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[CrossRef]

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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]

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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).

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

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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]

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. 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]

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[CrossRef]

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[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).

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[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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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, “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, “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, “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]

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

[CrossRef]

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]

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. 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]

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]

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]

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]

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]

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]

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. 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]

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. 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]

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]

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]

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]

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]

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]

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, “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, “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]

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]

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]

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]

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]

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]

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]

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]

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]

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

[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]

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]

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]

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

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]

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]

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]

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, 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]

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

[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]

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]

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]

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. 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. 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]

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]

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]

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. 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]

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]

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]

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

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]

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]

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. 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]

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]

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

[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]

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]

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]

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

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]

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

[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]

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]

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]

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. 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]

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]

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]

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]

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]

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. 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]

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]

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]

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]

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]

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]

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

[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]

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]

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]

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]

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

[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]

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]

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]

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]

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, 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]

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, “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, “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, “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, “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, “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]

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]

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]

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, 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]

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]

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]

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]

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]

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]

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

[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]

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]

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