back to reference Koch, J., Yu, T.M.: Charge-insensitive qubit design derived from the cooper pair box. Phys. Rev. A 76, 042319 (2007)CrossRefADS Koch, J., Yu, T.M.: Charge-insensitive qubit design derived from the cooper pair box. Phys. Rev. A 76, 042319 (2007)CrossRefADS
30.
go back to reference Bishop, Lev S., Chow, J.M., Koch, J., Houck, A.A., Devoret, M.H., Thuneberg, E., Girvin, S.M., Schoelkopf, R.J.: Nonlinear response of the vacuum Rabi resonance. Nat. Phys. 5, 105–109 (2009)CrossRef Bishop, Lev S., Chow, J.M., Koch, J., Houck, A.A., Devoret, M.H., Thuneberg, E., Girvin, S.M., Schoelkopf, R.J.: Nonlinear response of the vacuum Rabi resonance. Nat. Phys. 5, 105–109 (2009)CrossRef
31.
go back to reference Blais, A., Huang, R.-S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)CrossRefADS Blais, A., Huang, R.-S., Wallraff, A., Girvin, S.M., Schoelkopf, R.J.: Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation. Phys. Rev. A 69, 062320 (2004)CrossRefADS
32.
go back to reference Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120126 (1998)CrossRef Loss, D., DiVincenzo, D.P.: Quantum computation with quantum dots. Phys. Rev. A 57, 120126 (1998)CrossRef
33.
go back to reference Eckert, K., Mompart, J., Yi, X.X., Schliemann, J., Bruß, D., Birkl, G., Lewenstein, M.: Quantum computing in optical microtraps based on the motional states of neutral atoms. Phys. Rev. A 66, 042317 (2002)CrossRefADS Eckert, K., Mompart, J., Yi, X.X., Schliemann, J., Bruß, D., Birkl, G., Lewenstein, M.: Quantum computing in optical microtraps based on the motional states of neutral atoms. Phys. Rev. A 66, 042317 (2002)CrossRefADS
34.
go back to reference Poyatos, J.F., Cirac, J.I., Zoller, P.: Complete characterization of a quantum process: the two-bit quantum gate. Phys. Rev. Lett. 78, 390393 (1997)CrossRefADS Poyatos, J.F., Cirac, J.I., Zoller, P.: Complete characterization of a quantum process: the two-bit quantum gate. Phys. Rev. Lett. 78, 390393 (1997)CrossRefADS
35.
go back to reference Vion, D., Aassime, A., Cottet, A., Joyez, P., Pothier, H., Urbinay, C., Esteve, D., Devoret, M.H.: Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002)CrossRefADS Vion, D., Aassime, A., Cottet, A., Joyez, P., Pothier, H., Urbinay, C., Esteve, D., Devoret, M.H.: Manipulating the quantum state of an electrical circuit. Science 296, 886–889 (2002)CrossRefADS
36.
go back to reference Buluta, I., Ashhab, S., Nori, F.: Natural and artificial atoms for quantum computation. Rep. Prog. Phys. 74, 104401 (2011)CrossRefADS Buluta, I., Ashhab, S., Nori, F.: Natural and artificial atoms for quantum computation. Rep. Prog. Phys. 74, 104401 (2011)CrossRefADS
Metadata
Title
Efficient protocol of -bit discrete quantum Fourier transform via transmon qubits coupled to a resonator
Authors
A.-S. F. Obada
H. A. Hessian
A.-B. A. Mohamed
Ali H. Homid
Publication date
01-02-2014
Publisher
Springer US
Published in
Quantum Information Processing / Issue 2/2014
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-013-0664-z

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