Abstract

A scheme for one-step implementation of an n-qubit controlled-phase gate is proposed in a superconducting quantum interference device (SQUID) system. The distinguishing feature of this scheme is the simultaneous and nonidentical off-resonant Raman coupling of the n SQUID qubits to a single-mode resonator and the microwave pulses. The scheme is efficient and simple because it requires only one-step evolution, and no adjustments of the experimental parameters are needed during the operation.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  29. C. P. Yang and S. Han, “n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,” Phys. Rev. A 72, 032311 (2005).
    [CrossRef]
  30. C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
    [CrossRef]
  31. C. P. Yang, Y. X. Liu, and F. Nori, “Phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 81, 062323 (2010).
    [CrossRef]
  32. C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010).
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    [CrossRef]
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    [CrossRef]
  36. S. B. Zheng, “One-step synthesis of multiatom Greenberger-Horne-Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
    [CrossRef]
  37. J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
    [CrossRef]
  38. L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
    [CrossRef]
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    [CrossRef]
  40. P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
    [CrossRef]
  41. W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
    [CrossRef]

2011 (1)

C. P. Yang, “Preparation of n-qubit Greenberger-Horne-Zeilinger entangled states in cavity QED: an approach with tolerance to nonidentical qubit-cavity coupling constants,” Phys. Rev. A 83, 062302 (2011).
[CrossRef]

2010 (3)

C. P. Yang, Y. X. Liu, and F. Nori, “Phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 81, 062323 (2010).
[CrossRef]

C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010).
[CrossRef]

X. L. He, C. P. Yang, S. Li, J. Y. Luo, and S. Han, “Quantum logical gates with four-level superconducting quantum interference devices coupled to a superconducting resonator,” Phys. Rev. A 82, 024301 (2010).
[CrossRef]

2009 (2)

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
[CrossRef]

P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
[CrossRef]

2008 (3)

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[CrossRef]

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
[CrossRef]

C. F. Wu, X. L. Feng, X. X. Yi, I. M. Chen, and C. H. Oh, “Quantum gate operations in the decoherence-free subspace of superconducting quantum-interference devices,” Phys. Rev. A 78, 062321 (2008).
[CrossRef]

2007 (2)

J. H. Plantenberg, P. C. de Groot, C. J. P. M. Harmans, and J. E. Mooij, “Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits,” Nature 447, 836–839 (2007).
[CrossRef]

J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Coupling superconducting qubits via a cavity bus,” Nature 449, 443–447 (2007).
[CrossRef]

2006 (2)

C. P. Yang and S. Han, “Rotation gate for a three-level superconducting quantum interference device qubit with resonant interaction,” Phys. Rev. A 74, 044302 (2006).
[CrossRef]

C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
[CrossRef]

2005 (3)

K. H. Song, Z. W. Zhou, and G. C. Guo, “Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition,” Phys. Rev. A 71, 052310 (2005).
[CrossRef]

P. Zhang, Z. D. Wang, J. D. Sun, and C. P. Sun, “Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity,” Phys. Rev. A 71, 042301 (2005).
[CrossRef]

C. P. Yang and S. Han, “n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,” Phys. Rev. A 72, 032311 (2005).
[CrossRef]

2004 (9)

M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, “Quantum circuits for general multiqubit gates,” Phys. Rev. Lett. 93, 130502 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED,” Phys. Rev. A 70, 044303 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “An energy relaxation tolerant approach to quantum entanglement, information transfer, and gates with superconducting-quantum-interference-device qubits in cavity QED,” J. Phys. Condens. Matter 16, 1907–1914 (2004).
[CrossRef]

Z. Kis and E. Paspalakis, “Arbitrary rotation and entanglement of flux SQUID qubits,” Phys. Rev. B 69, 024510 (2004).
[CrossRef]

Z. Y. Zhou, S. I. Chu, and S. Han, “Suppression of energy-relaxation-induced decoherence in Λ-type three-level SQUID flux qubits: A dark-state approach,” Phys. Rev. B 70, 094513 (2004).
[CrossRef]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[CrossRef]

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162(2004).
[CrossRef]

2003 (5)

T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
[CrossRef]

J. Q. You, J. S. Tsai, and F. Nori, “Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits,” Phys. Rev. B 68, 024510 (2003).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED,” Phys. Rev. A 67, 042311 (2003).
[CrossRef]

M. H. S. Amin, A. Yu. Smirnov, and A. M. van den Brink, “Josephson-phase qubit without tunneling,” Phys. Rev. B 67, 100508(R) (2003).
[CrossRef]

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
[CrossRef]

2002 (1)

Z. Y. Zhou, S. I. Chu, and S. Han, “Quantum computing with superconducting devices: A three-level SQUID qubit,” Phys. Rev. B 66, 054527 (2002).
[CrossRef]

2001 (3)

M. Šašura and V. Bužek, “Multiparticle entanglement with quantum logic networks: application to cold trapped ions,” Phys. Rev. A 64, 012305 (2001).
[CrossRef]

S. L. Braunstein, V. Bužek, and M. Hillery, “Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit,” Phys. Rev. A 63, 052313 (2001).
[CrossRef]

S. B. Zheng, “One-step synthesis of multiatom Greenberger-Horne-Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
[CrossRef]

2000 (2)

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef]

1996 (1)

S. Han, R. Rouse, and J. E. Lukens, “Generation of a population inversion between quantum states of a macroscopic variable,” Phys. Rev. Lett. 76, 3404–3407 (1996).
[CrossRef]

1995 (3)

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[CrossRef]

P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, “Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances,” Phys. Rev. A 52, 3554–3559 (1995).
[CrossRef]

Amin, M. H. S.

M. H. S. Amin, A. Yu. Smirnov, and A. M. van den Brink, “Josephson-phase qubit without tunneling,” Phys. Rev. B 67, 100508(R) (2003).
[CrossRef]

Astafiev, O.

T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
[CrossRef]

Barenco, A.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Baur, M.

P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
[CrossRef]

Bennett, C. H.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Bergholm, V.

M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, “Quantum circuits for general multiqubit gates,” Phys. Rev. Lett. 93, 130502 (2004).
[CrossRef]

Bertet, P.

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162(2004).
[CrossRef]

Beth, T.

T. Beth and M. Rötteler, Quantum Information (Springer, 2001).

Bianchetti, R.

P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
[CrossRef]

Bishop, L. S.

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
[CrossRef]

Blais, A.

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
[CrossRef]

J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Coupling superconducting qubits via a cavity bus,” Nature 449, 443–447 (2007).
[CrossRef]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[CrossRef]

Braunstein, S. L.

S. L. Braunstein, V. Bužek, and M. Hillery, “Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit,” Phys. Rev. A 63, 052313 (2001).
[CrossRef]

Brune, M.

P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, “Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances,” Phys. Rev. A 52, 3554–3559 (1995).
[CrossRef]

Bužek, V.

S. L. Braunstein, V. Bužek, and M. Hillery, “Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit,” Phys. Rev. A 63, 052313 (2001).
[CrossRef]

M. Šašura and V. Bužek, “Multiparticle entanglement with quantum logic networks: application to cold trapped ions,” Phys. Rev. A 64, 012305 (2001).
[CrossRef]

Chen, I. M.

C. F. Wu, X. L. Feng, X. X. Yi, I. M. Chen, and C. H. Oh, “Quantum gate operations in the decoherence-free subspace of superconducting quantum-interference devices,” Phys. Rev. A 78, 062321 (2008).
[CrossRef]

Chen, W.

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef]

Chiorescu, I.

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162(2004).
[CrossRef]

Chow, J. M.

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
[CrossRef]

J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Coupling superconducting qubits via a cavity bus,” Nature 449, 443–447 (2007).
[CrossRef]

Chu, S. I.

C. P. Yang, S. I. Chu, and S. Han, “Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED,” Phys. Rev. A 70, 044303 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “An energy relaxation tolerant approach to quantum entanglement, information transfer, and gates with superconducting-quantum-interference-device qubits in cavity QED,” J. Phys. Condens. Matter 16, 1907–1914 (2004).
[CrossRef]

Z. Y. Zhou, S. I. Chu, and S. Han, “Suppression of energy-relaxation-induced decoherence in Λ-type three-level SQUID flux qubits: A dark-state approach,” Phys. Rev. B 70, 094513 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED,” Phys. Rev. A 67, 042311 (2003).
[CrossRef]

Z. Y. Zhou, S. I. Chu, and S. Han, “Quantum computing with superconducting devices: A three-level SQUID qubit,” Phys. Rev. B 66, 054527 (2002).
[CrossRef]

Clarke, J.

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[CrossRef]

Cleve, R.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Day, P. K.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
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P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
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W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
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J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
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X. L. He, C. P. Yang, S. Li, J. Y. Luo, and S. Han, “Quantum logical gates with four-level superconducting quantum interference devices coupled to a superconducting resonator,” Phys. Rev. A 82, 024301 (2010).
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L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
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P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
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C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
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J. H. Plantenberg, P. C. de Groot, C. J. P. M. Harmans, and J. E. Mooij, “Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits,” Nature 447, 836–839 (2007).
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J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
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P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
[CrossRef]

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P. Zhang, Z. D. Wang, J. D. Sun, and C. P. Sun, “Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity,” Phys. Rev. A 71, 042301 (2005).
[CrossRef]

Sun, J. D.

P. Zhang, Z. D. Wang, J. D. Sun, and C. P. Sun, “Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity,” Phys. Rev. A 71, 042301 (2005).
[CrossRef]

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J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef]

Tsai, J. S.

J. Q. You, J. S. Tsai, and F. Nori, “Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits,” Phys. Rev. B 68, 024510 (2003).
[CrossRef]

T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
[CrossRef]

van den Brink, A. M.

M. H. S. Amin, A. Yu. Smirnov, and A. M. van den Brink, “Josephson-phase qubit without tunneling,” Phys. Rev. B 67, 100508(R) (2003).
[CrossRef]

Vartiainen, J. J.

M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, “Quantum circuits for general multiqubit gates,” Phys. Rev. Lett. 93, 130502 (2004).
[CrossRef]

Vayonakis, A.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
[CrossRef]

Wallraff, A.

P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
[CrossRef]

J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Coupling superconducting qubits via a cavity bus,” Nature 449, 443–447 (2007).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[CrossRef]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[CrossRef]

Wang, Z. D.

P. Zhang, Z. D. Wang, J. D. Sun, and C. P. Sun, “Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity,” Phys. Rev. A 71, 042301 (2005).
[CrossRef]

Weinfurter, H.

A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Wilhelm, F. K.

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[CrossRef]

Wineland, D. J.

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[CrossRef]

Wu, C. F.

C. F. Wu, X. L. Feng, X. X. Yi, I. M. Chen, and C. H. Oh, “Quantum gate operations in the decoherence-free subspace of superconducting quantum-interference devices,” Phys. Rev. A 78, 062321 (2008).
[CrossRef]

Yamamoto, T.

T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
[CrossRef]

Yang, C. P.

C. P. Yang, “Preparation of n-qubit Greenberger-Horne-Zeilinger entangled states in cavity QED: an approach with tolerance to nonidentical qubit-cavity coupling constants,” Phys. Rev. A 83, 062302 (2011).
[CrossRef]

C. P. Yang, Y. X. Liu, and F. Nori, “Phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 81, 062323 (2010).
[CrossRef]

C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010).
[CrossRef]

X. L. He, C. P. Yang, S. Li, J. Y. Luo, and S. Han, “Quantum logical gates with four-level superconducting quantum interference devices coupled to a superconducting resonator,” Phys. Rev. A 82, 024301 (2010).
[CrossRef]

C. P. Yang and S. Han, “Rotation gate for a three-level superconducting quantum interference device qubit with resonant interaction,” Phys. Rev. A 74, 044302 (2006).
[CrossRef]

C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
[CrossRef]

C. P. Yang and S. Han, “n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,” Phys. Rev. A 72, 032311 (2005).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED,” Phys. Rev. A 70, 044303 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “An energy relaxation tolerant approach to quantum entanglement, information transfer, and gates with superconducting-quantum-interference-device qubits in cavity QED,” J. Phys. Condens. Matter 16, 1907–1914 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED,” Phys. Rev. A 67, 042311 (2003).
[CrossRef]

Yi, X. X.

C. F. Wu, X. L. Feng, X. X. Yi, I. M. Chen, and C. H. Oh, “Quantum gate operations in the decoherence-free subspace of superconducting quantum-interference devices,” Phys. Rev. A 78, 062321 (2008).
[CrossRef]

You, J. Q.

J. Q. You, J. S. Tsai, and F. Nori, “Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits,” Phys. Rev. B 68, 024510 (2003).
[CrossRef]

Zhang, P.

P. Zhang, Z. D. Wang, J. D. Sun, and C. P. Sun, “Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity,” Phys. Rev. A 71, 042301 (2005).
[CrossRef]

Zheng, S. B.

C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010).
[CrossRef]

S. B. Zheng, “One-step synthesis of multiatom Greenberger-Horne-Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
[CrossRef]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

Zhou, Z. W.

K. H. Song, Z. W. Zhou, and G. C. Guo, “Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition,” Phys. Rev. A 71, 052310 (2005).
[CrossRef]

Zhou, Z. Y.

Z. Y. Zhou, S. I. Chu, and S. Han, “Suppression of energy-relaxation-induced decoherence in Λ-type three-level SQUID flux qubits: A dark-state approach,” Phys. Rev. B 70, 094513 (2004).
[CrossRef]

Z. Y. Zhou, S. I. Chu, and S. Han, “Quantum computing with superconducting devices: A three-level SQUID qubit,” Phys. Rev. B 66, 054527 (2002).
[CrossRef]

Zmuidzinas, J.

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
[CrossRef]

J. Phys. Condens. Matter (1)

C. P. Yang, S. I. Chu, and S. Han, “An energy relaxation tolerant approach to quantum entanglement, information transfer, and gates with superconducting-quantum-interference-device qubits in cavity QED,” J. Phys. Condens. Matter 16, 1907–1914 (2004).
[CrossRef]

Nature (9)

J. H. Plantenberg, P. C. de Groot, C. J. P. M. Harmans, and J. E. Mooij, “Demonstration of controlled-NOT quantum gates on a pair of superconducting quantum bits,” Nature 447, 836–839 (2007).
[CrossRef]

J. Clarke and F. K. Wilhelm, “Superconducting quantum bits,” Nature 453, 1031–1042 (2008).
[CrossRef]

L. DiCarlo, J. M. Chow, J. M. Gambetta, L. S. Bishop, B. R. Johnson, D. I. Schuster, J. Majer, A. Blais, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, “Demonstration of two-qubit algorithms with a superconducting quantum processor,” Nature 460, 240–244 (2009).
[CrossRef]

T. Yamamoto, Yu. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai, “Demonstration of conditional gate operation using superconducting charge qubits,” Nature 425, 941–944 (2003).
[CrossRef]

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature 431, 162–167 (2004).
[CrossRef]

I. Chiorescu, P. Bertet, K. Semba, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, “Coherent dynamics of a flux qubit coupled to a harmonic oscillator,” Nature 431, 159–162(2004).
[CrossRef]

J. Majer, J. M. Chow, J. M. Gambetta, J. Koch, B. R. Johnson, J. A. Schreier, L. Frunzio, D. I. Schuster, A. A. Houck, A. Wallraff, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Coupling superconducting qubits via a cavity bus,” Nature 449, 443–447 (2007).
[CrossRef]

J. R. Friedman, V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens, “Quantum superposition of distinct macroscopic states,” Nature 406, 43–46 (2000).
[CrossRef]

P. K. Day, H. G. LeDuc, B. A. Mazin, A. Vayonakis, and J. Zmuidzinas, “A broadband superconducting detector suitable for use in large arrays,” Nature 425, 817–821 (2003).
[CrossRef]

New J. Phys. (1)

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” New J. Phys. 10, 013026 (2008).
[CrossRef]

Phys. Rev. A (17)

C. P. Yang, S. I. Chu, and S. Han, “Simplified realization of two-qubit quantum phase gate with four-level systems in cavity QED,” Phys. Rev. A 70, 044303 (2004).
[CrossRef]

P. Domokos, J. M. Raimond, M. Brune, and S. Haroche, “Simple cavity-QED two-bit universal quantum logic gate: The principle and expected performances,” Phys. Rev. A 52, 3554–3559 (1995).
[CrossRef]

A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, “Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation,” Phys. Rev. A 69, 062320 (2004).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Possible realization of entanglement, logical gates, and quantum-information transfer with superconducting-quantum-interference-device qubits in cavity QED,” Phys. Rev. A 67, 042311 (2003).
[CrossRef]

K. H. Song, Z. W. Zhou, and G. C. Guo, “Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition,” Phys. Rev. A 71, 052310 (2005).
[CrossRef]

P. Zhang, Z. D. Wang, J. D. Sun, and C. P. Sun, “Holonomic quantum computation using rf superconducting quantum interference devices coupled through a microwave cavity,” Phys. Rev. A 71, 042301 (2005).
[CrossRef]

C. P. Yang and S. Han, “Rotation gate for a three-level superconducting quantum interference device qubit with resonant interaction,” Phys. Rev. A 74, 044302 (2006).
[CrossRef]

C. F. Wu, X. L. Feng, X. X. Yi, I. M. Chen, and C. H. Oh, “Quantum gate operations in the decoherence-free subspace of superconducting quantum-interference devices,” Phys. Rev. A 78, 062321 (2008).
[CrossRef]

C. P. Yang, “Preparation of n-qubit Greenberger-Horne-Zeilinger entangled states in cavity QED: an approach with tolerance to nonidentical qubit-cavity coupling constants,” Phys. Rev. A 83, 062302 (2011).
[CrossRef]

C. P. Yang and S. Han, “n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator,” Phys. Rev. A 72, 032311 (2005).
[CrossRef]

C. P. Yang and S. Han, “Realization of an n-qubit controlled-U gate with superconducting quantum interference devices or atoms in cavity QED,” Phys. Rev. A 73, 032317 (2006).
[CrossRef]

C. P. Yang, Y. X. Liu, and F. Nori, “Phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 81, 062323 (2010).
[CrossRef]

C. P. Yang, S. B. Zheng, and F. Nori, “Multiqubit tunable phase gate of one qubit simultaneously controlling n qubits in a cavity,” Phys. Rev. A 82, 062326 (2010).
[CrossRef]

X. L. He, C. P. Yang, S. Li, J. Y. Luo, and S. Han, “Quantum logical gates with four-level superconducting quantum interference devices coupled to a superconducting resonator,” Phys. Rev. A 82, 024301 (2010).
[CrossRef]

M. Šašura and V. Bužek, “Multiparticle entanglement with quantum logic networks: application to cold trapped ions,” Phys. Rev. A 64, 012305 (2001).
[CrossRef]

S. L. Braunstein, V. Bužek, and M. Hillery, “Quantum-information distributors: quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit,” Phys. Rev. A 63, 052313 (2001).
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A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, “Elementary gates for quantum computation,” Phys. Rev. A 52, 3457–3467 (1995).
[CrossRef]

Phys. Rev. B (6)

Z. Kis and E. Paspalakis, “Arbitrary rotation and entanglement of flux SQUID qubits,” Phys. Rev. B 69, 024510 (2004).
[CrossRef]

Z. Y. Zhou, S. I. Chu, and S. Han, “Suppression of energy-relaxation-induced decoherence in Λ-type three-level SQUID flux qubits: A dark-state approach,” Phys. Rev. B 70, 094513 (2004).
[CrossRef]

P. J. Leek, S. Filipp, P. Maurer, M. Baur, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, and A. Wallraff, “Using sideband transitions for two-qubit operations in superconducting circuits,” Phys. Rev. B 79, 180511(R) (2009).
[CrossRef]

M. H. S. Amin, A. Yu. Smirnov, and A. M. van den Brink, “Josephson-phase qubit without tunneling,” Phys. Rev. B 67, 100508(R) (2003).
[CrossRef]

J. Q. You, J. S. Tsai, and F. Nori, “Controllable manipulation and entanglement of macroscopic quantum states in coupled charge qubits,” Phys. Rev. B 68, 024510 (2003).
[CrossRef]

Z. Y. Zhou, S. I. Chu, and S. Han, “Quantum computing with superconducting devices: A three-level SQUID qubit,” Phys. Rev. B 66, 054527 (2002).
[CrossRef]

Phys. Rev. Lett. (6)

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, “Demonstration of a fundamental quantum logic gate,” Phys. Rev. Lett. 75, 4714–4717 (1995).
[CrossRef]

C. P. Yang, S. I. Chu, and S. Han, “Quantum information transfer and entanglement with SQUID qubits in cavity QED: a dark-state scheme with tolerance for nonuniform device parameter,” Phys. Rev. Lett. 92, 117902 (2004).
[CrossRef]

S. B. Zheng and G. C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett. 85, 2392–2395 (2000).
[CrossRef]

S. B. Zheng, “One-step synthesis of multiatom Greenberger-Horne-Zeilinger states,” Phys. Rev. Lett. 87, 230404 (2001).
[CrossRef]

S. Han, R. Rouse, and J. E. Lukens, “Generation of a population inversion between quantum states of a macroscopic variable,” Phys. Rev. Lett. 76, 3404–3407 (1996).
[CrossRef]

M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, “Quantum circuits for general multiqubit gates,” Phys. Rev. Lett. 93, 130502 (2004).
[CrossRef]

Other (1)

T. Beth and M. Rötteler, Quantum Information (Springer, 2001).

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Figures (1)

Fig. 1.
Fig. 1.

Nonidentical SQUID-resonator-pulse off-resonant Raman coupling for n SQUID qubits placed in a single-mode resonator. (a) Energy levels for SQUID 1 and its coupling to the resonator (with coupling strength g 1 and detuning Δ ˜ 1 ) and the pulse (with coupling strength Ω 1 and detuning Δ 1 ). (b) Energy levels for SQUID j ( = 2 , 3 , , n ) and its coupling to the resonator (with coupling strength g j and detuning Δ ˜ j ) and the pulse (with coupling strength Ω j and detuning Δ j ).

Equations (13)

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H s = Q 2 2 C + ( Φ Φ x ) 2 2 L E J cos ( 2 π Φ Φ 0 ) .
H i = j = 1 n [ Ω j 2 Δ j | 2 j 2 | + g j 2 Δ ˜ j a a | 1 j 1 | + λ j ( a | 1 j 2 | e i δ j t + a | 2 j 1 | e i δ j t ) ] ,
H eff = ( Ω 1 2 Δ 1 | 2 1 2 | + g 1 2 Δ ˜ 1 a a | 1 1 1 | ) j = 2 n ( Ω 2 Δ | 2 j 2 | + g 2 Δ ˜ a a | 1 j 1 | ) + η 1 ( | 2 1 2 | a a | 1 1 1 | a a ) + j = 2 n η ( | 2 j 2 | a a | 1 j 1 | a a ) + η j , k = 2 , j k n S j + S k + η η 1 j = 2 n ( S 1 + S j + S 1 S j + ) ,
H eff = Ω 1 2 Δ 1 | 2 1 2 | j = 2 n Ω 2 Δ | 2 j 2 | + η 1 | 2 1 2 | + j = 2 n η | 2 j 2 | + η j , k = 2 , j k n S j + S k + η η 1 j = 2 n ( S 1 + S j + S 1 S j + ) .
H eff = η 1 | 2 1 2 | + j = 2 n η | 2 j 2 | + η j , k = 2 , j k n S j + S k + η η 1 j = 2 n ( S 1 + S j + S 1 S j + ) .
| 2 , 1 , 1 123 α 2 | 2 , 1 , 1 123 + β 2 ( | 1 , 2 , 1 123 + | 1 , 1 , 2 123 ) , | 2 , 1 , 0 123 α 1 | 2 , 1 , 0 123 + β 1 | 1 , 2 , 0 123 , | 2 , 0 , 1 123 α 1 | 2 , 0 , 1 123 + β 1 | 1 , 0 , 2 123 , | 2 , 0 , 0 123 γ | 2 , 0 , 0 123 ,
α 2 = 2 η + η 1 e i ( 2 η + η 1 ) t 2 η + η 1 , α 1 = η + η 1 e i ( η + η 1 ) t η + η 1 , γ = e i η 1 t , β 2 = η η 1 + η η 1 e i ( 2 η + η 1 ) t η η 1 ( 2 η + η 1 ) , β 1 = η η 1 + η η 1 e i ( η + η 1 ) t η η 1 ( η + η 1 ) .
| 1 , 1 , 1 123 | 1 , 1 , 1 123 , | 1 , 1 , 0 123 | 1 , 1 , 0 123 , | 1 , 0 , 1 123 | 1 , 0 , 1 123 , | 1 , 0 , 0 123 | 1 , 0 , 0 123 , | 2 , 1 , 1 123 | 2 , 1 , 1 123 , | 2 , 1 , 0 123 | 2 , 1 , 0 123 , | 2 , 0 , 1 123 | 2 , 0 , 1 123 , | 2 , 0 , 0 123 | 2 , 0 , 0 123 .
| 2 1 j = 2 n | 1 j α n 1 | 2 1 j = 2 n | 1 j + β n 1 k = 2 n | 1 1 | 2 k j = 2 ( j k ) n | 1 j ,
| 2 1 | 1 k j = 2 , j k n | 0 j α 1 | 2 1 | 1 k j = 2 , j k n | 0 j + β 1 | 1 1 | 2 k j = 2 , j k n | 0 j ( k = 2 , 3 , , n ) ,
| 2 1 | 1 k | 1 ξ j = 2 , j k ξ n | 0 j α χ | 2 1 | 1 k | 1 ξ j = 2 , j k ξ n | 0 j + β χ | 1 1 ( | 2 k | 1 ξ + + | 1 k | 2 ξ ) j = 2 , j k ξ n | 0 j ( k , , ξ = 2 , 3 , , n , χ = k + + ξ ) ,
| 2 1 j = 2 n | 0 j γ | 2 1 j = 2 n | 0 j ,
α n 1 = ( n 1 ) η + η 1 e i [ ( n 1 ) η + η 1 ] t ( n 1 ) η + η 1 , β n 1 = η η 1 + η η 1 e i [ ( n 1 ) η + η 1 ] t η η 1 [ ( n 1 ) η + η 1 ] .

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