Efficient scheme for realizing a multiplex-controlled phase gate with photonic qubits in circuit quantum electrodynamics

Qi-Ping Su, Yu Zhang, Liang Bin, Chui-Ping Yang

PDF(2086 KB)
PDF(2086 KB)
Front. Phys. ›› 2022, Vol. 17 ›› Issue (5) : 53505. DOI: 10.1007/s11467-022-1163-4
RESEARCH ARTICLE

Efficient scheme for realizing a multiplex-controlled phase gate with photonic qubits in circuit quantum electrodynamics

Author information +
History +

Abstract

We propose an efficient scheme to implement a multiplex-controlled phase gate with multiple photonic qubits simultaneously controlling one target photonic qubit based on circuit quantum electrodynamics (QED). For convenience, we denote this multiqubit gate as MCP gate. The gate is realized by using a two-level coupler to couple multiple cavities. The coupler here is a superconducting qubit. This scheme is simple because the gate implementation requires only one step of operation. In addition, this scheme is quite general because the two logic states of each photonic qubit can be encoded with a vacuum state and an arbitrary non-vacuum state |φ> (e.g., a Fock state, a superposition of Fock states, a cat state, or a coherent state, etc.) which is orthogonal or quasi-orthogonal to the vacuum state. The scheme has some additional advantages: because only two levels of the coupler are used, i.e., no auxiliary levels are utilized, decoherence from higher energy levels of the coupler is avoided; the gate operation time does not depend on the number of qubits; and the gate is implemented deterministically because no measurement is applied. As an example, we numerically analyze the circuit-QED based experimental feasibility of implementing a three-qubit MCP gate with photonic qubits each encoded via a vacuum state and a cat state. The scheme can be applied to accomplish the same task in a wide range of physical system, which consists of multiple microwave or optical cavities coupled to a two-level coupler such as a natural or artificial atom.

Graphical abstract

Keywords

multiplex controlled / phase gate / circuit QED

Cite this article

Download citation ▾
Qi-Ping Su, Yu Zhang, Liang Bin, Chui-Ping Yang. Efficient scheme for realizing a multiplex-controlled phase gate with photonic qubits in circuit quantum electrodynamics. Front. Phys., 2022, 17(5): 53505 https://doi.org/10.1007/s11467-022-1163-4

References

[1]
P. W. Shor , in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser, IEEE Computer Society, Los Alamitos, CA, 1994, page 124
[2]
L. K. Grover , Quantum computers can search rapidly by using almost any transformation, Phys. Rev. Lett. 80 (19), 4329 (1998)
CrossRef ADS Google scholar
[3]
T. Beth and M. Röteler , in: Quantum Information, Springer, Berlin, 2001 Vol. 173, Chap. 4, p. 96
[4]
P. W. Shor , Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52 (4), R2493 (1995)
CrossRef ADS Google scholar
[5]
A. M. Steane , Error correcting codes in quantum theory, Phys. Rev. Lett. 77 (5), 793 (1996)
CrossRef ADS Google scholar
[6]
F. Gaitan , in: Quantum Error Correction and Fault Tolerant Quantum Computing, CRC Press, Boca Raton, FL, 2008, pp 1 312
[7]
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 (5), 052313 (2001)
CrossRef ADS Google scholar
[8]
M. Šašura and V. Bužek , Multiparticle entanglement with quantum logic networks: Application to cold trapped ions, Phys. Rev. A 64 (1), 012305 (2001)
CrossRef ADS Google scholar
[9]
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 (5), 3457 (1995)
CrossRef ADS Google scholar
[10]
N. Khaneja and S. J. Glaser , Cartan decomposition of SU(2n) and control of spin systems, Chem. Phys. 267 (1-3), 11 (2001)
CrossRef ADS Google scholar
[11]
M. Möttönen , J. J. Vartiainen , V. Bergholm , and M. M. Salomaa , Quantum circuits for general multiqubit gates, Phys. Rev. Lett. 93 (13), 130502 (2004)
CrossRef ADS Google scholar
[12]
Y. Liu , G. L. Long , and Y. Sun , Analytic one-bit and CNOT gate constructions of general n-qubit controlled gates, Int. J. Quant. Inf. 6 (3), 447 (2008)
CrossRef ADS Google scholar
[13]
M. A. Nielsen and I. L. Chuang , Quantum Computation and Quantum Information, Cambridge University Press, Cam bridge, England, 2001
[14]
X. Wang , A. Sørensen , and K. Mølmer , Multibit gates for quantum computing, Phys. Rev. Lett. 86 (17), 3907 (2001)
CrossRef ADS Google scholar
[15]
T. Monz , K. Kim , W. Hänsel , M. Riebe , A. S. Villar , P. Schindler , M. Chwalla , M. Hennrich , and R. Blatt , Realization of the quantum Toffoli gate with trapped ions, Phys. Rev. Lett. 102 (4), 040501 (2009)
CrossRef ADS Google scholar
[16]
P. Z. Zhao , G. F. Xu , and D. M. Tong , Nonadiabatic holonomic multiqubit controlled gates, Phys. Rev. A 99 (5), 052309 (2019)
CrossRef ADS Google scholar
[17]
H. R. Wei and F. G. Deng , Universal quantum gates for hybrid systems assisted by quantum dots inside doublesided optical microcavities, Phys. Rev. A 87 (2), 022305 (2013)
CrossRef ADS Google scholar
[18]
L. M. Duan , B. Wang , and H. J. Kimble , Robust quantum gates on neutral atoms with cavity-assisted photonscattering, Phys. Rev. A 72 (3), 032333 (2005)
CrossRef ADS Google scholar
[19]
X. Zou , Y. Dong , and G. C. Guo , Implementing a conditional z gate by a combination of resonant interaction and quantum interference, Phys. Rev. A 74 (3), 032325 (2006)
CrossRef ADS Google scholar
[20]
M. Waseem , M. Irfan , and S. Qamar , Realization of quantum gates with multiple control qubits or multiple target qubits in a cavity, Quantum Inform. Process. 14 (6), 1869 (2015)
CrossRef ADS Google scholar
[21]
Y. Liang , Q. C. Wu , S. L. Su , X. Ji , and S. Zhang , Shortcuts to adiabatic passage for multiqubit controlled-phase gate, Phys. Rev. A 91 (3), 032304 (2015)
CrossRef ADS Google scholar
[22]
S. L. Su , H. Z. Shen , E. Liang , and S. Zhang , One-step construction of the multiple-qubit Rydberg controlled-PHASE gate, Phys. Rev. A 98 (3), 032306 (2018)
CrossRef ADS Google scholar
[23]
Y. Hao , G. Lin , Y. Niu , and S. Gong , One-step implementation of a multiqubit controlled phase-flip gate in coupled cavities, Quantum Inform. Process. 18 (1), 18 (2019)
CrossRef ADS Google scholar
[24]
T. H. Xing , X. Wu , and G. F. Xu , Nonadiabatic holonomic three-qubit controlled gates realized by one-shot implementation, Phys. Rev. A 101 (1), 012306 (2020)
CrossRef ADS Google scholar
[25]
M. Khazali and K. Mølmer , Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits, Phys. Rev. X 10 (2), 021054 (2020)
CrossRef ADS Google scholar
[26]
W. L. Yang , Z. Q. Yin , Z. Y. Xu , M. Feng , and J. F. Du , One step implementation of multi-qubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity, Appl. Phys. Lett. 96 (24), 241113 (2010)
CrossRef ADS Google scholar
[27]
T. Wang and Y. Zhang , Scalable multi-qubit quantum gates in quantum networks based on the microtoroidalresonator mediated nitrogen-vacancy centers in diamond, J. Opt. Soc. Am. B 37 (5), 1372 (2020)
CrossRef ADS Google scholar
[28]
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)
CrossRef ADS Google scholar
[29]
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 (3), 032317 (2006)
CrossRef ADS Google scholar
[30]
W. A. Li and Y. Chen , Simplified proposal for realizing a multiqubit tunable phase gate in circuit QED, J. Opt. Soc. Am. B 34 (7), 1560 (2017)
CrossRef ADS Google scholar
[31]
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)
CrossRef ADS Google scholar
[32]
J. Zhang , W. Liu , Z. Deng , Z. Lu , and G. L. Long , Modularization of a multi-qubit controlled phase gate and its nuclear magnetic resonance implementation, J. Opt. B 7 (1), 22 (2005)
CrossRef ADS Google scholar
[33]
A. Fedorov , L. Steffen , M. Baur , M. P. da Silva , and A. Wallraff , Implementation of a Toffoli gate with superconducting circuits, Nature 481 (7380), 170 (2012)
CrossRef ADS Google scholar
[34]
C. Song , S. B. Zheng , P. Zhang , K. Xu , L. Zhang , Q. Guo , W. Liu , D. Xu , H. Deng , K. Huang , D. Zheng , X. Zhu , and H. Wang , Continuous-variable geometric phase and its manipulation for quantum computation in a superconducting circuit, Nat. Commun. 8 (1), 1061 (2017)
CrossRef ADS Google scholar
[35]
H. Levine , A. Keesling , G. Semeghini , A. Omran , T. T. Wang , S. Ebadi , H. Bernien , M. Greiner , V. Vuletić , H. Pichler , and M. D. Lukin , Parallel implementation of highfidelity multiqubit gates with neutral atoms, Phys. Rev. Lett. 123 (17), 170503 (2019)
CrossRef ADS Google scholar
[36]
J. Fiurášek , Linear-optics quantum Toffoli and Fredkin gates, Phys. Rev. A 73 (6), 062313 (2006)
CrossRef ADS Google scholar
[37]
T. C. Ralph , K. J. Resch , and A. Gilchrist , Effcient Toffoli gates using qudits, Phys. Rev. A 75 (2), 022313 (2007)
CrossRef ADS Google scholar
[38]
H. L. Huang , W. S. Bao , T. Li , F. G. Li , X. Q. Fu , S. Zhang , H. L. Zhang , and X. Wang , Deterministic linear optical quantum Toffoli gate, Phys. Lett. A 381 (33), 2673 (2017)
CrossRef ADS Google scholar
[39]
L. Dong , S. L. Wang , C. Cui , X. Geng , Q. Y. Li , H. K. Dong , X. M. Xiu , and Y. J. Gao , Polarization Toffoli gate assisted by multiple degrees of freedom, Opt. Lett. 43 (19), 4635 (2018)
CrossRef ADS Google scholar
[40]
X. Zou , K. Li , and G. Guo , Linear optical scheme for direct implementation of a nondestructive N-qubit controlled phase gate, Phys. Rev. A 74 (4), 044305 (2006)
CrossRef ADS Google scholar
[41]
H. R. Wei and G. L. Long , Universal photonic quantum gates assisted by ancilla diamond nitrogen-vacancy centers coupled to resonators, Phys. Rev. A 91 (3), 032324 (2015)
CrossRef ADS Google scholar
[42]
H. R. Wei , F. G. Deng , and G. L. Long , Hyper-parallel Toffoli gate on three-photon system with two degrees of freedom assisted by single-sided optical microcavities, Opt. Express 24 (16), 18619 (2016)
CrossRef ADS Google scholar
[43]
B. Y. Xia , C. Cao , Y. H. Han , and R. Zhang , Universal photonic three-qubit quantum gates with two degrees of freedom assisted by charged quantum dots inside singlesided optical microcavities, Laser Phys. 28 (9), 095201 (2018)
CrossRef ADS Google scholar
[44]
M. Mičuda , M. Sedlák , I. Straka , M. Miková , M. Dušek , M. Ježek , and J. Fiurášek , Effcient experimental estimation of fidelity of linear optical quantum Toffoli gate, Phys. Rev. Lett. 111 (16), 160407 (2013)
CrossRef ADS Google scholar
[45]
S. Ru , Y. Wang , M. An , F. Wang , P. Zhang , and F. Li , Realization of deterministic quantum Toffoli gate with a single photon, Phys. Rev. A 103 (2), 022606 (2021)
CrossRef ADS Google scholar
[46]
P. M. Lu , J. Song , and Y. Xia , Implementing a multi-qubit quantum phase gate encoded by photonic qubit, Chin. Phys. Lett. 27 (3), 030302 (2010)
CrossRef ADS Google scholar
[47]
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)
CrossRef ADS Google scholar
[48]
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)
CrossRef ADS Google scholar
[49]
J. X. Han , J. L. Wu , Y. Wang , Y. Y. Jiang , Y. Xian , and J. Song , Multi-qubit phase gate on multiple resonators mediated by a superconducting bus, Opt. Express 28 (2), 1954 (2020)
CrossRef ADS Google scholar
[50]
C. P. Yang , S. I. Chu , and S. Han , Possible realization of entanglement, logical gates and quantum information transfer with superconducting-quantum-interferencedevice qubits in cavity QED, Phys. Rev. A 67 (4), 042311 (2003)
CrossRef ADS Google scholar
[51]
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
[52]
A. Blais , R. S. Huang , A. Wallraff , S. M. Girvin , and R. J. Schoelkopf , Cavity quantum electrodynamics for superconduct ing electrical circuits: An architecture for quantum computation, Phys. Rev. A 69 (6), 062320 (2004)
CrossRef ADS Google scholar
[53]
J. Q. You and F. Nori , Superconducting circuits and quantum information, Phys. Today 58 (11), 42 (2005)
CrossRef ADS Google scholar
[54]
J. Q. You and F. Nori , Atomic physics and quantum optics using superconducting circuits, Nature 474 (7353), 589 (2011)
CrossRef ADS Google scholar
[55]
I. Buluta , S. Ashhab , and F. Nori , Natural and artificial atoms for quantum computation, Rep. Prog. Phys. 74 (10), 104401 (2011)
CrossRef ADS Google scholar
[56]
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)
CrossRef ADS Google scholar
[57]
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
[58]
Q. P. Su , H. Zhang , and C. P. Yang , Transferring quantum entangled states between multiple single-photon-state qubits and coherent-state qubits in circuit QED, Front. Phys. 16 (6), 61501 (2021)
CrossRef ADS Google scholar
[59]
M. H. Devoret and R. J. Schoelkopf , Superconducting circuits for quantum information: An outlook, Science 339 (6124), 1169 (2013)
CrossRef ADS Google scholar
[60]
C. H. Bai , D. Y. Wang , S. Hu , W. X. Cui , X. X. Jiang , and H. F. Wang , Scheme for implementing multitarget qubit controlled-NOT gate of photons and controlled-phase gate of electron spins via quantum dot-microcavity coupled system, Quantum Inform. Process. 15 (4), 1485 (2016)
CrossRef ADS Google scholar
[61]
B. Ye , Z. F. Zheng , Y. Zhang , and C. P. Yang , QED 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)
CrossRef ADS Google scholar
[62]
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 (6), 062323 (2010)
CrossRef ADS Google scholar
[63]
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 (6), 062326 (2010)
CrossRef ADS Google scholar
[64]
M. Waseem , M. Irfan , and S. Qamar , Multiqubit quantum phase gate using four-level superconducting quantum interference devices coupled to superconducting resonator, Physica C 477, 24 (2012)
CrossRef ADS Google scholar
[65]
C. P. Yang , Q. P. Su , F. Y. Zhang , and S. B. Zheng , Single-step implementation of a multipletarget-qubit controlled phase gate without need of classical pulses, Opt. Lett. 39 (11), 3312 (2014)
CrossRef ADS Google scholar
[66]
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)
CrossRef ADS Google scholar
[67]
T. Liu , X. Z. Cao , Q. P. Su , S. J. Xiong , and C. P. Yang , Multi-target-qubit unconventional geometric phase gate in a multicavity system, Sci. Rep. 6 (1), 21562 (2016)
CrossRef ADS Google scholar
[68]
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)
CrossRef ADS Google scholar
[69]
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)
CrossRef ADS Google scholar
[70]
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 (8), 080502 (2013)
CrossRef ADS Google scholar
[71]
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. Phys. 4 (7), 523 (2008)
CrossRef ADS Google scholar
[72]
A. Sørensen and K. Mølmer , Quantum Computation with Ions in Thermal Motion, Phys. Rev. Lett. 82 (9), 1971 (1999)
CrossRef ADS Google scholar
[73]
D. F. V. 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. P. 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]
Z. Leghtas , G. Kirchmair , B. Vlastakis , R. J. Schoelkopf , M. H. Devoret , and M. Mirrahimi , Hardware-effcient autonomous quantum memory protection, Phys. Rev. Lett. 111 (12), 120501 (2013)
CrossRef ADS Google scholar
[78]
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)
CrossRef ADS Google scholar
[79]
J. Guillaud and M. Mirrahimi , Repetition cat qubits for fault-tolerant quantum computation, Phys. Rev. X 9 (4), 041053 (2019)
CrossRef ADS Google scholar
[80]
C. Chamberland , K. Noh , P. Arrangoiz-Arriola , E. T. Campbell , C. T. Hann , J. Iverson , H. Putterman , T. C. Bohdanowicz , S. T. Flammia , A. Keller , et al. , Building a fault-tolerant quantum computer using concatenated cat codes, PRX Quantum 3, 010329 (2022)
CrossRef ADS Google scholar
[81]
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
[82]
A. O. Niskanen , K. Harrabi , F. Yoshihara , Y. Nakamura , S. Lloyd , and J. S. Tsai , Quantum coherent tunable coupling of superconducting qubits, Science 316 (5825), 723 (2007)
CrossRef ADS Google scholar
[83]
K. Inomata , T. Yamamoto , P. M. Billangeon , Y. Nakamura , and J. S. Tsai , Large dispersive shift of cavity resonance induced by a superconducting flux qubit in the straddling regime, Phys. Rev. B 86 (14), 140508 (2012)
CrossRef ADS Google scholar
[84]
Z. H. Peng , Y. X. Liu , J. T. Peltonen , T. Yamamoto , J. S. Tsai , and O. Astafiev , Correlated emission lasing in harmonic oscillators coupled via a single three-level artificial atom, Phys. Rev. Lett. 115 (22), 223603 (2015)
CrossRef ADS Google scholar
[85]
Y. X. Liu , J. Q. You , L. F. Wei , C. P. Sun , and F. Nori , Optical selection rules and phase dependent adiabatic state control in a superconducting quantum circuit, Phys. Rev. Lett. 95 (8), 087001 (2005)
CrossRef ADS Google scholar
[86]
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
[87]
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)
CrossRef ADS Google scholar
[88]
J. Q. You , X. Hu , S. Ashhab , and F. Nori , Lowdecoherence flux qubit, Phys. Rev. B 75 (14), 140515 (2007)
CrossRef ADS Google scholar
[89]
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
[90]
G. Calusine , A. Melville , W. Woods , R. Das , C. Stull , V. Bolkhovsky , D. Braje , D. Hover , D. K. Kim , X. Miloshi , D. Rosenberg , A. Sevi , J. L. Yoder , E. Dauler , and W. D. Oliver , Analysis and mitigation of interface losses in trenched superconducting coplanar waveguide resonators, Appl. Phys. Lett. 112 (6), 062601 (2018)
CrossRef ADS Google scholar
[91]
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

RIGHTS & PERMISSIONS

2022 Higher Education Press
AI Summary AI Mindmap
PDF(2086 KB)

Accesses

Citations

Detail

Sections
Recommended

/