1. Quantum Information Research Center, Shangrao Normal University, Shangrao 334001, China 2. Key Laboratory of Quantum Information, University of Science and Technology of China, Heifei 230026, China 3. School of Physics, Nanjing University, Nanjing 210093, China
We propose a method for transferring quantum entangled states of two photonic cat-state qubits (cqubits) from two microwave cavities to the other two microwave cavities. This proposal is realized by using four microwave cavities coupled to a superconducting flux qutrit. Because of using four cavities with different frequencies, the inter-cavity crosstalk is significantly reduced. Since only one coupler qutrit is used, the circuit resource is minimized. The entanglement transfer is completed with a singlestep operation only, thus this proposal is quite simple. The third energy level of the coupler qutrit is not populated during the state transfer, therefore decoherence from the higher energy level is greatly suppressed. Our numerical simulations show that high-fidelity transfer of two-cqubits entangled states from two transmission line resonators to the other two transmission line resonators is feasible with current circuit QED technology. This proposal is universal and can be applied to accomplish the same task in a wide range of physical systems, such as four microwave or optical cavities, which are coupled to a natural or artificial three-level atom.
C. P. Yang, S. I. Chu, and S. Han, Possible realization of entanglement, logical gates, and quantum information transfer with superconducting-quantuminterferencedevice qubits in cavity QED, Phys. Rev. A 67(4), 042311 (2003) https://doi.org/10.1103/PhysRevA.67.042311
2
J. Q. You and F. Nori, Quantum information processing with superconducting qubits in a microwave field, Phys. Rev. B 68(6), 064509 (2003) https://doi.org/10.1103/PhysRevB.68.064509
3
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(6), 062320 (2004) https://doi.org/10.1103/PhysRevA.69.062320
4
J. Q. You and F. Nori, Superconducting circuits and quantum information, Phys. Today 58(11), 42 (2005) https://doi.org/10.1063/1.2155757
J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474(7353), 589 (2011) https://doi.org/10.1038/nature10122
7
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(2), 623 (2013) https://doi.org/10.1103/RevModPhys.85.623
8
X. Gu, A. F. Kockum, A. Miranowicz, Y. X. Liu, and F. Nori, Microwave photonics with superconducting quantum circuits, Phys. Rep. 718–719, 1 (2017) https://doi.org/10.1016/j.physrep.2017.10.002
9
P. B. Li, Y. C. Liu, S. Y. Gao, Z. L. Xiang, P. Rabl, Y. F. Xiao, and F. L. Li, Hybrid quantum device based on NV centers in diamond nanomechanical resonators plus superconducting waveguide cavities, Phys. Rev. Appl. 4(4), 044003 (2015) https://doi.org/10.1103/PhysRevApplied.4.044003
10
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(11), 117902 (2004) https://doi.org/10.1103/PhysRevLett.92.117902
11
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(7005), 162 (2004) https://doi.org/10.1038/nature02851
12
T. Niemczyk, F. Deppe, H. Huebl, E. P. Menzel, F. Hocke, M. J. Schwarz, J. J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, and R. Gross, Circuit quantum electrodynamics in the ultrastrong coupling regime, Nat. Phys. 6(10), 772 (2010) https://doi.org/10.1038/nphys1730
13
Q. Q. Wu, J. Q. Liao, and L. M. Kuang, Quantum state transfer between charge and flux qubits in circuit-QED, Chin. Phys. Lett. 25(4), 1179 (2008) https://doi.org/10.1088/0256-307X/25/4/005
C. P. Yang, Q. P. Su, and F. Nori, Entanglement generation and quantum information transfer between spatially-separated qubits in different cavities, New J. Phys. 15(11), 115003 (2013) https://doi.org/10.1088/1367-2630/15/11/115003
16
C. P. Yang and S. Han, n-qubit-controlled phase gate with superconducting quantum interference devices coupled to a resonator, Phys. Rev. A 72(3), 032311 (2005) https://doi.org/10.1103/PhysRevA.72.032311
17
C. P. Yang, Y. X. Liu, and F. Nori, Phase gate of one qubit simultaneously controlling nqubits in a cavity, Phys. Rev. A 81(6), 062323 (2010) https://doi.org/10.1103/PhysRevA.81.062323
18
C. P. Yang, Q. P. Su, F. Y. Zhang, and S. B. Zheng, Single-step implementation of a multiple target-qubit controlled phase gate without need of classical pulses, Opt. Lett. 39(11), 3312 (2014) https://doi.org/10.1364/OL.39.003312
19
H. F. Wang, A. D. Zhu, and S. Zhang, One-step implementation of a multiqubit phase gate with one control qubit and multiple target qubits in coupled cavities, Opt. Lett. 39(6), 1489 (2014) https://doi.org/10.1364/OL.39.001489
20
Z. P. Hong, B. J. Liu, J. Q. Cai, X. D. Zhang, Y. Hu, Z. D. Wang, and Z. Y. Xue, Implementing universal nonadiabatic holonomic quantum gates with transmons, Phys. Rev. A 97(2), 022332 (2018) https://doi.org/10.1103/PhysRevA.97.022332
21
B. Ye, Z. F. Zheng, and C. P. Yang, Multiplex-controlled phase gate with qubits distributed in a multicavity system, Phys. Rev. A 97(6), 062336 (2018) https://doi.org/10.1103/PhysRevA.97.062336
22
S. L. Zhu, Z. D. Wang, and P. Zanardi, Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity, Phys. Rev. Lett. 94(10), 100502 (2005) https://doi.org/10.1103/PhysRevLett.94.100502
23
X. L. Zhang, K. L. Gao, and M. Feng, Preparation of cluster states and W states with superconducting quantuminterference-device qubits in cavity QED, Phys. Rev. A 74(2), 024303 (2006) https://doi.org/10.1103/PhysRevA.74.024303
24
Z. J. Deng, K. L. Gao, and M. Feng, Generation of Nqubit W states with rf SQUID qubits by adiabatic passage, Phys. Rev. A 74(6), 064303 (2006) https://doi.org/10.1103/PhysRevA.74.064303
25
F. Helmer, and F. Marquardt, Measurement-based synthesis of multiqubit entangled states in superconducting cavity QED, Phys. Rev. A 79(5), 052328 (2009) https://doi.org/10.1103/PhysRevA.79.052328
26
S. Aldana, Y. D. Wang, and C. Bruder, Greenberger- Horne-Zeilinger generation protocol for N superconducting transmon qubits capacitively coupled to a quantum bus, Phys. Rev. B 84(13), 134519 (2011) https://doi.org/10.1103/PhysRevB.84.134519
27
C. P. Yang, Q. P. Su, S. B. Zheng, and F. Nori, Entangling superconducting qubits in a multi-cavity system, New J. Phys. 18(1), 013025 (2016) https://doi.org/10.1088/1367-2630/18/1/013025
28
X. T. Mo, and Z. Y. Xue, Single-step multipartite entangled states generation from coupled circuit cavities, Front. Phys. 14(3), 31602 (2019) https://doi.org/10.1007/s11467-019-0888-1
29
Y. Xu, W. Cai, Y. Ma, X. Mu, L. Hu, T. Chen, H. Wang, Y. P. Song, Z. Y. Xue, Z. Q. Yin, and L. Sun, Single-loop realization of arbitrary non-adiabatic holonomic singlequbit quantum gates in a superconducting circuit, Phys. Rev. Lett. 121(11), 110501 (2018) https://doi.org/10.1103/PhysRevLett.121.110501
30
T. Wang, Z. Zhang, L. Xiang, Z. Jia, P. Duan, W. Cai, Z. Gong, Z. Zong, M. Wu, J. Wu, L. Sun, Y. Yin, and G. Guo, The experimental realization of high-fidelity “shortcut-to-adiabaticity” quantum gates in a superconducting Xmon qubit, arXiv: 1804.08247 (2018) https://doi.org/10.1088/1367-2630/aac9e7
31
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) https://doi.org/10.1103/PhysRevB.79.180511
32
J. M. Chow, A. D. Córcoles, J. M. Gambetta, C. Rigetti, B. R. Johnson, J. A. Smolin, J. R. Rozen, G. A. Keefe, M. B. Rothwell, M. B. Ketchen, and M. Steffen, Simple All-microwave entangling gate for fixed-frequency superconducting qubits, Phys. Rev. Lett. 107(8), 080502 (2011) https://doi.org/10.1103/PhysRevLett.107.080502
33
M. Mariantoni, H. Wang, T. Yamamoto, M. Neeley, R. C. Bialczak, Y. Chen, M. Lenander, E. Lucero, A. D. O’Connell, D. Sank, M. Weides, J. Wenner, Y. Yin, J. Zhao, A. N. Korotkov, A. N. Cleland, and J. M. Martinis, Implementing the quantum von neumann architecture with superconducting circuits, Science 334(6052), 61 (2011) https://doi.org/10.1126/science.1208517
34
A. Fedorov, L. Steffen, M. Baur, M. P. daSilva, and A. Wallraff, Implementation of a Toffoli gate with superconducting circuits, Nature 481(7380), 170 (2012) https://doi.org/10.1038/nature10713
35
C. Song, K. Xu, W. Liu, C. Yang, S. B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y. A. Chen, C. Y. Lu, S. Han, and J .W. Pan, 10-qubit entanglement and parallel logic operations with a superconducting circuit, Phys. Rev. Lett. 119(18), 180511 (2017) https://doi.org/10.1103/PhysRevLett.119.180511
36
M. Gong, M. C. Chen, Y. Zheng, S. Wang, C. Zha, H. Deng, Z. Yan, H. Rong, Y. Wu, S. Li, F. Chen, Y. Zhao, F. Liang, J. Lin, Y. Xu, C. Guo, L. Sun, A. D. Castellano, H. Wang, C. Peng, C.Y. Lu, X. Zhu, and J. W. Pan, Genuine12-qubit entanglement on a superconducting quantum processor, Phys. Rev. Lett. 122(11), 110501 (2019) https://doi.org/10.1103/PhysRevLett.122.110501
37
C. Song, K. Xu, H. Li, Y. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, H. Feng, H. Fan, D. Zheng, D. Wang, H. Wang, and S. Zhu, Observation of multi-component atomic Schrodinger cat states of up to 20 qubits, Science 365(6453), 574 (2019) https://doi.org/10.1126/science.aay0600
38
L. Steffen, Y. Salathe, M. Oppliger, P. Kurpiers, M. Baur, C. Lang, C. Eichler, G. Puebla-Hellmann, A. Fedorov, and A. Wallraff, Deterministic quantum teleportation with feed-forward in a solid state system., Nature 500(7462), 319 (2013) https://doi.org/10.1038/nature12422
39
X. Li, Y. Ma, J. Han, T. Chen, Y. Xu, W. Cai, H. Wang, Y. P. Song, Z. Y. Xue, Z. Q. Yin, and L. Sun, Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings, Phys. Rev. Appl. 10(5), 054009 (2018) https://doi.org/10.1103/PhysRevApplied.10.054009
40
W. Ning, X. J. Huang, P. R. Han, H. Li, H. Deng, Z. B. Yang, Z. R. Zhong, Y. Xia, K. Xu, D. Zheng, and S. B. Zheng, Deterministic entanglement swapping in a superconducting circuit, arXiv: 1902.10959 (2019) https://doi.org/10.1103/PhysRevLett.123.060502
41
Z. Yan, Y. R. Zhang, M. Gong, Y. Wu, Y. Zheng, S. Li, C. Wang, F. Liang, J. Lin, Y. Xu, C. Guo, L. Sun, C. Z. Peng, K. Xia, H. Deng, H. Rong, J. Q. You, F. Nori, H. Fan, X. Zhu, and J. W. Pan, Strongly correlated quantum walks with a 12-qubit superconducting processor, Science 364(6442), 753 (2019) https://doi.org/10.1126/science.aaw1611
42
W. Chen, D. A. Bennett, V. Patel, and J. E. Lukens, Substrate and process dependent losses in superconducting thin film resonators, Supercond. Sci. Technol. 21(7), 075013 (2008) https://doi.org/10.1088/0953-2048/21/7/075013
43
P. J. Leek, M. Baur, J. M. Fink, R. Bianchetti, L. Steffen, S. Filipp, and A. Wallraff, Cavity quantum electrodynamics with separate photon storage and qubit readout modes, Phys. Rev. Lett. 104(10), 100504 (2010) https://doi.org/10.1103/PhysRevLett.104.100504
44
M. Reagor, W. Pfaff, C. Axline, R. W. Heeres, N. Ofek, K. Sliwa, E. Holland, C. Wang, J. Blumoff, K. Chou, M. J. Hatridge, L. Frunzio, M. H. Devoret, L. Jiang, and R. J. Schoelkopf, A quantum memory with near-millisecond coherence in circuit QED,Phys. Rev. B 94(1), 014506 (2016) https://doi.org/10.1103/PhysRevB.94.014506
45
M. H. Devoret and R. J. Schoelkopf, Superconducting circuits for quantum information: An outlook, Science 339(6124), 1169 (2013) https://doi.org/10.1126/science.1231930
46
M. Mariantoni, M. J. Storcz, F. K. Wilhelm, W. D. Oliver, A. Emmert, A. Marx, R. Gross, H. Christ, and E. Solano, On-chip microwave Fock states and quantum homodyne measurements, arXiv: cond-mat/0509737 (2005)
47
Y. X. Liu, L. F. Wei, and F. Nori, Generation of nonclassical photon states using a superconducting qubit in a microcavity, Europhys. Lett. 67(6), 941 (2004) https://doi.org/10.1209/epl/i2004-10144-3
48
K. Moon and S. M. Girvin, Theory of microwave parametric down-conversion and squeezing using circuit QED, Phys. Rev. Lett. 95(14), 140504 (2005) https://doi.org/10.1103/PhysRevLett.95.140504
49
F. Marquardt and C. Bruder, Superposition of two mesoscopically distinct quantum states: Coupling a Cooperpair box to a large superconducting island, Phys. Rev. B 63(5), 054514 (2001) https://doi.org/10.1103/PhysRevB.63.054514
50
Y. X. Liu, L. F. Wei, and F. Nori, Preparation of macroscopic quantum superposition states of a cavity field via coupling to a superconducting charge qubit, Phys. Rev. A 71(6), 063820 (2005) https://doi.org/10.1103/PhysRevA.71.063820
51
J. Q. Liao, J. F. Huang, and L. Tian, Generation of macroscopic Schrödinger-cat states in qubit-oscillator systems, Phys. Rev. A (Coll. Park) 93(3), 033853 (2016) https://doi.org/10.1103/PhysRevA.93.033853
52
X. Y. Lö, G. L. Zhu, L. L. Zheng, and Y. Wu, Entanglement and quantum superposition induced by a single photon, Phys. Rev. A (Coll. Park) 97(3), 033807 (2018) https://doi.org/10.1103/PhysRevA.97.033807
53
F. W. Strauch, K. Jacobs, and R. W. Simmonds, Arbitrary control of entanglement between two superconducting resonators, Phys. Rev. Lett. 105(5), 050501 (2010) https://doi.org/10.1103/PhysRevLett.105.050501
54
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(2), 022329 (2012) https://doi.org/10.1103/PhysRevA.86.022329
55
P. B. Li, S. Y. Gao, and F. L. Li, Engineering two-mode entangled states between two superconducting resonators by dissipation, Phys. Rev. A 86(1), 012318 (2012) https://doi.org/10.1103/PhysRevA.86.012318
56
C. P. Yang, Q. P. Su, S. B. Zheng, and S. Han, Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit, Phys. Rev. A 87(2), 022320 (2013) https://doi.org/10.1103/PhysRevA.87.022320
57
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(2), 022339 (2017) https://doi.org/10.1103/PhysRevA.95.022339
58
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(5), 052341 (2017) https://doi.org/10.1103/PhysRevA.95.052341
59
S. T. Merkel and F. K. Wilhelm, Generation and detection of NOON states in superconducting circuits, New J. Phys. 12(9), 093036 (2010) https://doi.org/10.1088/1367-2630/12/9/093036
60
Y. J. Zhao, C. Q. Wang, X. Zhu, and Y. X. Liu, Engineering entangled microwave photon states via multiphoton transitions between two cavities and a superconducting qubit, arXiv: 1506.06363 (2015)
61
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(10), 2221 (2015) https://doi.org/10.1364/OL.40.002221
62
M. Hua, M. J. Tao, and F. G. Deng, Universal quantum gates on microwave photons assisted by circuit quantum electrodynamics, Phys. Rev. A 90(1), 012328 (2014) https://doi.org/10.1103/PhysRevA.90.012328
63
M. Hua, M. J. Tao, and F. G. Deng, Fast universal quantum gates on microwave photons with all-resonance operations in circuit QED, Sci. Rep. 5(1), 9274 (2015) https://doi.org/10.1038/srep09274
64
B. Ye, Z. F. Zheng, Y. Zhang, C. P. Yang, and Q. E. D. Circuit, single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling n−1 microwave photonic qubits, Opt. Express 26(23), 30689 (2018) https://doi.org/10.1364/OE.26.030689
65
M. Hofheinz, H. Wang, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, J. M. Martinis, and A. N. Cleland, Synthesizing arbitrary quantum states in a superconducting resonator, Nature 459(7246), 546 (2009) https://doi.org/10.1038/nature08005
66
M. Hofheinz, E. M. Weig, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, H. Wang, J. M. Martinis, and A. N. Cleland, Generation of Fock states in a superconducting quantum circuit, Nature 454(7202), 310 (2008) https://doi.org/10.1038/nature07136
67
H. Wang, M. Hofheinz, M. Ansmann, R. C. Bialczak, E. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, A. N. Cleland, and J. M. Martinis, Measurement of the decay of Fock states in a superconducting quantum circuit, Phys. Rev. Lett. 101(24), 240401 (2008) https://doi.org/10.1103/PhysRevLett.101.240401
68
Y. Xu, W. Cai, Y. Ma, X. Mu, W. Dai, W. Wang, L. Hu, X. Li, J. Han, H. Wang, Y. Song, Z. B. Yang, S. B. Zheng, and L. Sun, Geometrically manipulating photonic Schrödinger cat states and realizing cavity phase gates, arXiv: 1810.04690 (2018)
69
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(6), 060401 (2011) https://doi.org/10.1103/PhysRevLett.106.060401
70
M. Mariantoni, H. Wang, 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, Photon shell game in threeresonator circuit quantum electrodynamics, Nat. Phys. 7(4), 287 (2011) https://doi.org/10.1038/nphys1885
71
L. Hu, Y. Ma, W. Cai, X. Mu, Y. Xu, W. Wang, Y. Wu, H. Wang, Y. P. Song, C. L. Zou, S. M. Girvin, L. M. Duan, and L. Sun, Quantum error correction and universal gate set operation on a binomial bosonic logical qubit., Nat. Phys. 15(5), 503 (2019) https://doi.org/10.1038/s41567-018-0414-3
72
R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a universal gate set on a logical qubit encoded in an oscillator, Nat. Commun. 8(1), 94 (2017) https://doi.org/10.1038/s41467-017-00045-1
73
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(7617), 441 (2016) https://doi.org/10.1038/nature18949
74
C. P. Yang and Z. F. Zheng, Deterministic generation of Greenberger-Horne-Zeilinger entangled states of cat-state qubits in circuit QED, Opt. Lett. 43(20), 5126 (2018) https://doi.org/10.1364/OL.43.005126
75
M. Mirrahimi, Z. Leghtas, V. V. Albert, S. Touzard, R. J. Schoelkopf, L. Jiang, and M. H. Devoret, Dynamically protected cat-qubits: A new paradigm for universal quantum computation, New J. Phys. 16(4), 045014 (2014) https://doi.org/10.1088/1367-2630/16/4/045014
Y. Zhang, X. Zhao, Z. F. Zheng, L. Yu, Q. P. Su, and C. P. Yang, Universal controlled-phase gate with cat-state qubits in circuit QED, Phys. Rev. A 96(5), 052317 (2017) https://doi.org/10.1103/PhysRevA.96.052317
78
Y. J. Fan, Z. F. Zheng, Y. Zhang, D. M. Lu, and C. P. Yang, One-step implementation of a multi-target-qubit controlled phase gate with cat-state qubits in circuit QED, Front. Phys. 14(2), 21602 (2019) https://doi.org/10.1007/s11467-018-0875-y
79
R. W. Heeres, P. Reinhold, N. Ofek, L. Frunzio, L. Jiang, M. H. Devoret, and R. J. Schoelkopf, Implementing a universal gate set on a logical qubit encoded in an oscillator, Nat. Commun. 8(1), 94 (2017) https://doi.org/10.1038/s41467-017-00045-1
80
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 Schrodinger cat living in two boxes, Science 352(6289), 1087 (2016) https://doi.org/10.1126/science.aaf2941
81
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(18), 180511 (2009) https://doi.org/10.1103/PhysRevB.79.180511
82
M. Sandberg, C. M. Wilson, F. Persson, T. Bauch, G. Johansson, V. Shumeiko, T. Duty, and P. Delsing, Tuning the field in a microwave resonator faster than the photon lifetime, Appl. Phys. Lett. 92(20), 203501 (2008) https://doi.org/10.1063/1.2929367
83
D. F. V. James and J. Jerke, Effective Hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007) https://doi.org/10.1139/p07-060
M. Steffen, S. Kumar, D. P. DiVincenzo, J. R. Rozen, G. A. Keefe, M. B. Rothwell, and M. B. Ketchen, Highcoherence hybrid superconducting qubit, Phys. Rev. Lett. 105(10), 100502 (2010) https://doi.org/10.1103/PhysRevLett.105.100502
86
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, Nat. Commun. 7(1), 12964 (2016) https://doi.org/10.1038/ncomms12964
87
M. Baur, S. Filipp, R. Bianchetti, J. M. Fink, M. Göppl, L. Steffen, P. J. Leek, A. Blais, and A. Wallraff, Measurement of Autler-Townes and Mollow transitions in a strongly driven superconducting qubit, Phys. Rev. Lett. 102(24), 243602 (2009) https://doi.org/10.1103/PhysRevLett.102.243602
88
F. Yoshihara, Y. Nakamura, F. Yan, S. Gustavsson, J. Bylander, W. D. Oliver, and J. S. Tsai, Flux qubit noise spectroscopy using Rabi oscillations under strong driving conditions, Phys. Rev. B 89(2), 020503 (2014) https://doi.org/10.1103/PhysRevB.89.020503
