Transfer of quantum entangled states between superconducting qubits and microwave field qubits
Tong Liu, Bao-Qing Guo, Yan-Hui Zhou, Jun-Long Zhao, Yu-Liang Fang, Qi-Cheng Wu, Chui-Ping Yang
Transfer of quantum entangled states between superconducting qubits and microwave field qubits
Transferring entangled states between matter qubits and microwave-field (or optical-field) qubits is of fundamental interest in quantum mechanics and necessary in hybrid quantum information processing and quantum communication. We here propose a way for transferring entangled states between superconducting qubits (matter qubits) and microwave-field qubits. This proposal is realized by a system consisting of multiple superconducting qutrits and microwave cavities. Here, „qutrit” refers to a three-level quantum system with the two lowest levels encoding a qubit while the third level acting as an auxiliary state. In contrast, the microwave-field qubits are encoded with coherent states of microwave cavities. Because the third energy level of each qutrit is not populated during the operation, decoherence from the higher energy levels is greatly suppressed. The entangled states can be deterministically transferred because measurement on the states is not needed. The operation time is independent of the number of superconducting qubits or microwave-field qubits. In addition, the architecture of the circuit system is quite simple because only a coupler qutrit and an auxiliary cavity are required. As an example, our numerical simulations show that high-fidelity transfer of entangled states from two superconducting qubits to two microwave-field qubits is feasible with present circuit QED technology. This proposal is quite general and can be extended to transfer entangled states between other matter qubits (e.g., atoms, quantum dots, and NV centers) and microwave- or optical-field qubits encoded with coherent states.
tranferring entangled states / superconducting qubits / microwave field qubits / coherent states / circuit QED
[1] |
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(4), 042311 (2003)
CrossRef
ADS
Google scholar
|
[2] |
J. Q. You and F. Nori, Quantum information processing with superconducting qubits in a microwave field, Phys. Rev. B 68(6), 064509 (2003)
CrossRef
ADS
Google scholar
|
[3] |
A. Blais, R. S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf, Cavity quantum electrodynamics for super-conducting electrical circuits: An architecture for quantum computation, Phys. Rev. A 69(6), 062320 (2004)
CrossRef
ADS
Google scholar
|
[4] |
J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474(7353), 589 (2011)
CrossRef
ADS
Google scholar
|
[5] |
S. Schmidt and J. Koch, Circuit QED lattices: Towards quantum simulation with superconducting circuits, Ann. Phys. 525(6), 395 (2013)
CrossRef
ADS
Google scholar
|
[6] |
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)
CrossRef
ADS
Google scholar
|
[7] |
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)
CrossRef
ADS
Google scholar
|
[8] |
F. Yoshihara, T. Fuse, S. Ashhab, K. Kakuyanagi, S. Saito, and K. Semba, Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime, Nat. Phys. 13(1), 44 (2017)
CrossRef
ADS
Google scholar
|
[9] |
Y. H. Lin, L. B. Nguyen, N. Grabon, J. S. Miguel, N. Pankratova, and V. E. Manucharyan, Demonstration of protection of a superconducting qubit from energy decay, Phys. Rev. Lett. 120, 150503 (2018)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[11] |
Z. Kis and E. Paspalakis, Arbitrary rotation and entanglement of flux SQUID qubits, Phys. Rev. B 69(2), 024510 (2004)
CrossRef
ADS
Google scholar
|
[12] |
F. W. Strauch and C. J. Williams, Theoretical analysis of perfect quantum state transfer with superconducting qubits, Phys. Rev. B 78(9), 094516 (2008)
CrossRef
ADS
Google scholar
|
[13] |
C. P. Yang, Quantum information transfer with superconducting flux qubits coupled to a resonator, Phys. Rev. A 82(5), 054303 (2010)
CrossRef
ADS
Google scholar
|
[14] |
F. Mei, G. Chen, L. Tian, S. L. Zhu, and S. Jia, Robust quantum state transfer via topological edge states in superconducting qubit chains, Phys. Rev. A 98(1), 012331 (2018)
CrossRef
ADS
Google scholar
|
[15] |
M. A. Sillanpää, J. I. Park, and R. W. Simmonds, Coherent quantum state storage and transfer between two phase qubits via a resonant cavity, Nature 449(7161), 438 (2007)
CrossRef
ADS
Google scholar
|
[16] |
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)
CrossRef
ADS
Google scholar
|
[17] |
C. P. Yang and S. Han, Preparation of Greenberger–Horne–Zeilinger entangled states with multiple superconducting quantum-interference device qubits or atoms in cavity QED, Phys. Rev. A 70(6), 062323 (2004)
CrossRef
ADS
Google scholar
|
[18] |
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)
CrossRef
ADS
Google scholar
|
[19] |
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(5), 052310 (2005)
CrossRef
ADS
Google scholar
|
[20] |
T. Tanamoto, Y. Liu, S. Fujita, X. Hu, and F. Nori, Producing cluster states in charge qubits and flux qubits, Phys. Rev. Lett. 97(23), 230501 (2006)
CrossRef
ADS
Google scholar
|
[21] |
X. L. Zhang, K. L. Gao, and M. Feng, Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED, Phys. Rev. A 74(2), 024303 (2006)
CrossRef
ADS
Google scholar
|
[22] |
J. Q. You, X. Wang, T. Tanamoto, and F. Nori, Efficient one-step generation of large cluster states with solid-state circuits, Phys. Rev. A 75(5), 052319 (2007)
CrossRef
ADS
Google scholar
|
[23] |
Y. D. Wang, S. Chesi, D. Loss, and C. Bruder, One-step multiqubit Greenberger–Horne–Zeilinger state generation in a circuit QED system, Phys. Rev. B 81(10), 104524 (2010)
CrossRef
ADS
Google scholar
|
[24] |
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(6), 062302 (2011)
CrossRef
ADS
Google scholar
|
[25] |
W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, Generating and stabilizing the Greenberger–Horne–Zeilinger state in circuit QED: Joint measurement, Zeno effect, and feedback, Phys. Rev. A 83(4), 042313 (2011)
CrossRef
ADS
Google scholar
|
[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)
CrossRef
ADS
Google scholar
|
[27] |
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(1), 32004 (2016)
CrossRef
ADS
Google scholar
|
[28] |
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)
CrossRef
ADS
Google scholar
|
[29] |
Y. H. Kang, Y. H. Chen, Z. C. Shi, J. Song, and Y. Xia, Fast preparation of W states with superconducting quantum interference devices by using dressed states, Phys. Rev. A 94(5), 052311 (2016)
|
[30] |
X. T. Mo and Z. Y. Xue, Single-step multipartite entangled states generation from coupled circuit cavities, Front. Phys. 14(3), 31602 (2019)
CrossRef
ADS
Google scholar
|
[31] |
T. Liu, Q. P. Su, Y. Zhang, Y. L. Fang, and C. P. Yang, Generation of quantum entangled states of multiple groups of qubits distributed in multiple cavities, Phys. Rev. A 101(1), 012337 (2020)
CrossRef
ADS
Google scholar
|
[32] |
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)
CrossRef
ADS
Google scholar
|
[33] |
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, Genuine 12-qubit entanglement on a superconducting quantum processor, Phys. Rev. Lett. 122(11), 110501 (2019)
CrossRef
ADS
Google scholar
|
[34] |
C. Song, K. Xu, H. Li, Y. R. Zhang, X. Zhang, W. Liu, Q. Guo, Z. Wang, W. Ren, J. Hao, H. Feng, H. Fan, D. Zheng, D. W. Wang, H. Wang, and S. Y. Zhu, Generation of multicomponent atomic Schrödinger cat states of up to 20 qubits, Science 365(6453), 574 (2019)
CrossRef
ADS
Google scholar
|
[35] |
A. Romanenko, R. Pilipenko, S. Zorzetti, D. Frolov, M. Awida, S. Belomestnykh, S. Posen, and A. Grassellino, Three-dimensional superconducting resonators at T < 20 mK with photon lifetimes up to τ = 2 s, Phys. Rev. Appl. 13(3), 034032 (2020)
CrossRef
ADS
Google scholar
|
[36] |
M. Mariantoni, F. Deppe, A. Marx, R. Gross, F. K. Wilhelm, and E. Solano, Two-resonator circuit quantum electrodynamics: A superconducting quantum switch, Phys. Rev. B 78(10), 104508 (2008)
CrossRef
ADS
Google scholar
|
[37] |
S. T. Merkel and F. K. Wilhelm, Generation and detection of NOON states in superconducting circuits, New J. Phys. 12(9), 093036 (2010)
CrossRef
ADS
Google scholar
|
[38] |
F. W. Strauch, K. Jacobs, and R. W. Simmonds, Arbitrary control of entanglement between two superconducting resonators, Phys. Rev. Lett. 105(5), 050501 (2010)
CrossRef
ADS
Google scholar
|
[39] |
Y. Hu and L. Tian, Deterministic generation of entangled photons in superconducting resonator arrays, Phys. Rev. Lett. 106(25), 257002 (2011)
CrossRef
ADS
Google scholar
|
[40] |
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)
CrossRef
ADS
Google scholar
|
[41] |
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)
CrossRef
ADS
Google scholar
|
[42] |
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)
CrossRef
ADS
Google scholar
|
[43] |
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)
CrossRef
ADS
Google scholar
|
[44] |
R. Sharma and F. W. Strauch, Quantum state synthesis of superconducting resonators, Phys. Rev. A 93(1), 012342 (2016)
CrossRef
ADS
Google scholar
|
[45] |
Z. Li, S. Ma, Z. P. Yang, A. P. Fang, P. Li, S. Y. Gao, and F. L. Li, Generation and replication of continuousvariable quadripartite cluster and Greenberger–Horne–Zeilinger states in four chains of superconducting transmission line resonators, Phys. Rev. A 93(4), 042305 (2016)
CrossRef
ADS
Google scholar
|
[46] |
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(1), 23646 (2016)
CrossRef
ADS
Google scholar
|
[47] |
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)
CrossRef
ADS
Google scholar
|
[48] |
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)
CrossRef
ADS
Google scholar
|
[49] |
M. Li, M. Hua, M. Zhang, and F. G. Deng, Entangling two high-Q microwave resonators assisted by a resonator terminated with SQUIDs, New J. Phys. 21(7), 073025 (2019)
CrossRef
ADS
Google scholar
|
[50] |
T. Liu, Y. Zhang, B. Q. Guo, C. S. Yu, and W. N. Zhang, Creation of superposition of arbitrary states encoded in two high-Q cavities, Opt. Express 27(19), 27168 (2019)
CrossRef
ADS
Google scholar
|
[51] |
Y. Zhang, T. Liu, J. Zhao, Y. Yu, and C. P. Yang, Generation of hybrid Greenberger–Horne–Zeilinger entangled states of particlelike and wavelike optical qubits in circuit QED, Phys. Rev. A 101(6), 062334 (2020)
CrossRef
ADS
Google scholar
|
[52] |
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)
CrossRef
ADS
Google scholar
|
[53] |
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 Schröinger cat states, Science 342(6158), 607 (2013)
CrossRef
ADS
Google scholar
|
[54] |
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(6289), 1087 (2016)
CrossRef
ADS
Google scholar
|
[55] |
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)
CrossRef
ADS
Google scholar
|
[56] |
A. Karlsson and M. Bourennane, Quantum teleportation using three-particle entanglement, Phys. Rev. A 58(6), 4394 (1998)
CrossRef
ADS
Google scholar
|
[57] |
D. P. DiVincenzo and P. W. Shor, Fault-tolerant error correction with efficient quantum codes, Phys. Rev. Lett. 77(15), 3260 (1996)
CrossRef
ADS
Google scholar
|
[58] |
V. Giovannetti, S. Lloyd, and L. Maccone, Quantumenhanced measurements: Beating the standard quantum limit, Science 306(5700), 1330 (2004)
CrossRef
ADS
Google scholar
|
[59] |
X. Wang, Quantum teleportation of entangled coherent states, Phys. Rev. A 64(2), 022302 (2001)
CrossRef
ADS
Google scholar
|
[60] |
H. Jeong and M. S. Kim, Efficient quantum computation using coherent states, Phys. Rev. A 65(4), 042305 (2002)
CrossRef
ADS
Google scholar
|
[61] |
J. Joo, W. J. Munro, and T. P. Spiller, Quantum metrology with entangled coherent states, Phys. Rev. Lett. 107(8), 083601 (2011)
CrossRef
ADS
Google scholar
|
[62] |
P. T. Cochrane, G. J. Milburn, and W. J. Munro, Macroscopically distinct quantumsuperposition states as a bosonic code for amplitude damping, Phys. Rev. A 59(4), 2631 (1999)
CrossRef
ADS
Google scholar
|
[63] |
Q. C. Wu, Y. H. Zhou, B. L. Ye, T. Liu, and C. P. Yang, Nonadiabatic quantum state engineering by time-dependent decoherence-free subspaces in open quantum systems, New J. Phys. 23(11), 113005 (2021)
CrossRef
ADS
Google scholar
|
[64] |
H. Jeong and N. B. An, Greenberger–Horne–Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting, Phys. Rev. A 74(2), 022104 (2006)
CrossRef
ADS
Google scholar
|
[65] |
A. Blais, S. M. Girvin, and W. D. Oliver, Quantum information processing and quantum optics with circuit quantum electrodynamics, Nat. Phys. 16(3), 247 (2020)
CrossRef
ADS
Google scholar
|
[66] |
W. Cai, Y. Ma, W. Wang, C. L. Zou, and L. Sun, Bosonic quantum error correction codes in superconducting quantum circuits, Fundamental Research 1(1), 50 (2021)
CrossRef
ADS
Google scholar
|
[67] |
D. Gottesman, A. Kitaev, and J. Preskill, Encoding a qubit in an oscillator, Phys. Rev. A 64(1), 012310 (2001)
CrossRef
ADS
Google scholar
|
[68] |
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)
CrossRef
ADS
Google scholar
|
[69] |
M. H. Michael, M. Silveri, R. T. Brierley, V. V. Albert, J. Salmilehto, L. Jiang, and S. M. Girvin, New class of quantum error-correcting codes for a bosonic mode, Phys. Rev. X 6(3), 031006 (2016)
CrossRef
ADS
Google scholar
|
[70] |
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)
CrossRef
ADS
Google scholar
|
[71] |
A. Sørensen and K. Mølmer, Quantum computation with ions in thermal motion, Phys. Rev. Lett. 82(9), 1971 (1999)
CrossRef
ADS
Google scholar
|
[72] |
S. B. Zheng and G. C. Guo, Efficient scheme for two-atom entanglement and quantum information processing in cavity QED, Phys. Rev. Lett. 85(11), 2392 (2000)
CrossRef
ADS
Google scholar
|
[73] |
D. F. James and J. Jerke, Effective Hamiltonian theory and its applications in quantum information, Can. J. Phys. 85(6), 625 (2007)
CrossRef
ADS
Google scholar
|
[74] |
Y. Xu, Y. Ma, W. Cai, 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, Demonstration of controlled-phase gates between two error-correctable photonic qubits, Phys. Rev. Lett. 124(12), 120501 (2020)
CrossRef
ADS
Google scholar
|
[75] |
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)
CrossRef
ADS
Google scholar
|
[76] |
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(16), 163503 (2013)
CrossRef
ADS
Google scholar
|
[77] |
M. Scully and M. S. Zubairy, Quantum optics, Cambridge University Press, Cambridge, 1997, Chapter 2
CrossRef
ADS
Google scholar
|
[78] |
G. Kirchmair, B. Vlastakis, Z. Leghtas, S. E. Nigg, H. Paik, E. Ginossar, M. Mirrahimi, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf, Observation of quantum state collapse and revival due to the single-photon Kerr effect, Nature 495(7440), 205 (2013)
CrossRef
ADS
Google scholar
|
[79] |
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(4), 042319 (2007)
CrossRef
ADS
Google scholar
|
[80] |
I. C. Hoi, C. M. Wilson, G. Johansson, T. Palomaki, B. Peropadre, and P. Delsing, Demonstration of a singlephoton router in the microwave regime, Phys. Rev. Lett. 107(7), 073601 (2011)
CrossRef
ADS
Google scholar
|
[81] |
M. Fitzpatrick, N. M. Sundaresan, A. C. Y. Li, J. Koch, and A. A. Houck, Observation of a dissipative phase transition in a one-dimensional circuit QED lattice, Phys. Rev. X 7(1), 011016 (2017)
CrossRef
ADS
Google scholar
|
[82] |
T. Liu, Z. F. Zheng, Y. Zhang, Y. L. Fang, and C. P. Yang, Transferring entangled states of photonic cat-state qubits in circuit QED, Front. Phys. 15(2), 21603 (2020)
CrossRef
ADS
Google scholar
|
[83] |
J. B. Chang, M. R. Vissers, A. D. Córcoles, M. Sandberg, J. Gao, D. W. Abraham, J. M. Chow, J. M. Gambetta, M. Beth Rothwell, G. A. Keefe, M. Steffen, and D. P. Pappas, Improved superconducting qubit coherence using titanium nitride, Appl. Phys. Lett. 103(1), 012602 (2013)
CrossRef
ADS
Google scholar
|
[84] |
A. P. M. Place, L. V. H. Rodgers, P. Mundada, B. M. Smitham, M. Fitzpatrick, Z. Leng, A. Premkumar, J. Bryon, S. Sussman, G. Cheng, et al., New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds, arXiv: 2003.00024 (2020)
|
[85] |
A. Megrant, C. Neill, R. Barends, B. Chiaro, Y. Chen, L. Feigl, J. Kelly, E. Lucero, M. Mariantoni, P. J. J. O’Malley, D. Sank, A. Vainsencher, J. Wenner, T. C. White, Y. Yin, J. Zhao, C. J. Palmstrøm, J. M. Martinis, and A. N. Cleland, Planar superconducting resonators with internal quality factors above one million, Appl. Phys. Lett. 100(11), 113510 (2012)
CrossRef
ADS
Google scholar
|
[86] |
P. W. Woods, G. Calusine, A. Melville, A. Sevi, E. Golden, D. K. Kim, D. Rosenberg, J. L. Yoder, and W. D. Oliver, Determining interface dielectric losses in superconducting coplanar waveguide resonators, Phys. Rev. Appl. 12(1), 014012 (2019)
CrossRef
ADS
Google scholar
|
/
〈 | 〉 |