Creation of superposition of arbitrary states encoded in two high-Q cavities

Tong Liu; Tong Liu; Yang Zhang; Bao-qing Guo; Chang-shui Yu; Wei-ning Zhang

doi:10.1364/OE.27.027168

Creation of superposition of arbitrary states encoded in two high-Q cavities

Tong Liu, Yang Zhang, Bao-qing Guo, Chang-shui Yu, and Wei-ning Zhang

Optics Express
Vol. 27,
Issue 19,
pp. 27168-27182
(2019)
•https://doi.org/10.1364/OE.27.027168

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Tong Liu, Yang Zhang, Bao-qing Guo, Chang-shui Yu, and Wei-ning Zhang, "Creation of superposition of arbitrary states encoded in two high-Q cavities," Opt. Express 27, 27168-27182 (2019)

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Table of Contents Category
- Quantum Optics
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: June 4, 2019
- Revised Manuscript: August 18, 2019
- Manuscript Accepted: August 18, 2019
- Published: September 12, 2019

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Open Access

Abstract

The principle of superposition is a key ingredient for quantum mechanics. A recent work [Phys. Rev. Lett. 116, 110403 (2016) [CrossRef] ] has shown that a quantum adder that deterministically generates a superposition of two unknown states is forbidden. Here we consider the implementation of the probabilistic quantum adder in the 3D cavity-transmon system. Our implementation is based on a three-level superconducting transmon qubit dispersively coupled to two cavities. Numerical simulations show that high-fidelity generation of the superposition of two coherent states is feasible with current circuit QED technology. Our method also works for other physical systems such as two optical cavities coupled to a three-level atom or two nitrogen-vacancy center ensembles interacted with one three-level superconducting flux qubit.

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2018 (4)

H. Zhang, A. Alsaedi, T. Hayat, and F. G. Deng, “Entanglement concentration and purification of two-mode squeezed microwave photons in circuit QED,” Ann. Phys. 391, 112–119 (2018).
[Crossref]

S. Rosenblum, Y. Y. Gao, P. Reinhold, C. Wang, C. J. Axline, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “A CNOT gate between multiphoton qubits encoded in two cavities,” Nature Comm. 9, 652 (2018).
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[Crossref] [PubMed]

T. Liu, B. Q. Guo, C. S. Yu, and W. N. Zhang, “One-step implementation of a hybrid Fredkin gate with quantum memories and single superconducting qubit in circuit QED and its applications,” Opt. Express 26, 4498–4511 (2018).
[Crossref] [PubMed]

2017 (9)

Q. P. Su, H. H. Zhu, L. Yu, Y. Zhang, S. J. Xiong, J. M. Liu, and C. P. Yang, “Generating double NOON states of photons in circuit QED,” Phys. Rev. A 95, 022339 (2017).
[Crossref]

M. Doosti, F. Kianvash, and V. Karimipour, “Universal superposition of orthogonal states,” Phys. Rev. A 96, 052318 (2017).
[Crossref]

G. Gatti, D. Barberena, M. Sanz, and E. Solano, “Protected state transfer via an approximate quantum adder,” Sci. Rep. 7, 6964 (2017).
[Crossref] [PubMed]

K. Li, G. Long, H. Katiyar, T. Xin, G. Feng, D. Lu, and R. Laflamme, “Experimentally superposing two pure states with partial prior knowledge,” Phys. Rev. A 95, 022334 (2017).
[Crossref]

X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
[Crossref]

C. S. Yu, “Quantum coherence via skew information and its polygamy,” Phys. Rev. A 95, 042337 (2017).
[Crossref]

F. Souris, H. Christiani, and J. P. Davis, “Tuning a 3D microwave cavity via superfluid helium at millikelvin temperatures,” Appl. Phys. Lett. 111, 172601 (2017).
[Crossref]

T. Liu, Y. Zhang, B. Q. Guo, C. S. Yu, and W. N. Zhang, “Circuit QED: cross-Kerr effect induced by a superconducting qutrit without classical pulses,” Quantum Inf. Process. 16, 209 (2017).
[Crossref]

C. P. Yang, Q. P. Su, S. B. Zheng, F. Nori, and S. Han, “Entangling two oscillators with arbitrary asymmetric initial states,” Phys. Rev. A 95, 052341 (2017).
[Crossref]

2016 (11)

T. Liu, Q. P. Su, S. J. Xiong, J. M. Liu, C. P. Yang, and F. Nori, “Generation of a macroscopic entangled coherent state using quantum memories in circuit QED,” Sci. Rep. 6, 32004 (2016).
[Crossref] [PubMed]

C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, “Entangling superconducting qubits in a multi-cavity system,” New J. Phys. 18, 013025 (2016).
[Crossref]

T. Liu, X. Z. Cao, Q. P. Su, S. J. Xiong, and C. P. Yang, “Multi-target-qubit unconventional geometric phase gate in a multi-cavity system,” Sci. Rep. 6, 21562 (2016).
[Crossref] [PubMed]

N. Ofek, A. Petrenko, R. Heeres, P. Reinhold, Z. Leghtas, B. Vlastakis, Y. Liu, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Extending the lifetime of a quantum bit with error correction in superconducting circuits,” Nature 536, 441–445 (2016).
[Crossref] [PubMed]

C. Wang, Y. Y. Gao, P. Reinhold, R. W. Heeres, N. Ofek, K. Chou, C. Axline, M. Reagor, J. Blumoff, K. M. Sliwa, L. Frunzio, S. M. Girvin, L. Jiang, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “A Schrödinger cat living in two boxes,” Science 352, 1087–1091 (2016).
[Crossref] [PubMed]

C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, “Crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators,” Phys. Rev. A 93, 042307 (2016).
[Crossref]

F. Yan, S. Gustavsson, A. Kamal, J. Birenbaum, A. P Sears, D. Hover, T. J. Gudmundsen, D. Rosenberg, G. Samach, S Weber, J. L. Yoder, T. P. Orlando, J. Clarke, A. J. Kerman, and W. D. Oliver, “The flux qubit revisited to enhance coherence and reproducibility,” Nature Commun. 7, 12964 (2016).
[Crossref]

M. Oszmaniec, A. Grudka, M. Horodecki, and A. Wójcik, “Creating a superposition of unknown quantum states,” Phys. Rev. Lett. 116, 110403 (2016).
[Crossref] [PubMed]

R. Sharma and F. W. Strauch, “Quantum state synthesis of superconducting resonators,” Phys. Rev. A 93, 012342 (2016).
[Crossref]

Y. J. Zhao, C. Q. Wang, X. B. Zhu, and Y. X. Liu, “Engineering entangled microwave photon states through multiphoton interactions between two cavity fields and a superconducting qubit,” Sci. Rep. 6, 23646 (2016).
[Crossref] [PubMed]

X. M. Hu, M. J. Hu, J. S. Chen, B. H. Liu, Y. F. Huang, C. F. Li, G. C. Guo, and Y. S. Zhang, “Experimental creation of superposition of unknown photonic quantum states,” Phys. Rev. A 94, 033844 (2016).
[Crossref]

2015 (3)

Y. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano, “The forbidden quantum adder,” Sci. Rep. 5, 11983 (2015).
[Crossref] [PubMed]

S. J. Xiong, Z. Sun, J. M. Liu, T. Liu, and C. P. Yang, “Efficient scheme for generation of photonic NOON states in circuit QED,” Opt. Lett. 40, 2221–2224 (2015).
[Crossref] [PubMed]

M. J. Peterer, S. J. Bader, X. Jin, F. Yan, A. Kamal, T. J. Gudmundsen, P. J. Leek, T. P. Orlando, W. D. Oliver, and S. Gustavsson, “Coherence and decay of higher energy levels of a superconducting transmon qubit,” Phys. Rev. Lett. 114, 010501 (2015).
[Crossref] [PubMed]

2014 (1)

T. Baumgratz, M. Cramer, and M. B. Plenio, “Quantifying coherence,” Phys. Rev. Lett. 113, 140401 (2014).
[Crossref] [PubMed]

2013 (6)

M. H. Devoret and R. J. Schoelkopf, “Superconducting circuits for quantum information: An outlook,” Science 339, 1169–1174 (2013).
[Crossref] [PubMed]

B. Vlastakis, G. Kirchmair, Z. Leghtas, S. E. Nigg, L. Frunzio, S. M. Girvin, M. Mirrahimi, M. H. Devoret, and R. J. Schoelkopf, “Deterministically encoding quantum information using 100-photon Schrödinger cat states,” Science 342, 607–610 (2013).
[Crossref] [PubMed]

Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
[Crossref]

R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O’Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, and J. M. Martinis, “Coherent josephson qubit suitable for scalable quantum integrated circuits,” Phys. Rev. Lett. 111, 080502 (2013).
[Crossref] [PubMed]

J. D. Strand, M. Ware, F. Beaudoin, T. A. Ohki, B. R. Johnson, A. Blais, and B. L. T. Plourde, “First-order sideband transitions with flux-driven asymmetric transmon qubits,” Phys. Rev. B 87, 220505 (2013).
[Crossref]

Z. L. Wang, Y. P. Zhong, L. J. He, H. Wang, J. M. Martinis, A. N. Cleland, and Q. W. Xie, “Quantum state characterization of a fast tunable superconducting resonator,” Appl. Phys. Lett. 102, 163503 (2013).
[Crossref]

2012 (2)

C. P. Yang, Q. P. Su, and S. Han, “Generation of Greenberger-Horne-Zeilinger entangled states of photons in multiple cavities via a superconducting qutrit or an atom through resonant interaction,” Phys. Rev. A 86, 022329 (2012).
[Crossref]

C. Rigetti, J. M. Gambetta, S. Poletto, B. L. T. Plourde, J. M. Chow, A. D. Córcoles, J. A. Smolin, S. T. Merkel, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, “Superconducting qubit in a waveguide cavity with a coherence time approaching 0.1 ms,” Phys. Rev. B 86, 100506 (2012).
[Crossref]

2011 (5)

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
[Crossref]

J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
[Crossref] [PubMed]

H. Paik, D. I. Schuster, L. S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf, “Observation of high coherence in Josephson junction qubits measured in a three-dimensional circuit QED architecture,” Phys. Rev. Lett. 107, 240501 (2011).
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H. Wang, M. Mariantoni, R. C. Bialczak, M. Lenander, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, T. Yamamoto, Y. Yin, J. Zhao, J. M. Martinis, and A. N. Cleland, “Deterministic entanglement of photons in two superconducting microwave resonators,” Phys. Rev. Lett. 106, 060401 (2011).
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X. Zhu, S. Saito, A. Kemp, K. Kakuyanagi, S. Karimoto, H. Nakano, W. J. Munro, Y. Tokura, M. S. Everitt, K. Nemoto, M. Kasu, N. Mizuochi, and K. Semba, “Coherent coupling of a superconducting flux qubit to an electron spin ensemble in diamond,” Nature 478, 221–224 (2011).
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2010 (4)

M. D. Reed, L. DiCarlo, B. R. Johnson, L. Sun, D. I. Schuster, L. Frunzio, and R. J. Schoelkopf, “High-fidelity readout in circuit quantum electrodynamics using the Jaynes-Cummings nonlinearity,” Phys. Rev. Lett. 105, 173601 (2010).
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S. B. Zheng, C. P. Yang, and F. Nori, “Arbitrary control of coherent dynamics for distant qubits in a quantum network,” Phys. Rev. A 82, 042327 (2010).
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F. W. Strauch, K. Jacobs, and R. W. Simmonds, “Arbitrary control of entanglement between two superconducting resonators,” Phys. Rev. Lett. 105, 050501 (2010).
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2009 (2)

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
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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 (2009).
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2008 (3)

M. Neeley, M. Ansmann, R. C. Bialczak, M. Hofheinz, N. Katz, E. Lucero, A. O’Connell, H. Wang, A. N. Cleland, and J. M. Martinis, “Process tomography of quantum memory in a Josephson-phase qubit coupled to a two-level state,” Nat. Physics 4, 523–526 (2008).
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2007 (3)

J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf, “Charge-insensitive qubit design derived from the Cooper pair box,” Phys. Rev. A 76, 042319 (2007).
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2005 (1)

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 745 (2002).
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1999 (1)

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Rev. 41, 303–332 (1999).
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Beaudoin, F.

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Bianchetti, R.

Birenbaum, J.

Birnbaum, K. M.

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Bishop, L. S.

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Blumoff, J. Z.

Boca, A.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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Boozer, A. D.

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Cao, X. Z.

T. Liu, X. Z. Cao, Q. P. Su, S. J. Xiong, and C. P. Yang, “Multi-target-qubit unconventional geometric phase gate in a multi-cavity system,” Sci. Rep. 6, 21562 (2016).
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Catelani, G.

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Chiaro, B.

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F. Souris, H. Christiani, and J. P. Davis, “Tuning a 3D microwave cavity via superfluid helium at millikelvin temperatures,” Appl. Phys. Lett. 111, 172601 (2017).
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Clarke, J.

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Davis, J. P.

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Delsing, P.

Deng, F. G.

H. Zhang, A. Alsaedi, T. Hayat, and F. G. Deng, “Entanglement concentration and purification of two-mode squeezed microwave photons in circuit QED,” Ann. Phys. 391, 112–119 (2018).
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Deppe, F.

Devoret, M. H.

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Göppl, M.

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M. Oszmaniec, A. Grudka, M. Horodecki, and A. Wójcik, “Creating a superposition of unknown quantum states,” Phys. Rev. Lett. 116, 110403 (2016).
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Hayat, T.

H. Zhang, A. Alsaedi, T. Hayat, and F. G. Deng, “Entanglement concentration and purification of two-mode squeezed microwave photons in circuit QED,” Ann. Phys. 391, 112–119 (2018).
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Heeres, R.

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R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
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Horodecki, M.

M. Oszmaniec, A. Grudka, M. Horodecki, and A. Wójcik, “Creating a superposition of unknown quantum states,” Phys. Rev. Lett. 116, 110403 (2016).
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R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
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R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81, 865 (2009).
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Hover, D.

Hu, E. L.

Hu, M. J.

Hu, X. M.

Huang, Y. F.

Imamoglu, A.

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F. W. Strauch, K. Jacobs, and R. W. Simmonds, “Arbitrary control of entanglement between two superconducting resonators,” Phys. Rev. Lett. 105, 050501 (2010).
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James, D. F.

D. F. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
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Jeffrey, E.

Jerke, J.

D. F. James and J. Jerke, “Effective Hamiltonian theory and its applications in quantum information,” Can. J. Phys. 85, 625–632 (2007).
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Jin, X.

Johansson, G.

Johnson, B. R.

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M. Doosti, F. Kianvash, and V. Karimipour, “Universal superposition of orthogonal states,” Phys. Rev. A 96, 052318 (2017).
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Karimoto, S.

Kasu, M.

Katiyar, H.

K. Li, G. Long, H. Katiyar, T. Xin, G. Feng, D. Lu, and R. Laflamme, “Experimentally superposing two pure states with partial prior knowledge,” Phys. Rev. A 95, 022334 (2017).
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Katz, N.

Keefe, G. A.

Kelly, J.

Kemp, A.

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M. Doosti, F. Kianvash, and V. Karimipour, “Universal superposition of orthogonal states,” Phys. Rev. A 96, 052318 (2017).
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Kimble, H. J.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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Kirchmair, G.

Koch, J.

Kockum, A. F.

X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
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Laflamme, R.

K. Li, G. Long, H. Katiyar, T. Xin, G. Feng, D. Lu, and R. Laflamme, “Experimentally superposing two pure states with partial prior knowledge,” Phys. Rev. A 95, 022334 (2017).
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Lamata, L.

Y. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano, “The forbidden quantum adder,” Sci. Rep. 5, 11983 (2015).
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Leghtas, Z.

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Li, C. F.

Li, K.

K. Li, G. Long, H. Katiyar, T. Xin, G. Feng, D. Lu, and R. Laflamme, “Experimentally superposing two pure states with partial prior knowledge,” Phys. Rev. A 95, 022334 (2017).
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Liu, B. H.

Liu, J. M.

Q. P. Su, H. H. Zhu, L. Yu, Y. Zhang, S. J. Xiong, J. M. Liu, and C. P. Yang, “Generating double NOON states of photons in circuit QED,” Phys. Rev. A 95, 022339 (2017).
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S. J. Xiong, Z. Sun, J. M. Liu, T. Liu, and C. P. Yang, “Efficient scheme for generation of photonic NOON states in circuit QED,” Opt. Lett. 40, 2221–2224 (2015).
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Liu, T.

T. Liu, X. Z. Cao, Q. P. Su, S. J. Xiong, and C. P. Yang, “Multi-target-qubit unconventional geometric phase gate in a multi-cavity system,” Sci. Rep. 6, 21562 (2016).
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S. J. Xiong, Z. Sun, J. M. Liu, T. Liu, and C. P. Yang, “Efficient scheme for generation of photonic NOON states in circuit QED,” Opt. Lett. 40, 2221–2224 (2015).
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Liu, Y.

Liu, Y. X.

X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
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Lloyd, S.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
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K. Li, G. Long, H. Katiyar, T. Xin, G. Feng, D. Lu, and R. Laflamme, “Experimentally superposing two pure states with partial prior knowledge,” Phys. Rev. A 95, 022334 (2017).
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Lu, D.

K. Li, G. Long, H. Katiyar, T. Xin, G. Feng, D. Lu, and R. Laflamme, “Experimentally superposing two pure states with partial prior knowledge,” Phys. Rev. A 95, 022334 (2017).
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Lucero, E.

Maccone, L.

V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photonics 5, 222–229 (2011).
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Majer, J.

Mariantoni, M.

Martinis, J. M.

Marx, A.

Maurer, P.

Megrant, A.

Merkel, S. T.

S. T. Merkel and F. K. Wilhelm, “Generation and detection of NOON states in superconducting circuits,” New J. Phys. 12, 093036 (2010).
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Miller, R.

K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
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Mirrahimi, M.

Mizuochi, N.

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Neeley, M.

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Nemoto, K.

Nigg, S. E.

Nori, F.

X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, “Microwave photonics with superconducting quantum circuits,” Phys. Rep. 718, 1–102 (2017).
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C. P. Yang, Q. P. Su, S. B. Zheng, F. Nori, and S. Han, “Entangling two oscillators with arbitrary asymmetric initial states,” Phys. Rev. A 95, 052341 (2017).
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C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, “Entangling superconducting qubits in a multi-cavity system,” New J. Phys. 18, 013025 (2016).
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C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, “Crosstalk-insensitive method for simultaneously coupling multiple pairs of resonators,” Phys. Rev. A 93, 042307 (2016).
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Z. L. Xiang, S. Ashhab, J. Q. You, and F. Nori, “Hybrid quantum circuits: Superconducting circuits interacting with other quantum systems,” Rev. Mod. Phys. 85, 623 (2013).
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J. Q. You and F. Nori, “Atomic physics and quantum optics using superconducting circuits,” Nature 474, 589–597 (2011).
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K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature 436, 87–90 (2005).
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G. Gatti, D. Barberena, M. Sanz, and E. Solano, “Protected state transfer via an approximate quantum adder,” Sci. Rep. 7, 6964 (2017).
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Y. Alvarez-Rodriguez, M. Sanz, L. Lamata, and E. Solano, “The forbidden quantum adder,” Sci. Rep. 5, 11983 (2015).
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M. H. Devoret and R. J. Schoelkopf, “Superconducting circuits for quantum information: An outlook,” Science 339, 1169–1174 (2013).
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P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM Rev. 41, 303–332 (1999).
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Simmonds, R. W.

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G. Gatti, D. Barberena, M. Sanz, and E. Solano, “Protected state transfer via an approximate quantum adder,” Sci. Rep. 7, 6964 (2017).
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F. Souris, H. Christiani, and J. P. Davis, “Tuning a 3D microwave cavity via superfluid helium at millikelvin temperatures,” Appl. Phys. Lett. 111, 172601 (2017).
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Strauch, F. W.

R. Sharma and F. W. Strauch, “Quantum state synthesis of superconducting resonators,” Phys. Rev. A 93, 012342 (2016).
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F. W. Strauch, K. Jacobs, and R. W. Simmonds, “Arbitrary control of entanglement between two superconducting resonators,” Phys. Rev. Lett. 105, 050501 (2010).
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Q. P. Su, H. H. Zhu, L. Yu, Y. Zhang, S. J. Xiong, J. M. Liu, and C. P. Yang, “Generating double NOON states of photons in circuit QED,” Phys. Rev. A 95, 022339 (2017).
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C. P. Yang, Q. P. Su, S. B. Zheng, F. Nori, and S. Han, “Entangling two oscillators with arbitrary asymmetric initial states,” Phys. Rev. A 95, 052341 (2017).
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C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, “Entangling superconducting qubits in a multi-cavity system,” New J. Phys. 18, 013025 (2016).
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T. Liu, X. Z. Cao, Q. P. Su, S. J. Xiong, and C. P. Yang, “Multi-target-qubit unconventional geometric phase gate in a multi-cavity system,” Sci. Rep. 6, 21562 (2016).
[Crossref] [PubMed]

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Winger, M.

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