Robust beam splitter with fast quantum state transfer through a topological interface

doi:10.1007/s11467-023-1289-z

Front. Phys.

2023, Vol. 18

Issue (5) : 51303 https://doi.org/10.1007/s11467-023-1289-z

RESEARCH ARTICLE

Robust beam splitter with fast quantum state transfer through a topological interface

Jia-Ning Zhang¹, Jin-Xuan Han², Jin-Lei Wu³(

), Jie Song², Yong-Yuan Jiang^1,^2,^4,^5,⁶(

)

¹. Department of Optoelectronics Science, Harbin Institute of Technology, Weihai 264209, China
². School of Physics, Harbin Institute of Technology, Harbin 150001, China
³. School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China
⁴. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
⁵. Key Laboratory of Micro-Nano Optoelectronic Information System, Ministry of Industry and Information Technology, Harbin 150001, China
⁶. Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin Institute of Technology, Harbin 150001, China

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Abstract

The Su−Schrieffer−Heeger (SSH) model, commonly used for robust state transfers through topologically protected edge pumping, has been generalized and exploited to engineer diverse functional quantum devices. Here, we propose to realize a fast topological beam splitter based on a generalized SSH model by accelerating the quantum state transfer (QST) process essentially limited by adiabatic requirements. The scheme involves delicate orchestration of the instantaneous energy spectrum through exponential modulation of nearest neighbor coupling strengths and onsite energies, yielding a significantly accelerated beam splitting process. Due to properties of topological pumping and accelerated QST, the beam splitter exhibits strong robustness against parameter disorders and losses of system. In addition, the model demonstrates good scalability and can be extended to two-dimensional crossed-chain structures to realize a topological router with variable numbers of output ports. Our work provides practical prospects for fast and robust topological QST in feasible quantum devices in large-scale quantum information processing.

Keywords quantum state transfer beam splitter topological router

Corresponding Author(s): Jin-Lei Wu,Yong-Yuan Jiang

Issue Date: 12 May 2023

Cite this article:

Jia-Ning Zhang,Jin-Xuan Han,Jin-Lei Wu, et al. Robust beam splitter with fast quantum state transfer through a topological interface[J]. Front. Phys. , 2023, 18(5): 51303.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1289-z
https://academic.hep.com.cn/fop/EN/Y2023/V18/I5/51303

Fig.1 Diagrammatic sketch of the generalized SSH model composed of N unit cells. Each unit cell contains a pair of a- (blue dot) and b-type (purple dot) sites with onsite energies

V a

and

V b

. Double lines and single lines denote the intracell coupling strength

J 1

and intercell coupling strength

J 2

between two adjacent sites, respectively.

Fig.2 (a−c) Energy spectrum of SSH lattice in the momentum space for three settings of the coupling strengths (a)

J 1 = 1, J 2 = 0.6

; (b)

J 1 = 1, J 2 = 1

; (c)

J 1 = 0.6, J 2 = 1

. (d−f) Winding of the bulk momentum-space Hamiltonian for the three settings as the wavenumber runs across the Brillouin zone.

Fig.3 (a) Energy spectrum of the SSH lattice with 40 sites with varying intracell coupling

J 1

but fixed intercell coupling

J 2 = 1

J 1 < 1 (J 1 > 1)

corresponds to the nontrivial (trivial) topological phase. (b) Energy spectrum (upper panel) and distribution of the gap state (lower panel) for

J 1 = 0.6

. (c) Energy spectrum (upper panel) and density distribution of one bulk state (lower panel) for

J 1 = 2

. (d−f) Energy spectra and distributions of the zero-energy edge state of the SSH lattice with 41 sites with the same coupling strengths as those in (a)−(c), respectively.

Fig.4 Schematic of SSH model with the size of

L = 2 N + 1

with alternate onsite energies and an interface. Double and single lines denote the intracell and intercell coupling strengths

J 1

and

J 2

between two adjacent sites, respectively. Intracell (intercell) coupling strengths and alternate onsite energies are mirror-symmetric with respect to the interface site.

N

is an even number, so that the topological interface falls on an a-type site.

Fig.5 Waveforms of coupling strengths and alternate onsite energy with (a)

α = 2

, (c)

α = 6

, and (e)

α = 10

. (b, d, f) Instantaneous energy spectrum as a function of time for different exponential parameters in (a), (c) and (e), respectively. The total evolution time is chosen to unity and the size of chain to be 21.

Fig.6 Distribution of the gap state [magenta lines in Fig.5(b), (d), and (f)] with eigenenergy

V a

with different values of (a)

α = 2

, (b)

α = 6

, and (c)

α = 10

. (d) Minimum energy gap between the gap state and the nearest-neighbor bulk states versus values of

α

with fixed chain size

L = 21

Fig.7 (a) Fidelity as a function with respect to the final time of QST for the cosine and exponential protocols. (b−e) Distribution of the gap state during the evolution and the phase distribution of the evolved final state for the cosine protocol in (b) and (c), and for the exponential protocol in (d) and (e), respectively. Other parameters take

L = 21

and

α = 3.2

Fig.8 Fidelity as a function of the transfer time for the exponential protocol with different values of

α

with

L = 21

Fig.9 Fidelity of QST versus varying

α

and

t ∗

for the exponential protocol with (a)

L = 21

, (b)

L = 33

, (c)

L = 45

, and (d)

L = 57

. The green and red solid lines represent 0.9 and 0.99 fidelity contour lines, respectively. (e) Optimal exponential parameters and (f) the corresponding total evolution time needed for 0.99-fidelity as a function of the size of the chain. The scattering dots and the lines represent the numerical and cubic polynomial fitting results, respectively.

Fig.10 Impact of diagonal and off-diagonal disorders with

ω s = 0.4

on the fidelity for (a) cosine and (b) exponential protocols. Each point corresponds to the mean value of fidelity averaged over 100 disorder realizations. Average fidelity as a function of the disorder strength for (c) diagonal and (d) off-diagonal disorders for different protocols. Other parameters take

L = 21

and

α = 3.2

Fig.11 Average fidelity and phase difference of the evolved final state at two-end sites versus disorder strength for asymmetric (a) diagonal and (b) off-diagonal disorders for different protocols. Other parameters take

L = 21

and

α = 3.2

Fig.12 (a) Final fidelity as a function of the loss rate

γ

for the cosine protocol with

t ∗ = 1080 / J 0

and the exponential protocol with

t ∗ = 100 / J 0

and

α = 3.2

under symmetrical losses. (b) Final fidelity and phase difference of the evolved final state at two-end sites versus loss rate

γ

for both protocols under asymmetrical losses.

Fig.13 Phase diagram of the QST in the parameter space

(t ∗, L)

of (a) cosine and (b) exponential protocols. (c) The total phase diagram derived from (a) and (b). (d) The transfer time

t 0.99 ∗

that each protocol takes to reach 0.99 fidelity as a function of the size of the system.

α = 3.2

is used here.

Fig.14 Fidelity as a function of the chain size with fixed loss parameter

γ = 2.5 × 10 − 5 J 0

for both protocols.

α = 3.2

is used here.

Fig.15 Schematic illustration of the crossed-chain structure comprised of four even-sized SSH chains connected to a mutual additional a-type site.

Fig.16 (a) Final fidelity of four-outport router as a function of the transfer time for the cosine and exponential protocols. (b−e) Distribution of the gap state with energy eigenvalue of

V a

during the evolution and amplitude distribution of the evolved final state for the exponential protocol in (b) and (c), and the cosine protocol in (d) and (e), respectively. Other parameters take

L = 4 N + 1 = 41

and

α = 3.2

Fig.17 Using the exponential protocol with

α = 3.2

for the four-outport router, transfer time

t 0.99 ∗

as a function of (a) the size of each constituent chain with

K = 4

and (b) the number of constituent chains with

N = 10

Fig.18 Equivalent circuit of the coupled superconducting resonator system. Circuit elements are used to model the microwave resonator

A n

(

B n

) and the coupler with the additional Josephson junction in a dilution refrigerator (with a temperature

T ∼

mK), which is placed in a magnetic shield. The microwave resonator

A n

(

B n

) is an

L C

circuit composed of a spiral inductor

L a

(

L b

) and a capacitor

C a

(

C b

). The external classical filed can be attained independently via changing the magnetic flux

ϕ

threading on the loop of coupler, which can add the FBL to connect with an AWG by adopting controlled voltage pulses [68, 69].

1	I. Cirac J., Zoller P., J. Kimble H., Mabuchi H.. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett., 1997, 78(16): 3221 https://doi.org/10.1103/PhysRevLett.78.3221
2	N. Matsukevich D., Kuzmich A.. Quantum state transfer between matter and light. Science, 2004, 306(5696): 663 https://doi.org/10.1126/science.1103346
3	Christandl M., Datta N., Ekert A., J. Landahl A.. Perfect state transfer in quantum spin networks. Phys. Rev. Lett., 2004, 92(18): 187902 https://doi.org/10.1103/PhysRevLett.92.187902
4	Banchi L., J. G. Apollaro T., Cuccoli A., Vaia R., Verrucchi P.. Long quantum channels for high-quality entanglement transfer. New J. Phys., 2011, 13(12): 123006 https://doi.org/10.1088/1367-2630/13/12/123006
5	D. Wang Y., A. Clerk A.. Using interference for high fidelity quantum state transfer in optomechanics. Phys. Rev. Lett., 2012, 108(15): 153603 https://doi.org/10.1103/PhysRevLett.108.153603
6	Tan S., W. Bomantara R., Gong J.. High-fidelity and long-distance entangled-state transfer with Floquet topological edge modes. Phys. Rev. A, 2020, 102(2): 022608 https://doi.org/10.1103/PhysRevA.102.022608
7	Ouyang M., D. Awschalom D.. Coherent spin transfer between molecularly bridged quantum dots. Science, 2003, 301(5636): 1074 https://doi.org/10.1126/science.1086963
8	D. Greentree A., H. Cole J., R. Hamilton A., C. L. Hollenberg L.. Coherent electronic transfer in quantum dot systems using adiabatic passage. Phys. Rev. B, 2004, 70(23): 235317 https://doi.org/10.1103/PhysRevB.70.235317
9	Chen B., H. Shen Q., Fan W., Xu Y.. Long-range adiabatic quantum state transfer through a linear array of quantum dots. Sci. China Phys. Mech. Astron., 2012, 55(9): 1635 https://doi.org/10.1007/s11433-012-4841-3
10	He Y., M. He Y., J. Wei Y., Jiang X., Chen K., Y. Lu C., W. Pan J., Schneider C., Kamp M., Höfling S.. Quantum state transfer from a single photon to a distant quantum-dot electron spin. Phys. Rev. Lett., 2017, 119(6): 060501 https://doi.org/10.1103/PhysRevLett.119.060501
11	P. Kandel Y., Qiao H., Fallahi S., C. Gardner G., J. Manfra M., M. Nichol J.. Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain. Nat. Commun., 2021, 12(1): 2156 https://doi.org/10.1038/s41467-021-22416-5
12	Perez-Leija A., Keil R., Kay A., Moya-Cessa H., Nolte S., C. Kwek L., M. Rodríguez-Lara B., Szameit A., N. Christodoulides D.. Coherent quantum transport in photonic lattices. Phys. Rev. A, 2013, 87(1): 012309 https://doi.org/10.1103/PhysRevA.87.012309
13	J. Chapman R., Santandrea M., Huang Z., Corrielli G., Crespi A., H. Yung M., Osellame R., Peruzzo A.. Experimental perfect state transfer of an entangled photonic qubit. Nat. Commun., 2016, 7(1): 11339 https://doi.org/10.1038/ncomms11339
14	Liu W., Wu C., Jia Y., Jia S., Chen G., Chen F.. Observation of edge-to-edge topological transport in a photonic lattice. Phys. Rev. A, 2022, 105(6): L061502 https://doi.org/10.1103/PhysRevA.105.L061502
15	F. Wei L., R. Johansson J., X. Cen L., Ashhab S., Nori F.. Controllable coherent population transfers in superconducting qubits for quantum computing. Phys. Rev. Lett., 2008, 100(11): 113601 https://doi.org/10.1103/PhysRevLett.100.113601
16	Mei F., Chen G., Tian L., L. Zhu S., Jia S.. Robust quantum state transfer via topological edge states in superconducting qubit chains. Phys. Rev. A, 2018, 98(1): 012331 https://doi.org/10.1103/PhysRevA.98.012331
17	Li X., Ma Y., Han J., Chen T., Xu Y., Cai W., Wang H., P. Song Y., Y. Xue Z., Yin Z., Sun L.. Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings. Phys. Rev. Appl., 2018, 10(5): 054009 https://doi.org/10.1103/PhysRevApplied.10.054009
18	M. A. Almeida G., Ciccarello F., J. G. Apollaro T., M. C. Souza A.. Quantum-state transfer in staggered coupled-cavity arrays. Phys. Rev. A, 2016, 93(3): 032310 https://doi.org/10.1103/PhysRevA.93.032310
19	Qin W., Nori F.. Controllable single-photon transport between remote coupled-cavity arrays. Phys. Rev. A, 2016, 93(3): 032337 https://doi.org/10.1103/PhysRevA.93.032337
20	Balachandran V., Gong J.. Adiabatic quantum transport in a spin chain with a moving potential. Phys. Rev. A, 2008, 77(1): 012303 https://doi.org/10.1103/PhysRevA.77.012303
21	Yang S., Bayat A., Bose S.. Spin-state transfer in laterally coupled quantum-dot chains with disorders. Phys. Rev. A, 2010, 82(2): 022336 https://doi.org/10.1103/PhysRevA.82.022336
22	M. Nikolopoulos G.. Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder. Phys. Rev. A, 2013, 87(4): 042311 https://doi.org/10.1103/PhysRevA.87.042311
23	Ashhab S.. Quantum state transfer in a disordered one-dimensional lattice. Phys. Rev. A, 2015, 92(6): 062305 https://doi.org/10.1103/PhysRevA.92.062305
24	Keele C., Kay A.. Combating the effects of disorder in quantum state transfer. Phys. Rev. A, 2022, 105(3): 032612 https://doi.org/10.1103/PhysRevA.105.032612
25	Niu Q., J. Thouless D., S. Wu Y.. Quantized hall conductance as a topological invariant. Phys. Rev. B, 1985, 31(6): 3372 https://doi.org/10.1103/PhysRevB.31.3372
26	E. Moore J.. The birth of topological insulators. Nature, 2010, 464(7286): 194 https://doi.org/10.1038/nature08916
27	L. Qi X., C. Zhang S.. The quantum spin Hall effect and topological insulators. Phys. Today, 2010, 63(1): 33 https://doi.org/10.1063/1.3293411
28	K. Chiu C., C. Y. Teo J., P. Schnyder A., Ryu S.. Classification of topological quantum matter with symmetries. Rev. Mod. Phys., 2016, 88(3): 035005 https://doi.org/10.1103/RevModPhys.88.035005
29	G. Wen X.. Colloquium: Zoo of quantum-topological phases of matter. Rev. Mod. Phys., 2017, 89(4): 041004 https://doi.org/10.1103/RevModPhys.89.041004
30	Z. Hasan M., L. Kane C.. Colloquium: Topological insulators. Rev. Mod. Phys., 2010, 82(4): 3045 https://doi.org/10.1103/RevModPhys.82.3045
31	L. Qi X., C. Zhang S.. Topological insulators and superconductors. Rev. Mod. Phys., 2011, 83(4): 1057 https://doi.org/10.1103/RevModPhys.83.1057
32	Bansil A., Lin H., Das T.. Colloquium: Topological band theory. Rev. Mod. Phys., 2016, 88(2): 021004 https://doi.org/10.1103/RevModPhys.88.021004
33	Ozawa T., M. Price H., Amo A., Goldman N., Hafezi M., Lu L., C. Rechtsman M., Schuster D., Simon J., Zilberberg O., Carusotto I.. Topological photonics. Rev. Mod. Phys., 2019, 91(1): 015006 https://doi.org/10.1103/RevModPhys.91.015006
34	Seo J., Roushan P., Beidenkopf H., S. Hor Y., J. Cava R., Yazdani A.. Transmission of topological surface states through surface barriers. Nature, 2010, 466(7304): 343 https://doi.org/10.1038/nature09189
35	Lang N., P. Büchler H.. Topological networks for quantum communication between distant qubits. npj Quantum Inf., 2017, 3: 47 https://doi.org/10.1038/s41534-017-0047-x
36	Dlaska C., Vermersch B., Zoller P.. Robust quantum state transfer via topologically protected edge channels in dipolar arrays. Quantum Sci. Technol., 2017, 2(1): 015001 https://doi.org/10.1088/2058-9565/2/1/015001
37	A. Lemonde M., Peano V., Rabl P., G. Angelakis D.. Quantum state transfer via acoustic edge states in a 2D optomechanical array. New J. Phys., 2019, 21(11): 113030 https://doi.org/10.1088/1367-2630/ab51f5
38	Cao J., X. Cui W., Yi X., F. Wang H.. Topological phase transition and topological quantum state transfer in periodically modulated circuit-QED lattice. Ann. Phys., 2021, 533(9): 2100120 https://doi.org/10.1002/andp.202100120
39	Y. Cheng L., N. Zheng L., Wu R., F. Wang H., Zhang S.. Change-over switch for quantum states transfer with topological channels in a circuit-QED lattice. Chin. Phys. B, 2022, 31(2): 020305 https://doi.org/10.1088/1674-1056/ac2f2e
40	Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Controllable photonic and phononic topological state transfers in a small optomechanical lattice. Opt. Lett., 2020, 45(7): 2018 https://doi.org/10.1364/OL.388835
41	Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice. Front. Phys., 2021, 16(1): 12503 https://doi.org/10.1007/s11467-020-0983-3
42	Stern A., H. Lindner N.. Topological quantum computation — from basic concepts to first experiments. Science, 2013, 339(6124): 1179 https://doi.org/10.1126/science.1231473
43	D. Sarma S., Freedman M., Nayak C.. Majorana zero modes and topological quantum computation. npj Quantum Inf., 2015, 1: 15001 https://doi.org/10.1038/npjqi.2015.1
44	He M., Sun H., H. Qing L.. Topological insulator: Spintronics and quantum computations. Front. Phys., 2019, 14(4): 43401 https://doi.org/10.1007/s11467-019-0893-4
45	Monkman K., Sirker J.. Operational entanglement of symmetry-protected topological edge states. Phys. Rev. Res., 2020, 2(4): 043191 https://doi.org/10.1103/PhysRevResearch.2.043191
46	Dai T., Ao Y., Bao J., Mao J., Chi Y., Fu Z., You Y., Chen X., Zhai C., Tang B., Yang Y., Li Z., Yuan L., Gao F., Lin X., G. Thompson M., L. O’Brien J., Li Y., Hu X., Gong Q., Wang J.. Topologically protected quantum entanglement emitters. Nat. Photonics, 2022, 16(3): 248 https://doi.org/10.1038/s41566-021-00944-2
47	X. Han J., L. Wu J., Wang Y., Xia Y., Y. Jiang Y., Song J.. Large-scale Greenberger−Horne−Zeilinger states through a topologically protected zero-energy mode in a superconducting qutrit-resonator chain. Phys. Rev. A, 2021, 103(3): 032402 https://doi.org/10.1103/PhysRevA.103.032402
48	X. Han J., L. Wu J., H. Yuan Z., Xia Y., Y. Jiang Y., Song J.. Fast topological pumping for the generation of large-scale Greenberger−Horne−Zeilinger states in a superconducting circuit. Front. Phys., 2022, 17(6): 62504 https://doi.org/10.1007/s11467-022-1193-y
49	Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Engineering the topological state transfer and topological beam splitter in an even-sized Su−Schrieffer−Heeger chain. Phys. Rev. A, 2020, 102(2): 022404 https://doi.org/10.1103/PhysRevA.102.022404
50	Qi L., Xing Y., D. Zhao X., Liu S., Zhang S., Hu S., F. Wang H.. Topological beam splitter via defect-induced edge channel in the Rice−Mele model. Phys. Rev. B, 2021, 103(8): 085129 https://doi.org/10.1103/PhysRevB.103.085129
51	Qi L., Yan Y., Xing Y., D. Zhao X., Liu S., X. Cui W., Han X., Zhang S., F. Wang H.. Topological router induced via long-range hopping in a Su−Schrieffer−Heeger chain. Phys. Rev. Res., 2021, 3(2): 023037 https://doi.org/10.1103/PhysRevResearch.3.023037
52	N. Zheng L., Yi X., F. Wang H.. Engineering a phase-robust topological router in a dimerized superconducting-circuit lattice with long-range hopping and chiral symmetry. Phys. Rev. Appl., 2022, 18(5): 054037 https://doi.org/10.1103/PhysRevApplied.18.054037
53	St-Jean P., Goblot V., Galopin E., Lemaȋtre A., Ozawa T., Le Gratiet L., Sagnes I., Bloch J., Amo A.. Lasing in topological edge states of a one-dimensional lattice. Nat. Photonics, 2017, 11(10): 651 https://doi.org/10.1038/s41566-017-0006-2
54	Parto M., Wittek S., Hodaei H., Harari G., A. Bandres M., Ren J., C. Rechtsman M., Segev M., N. Christodoulides D., Khajavikhan M.. Edge-mode lasing in 1D topological active arrays. Phys. Rev. Lett., 2018, 120(11): 113901 https://doi.org/10.1103/PhysRevLett.120.113901
55	Longhi S.. Non-Hermitian gauged topological laser arrays. Ann. Phys., 2018, 530(7): 1800023 https://doi.org/10.1002/andp.201800023
56	Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Robust interface-state laser in non-Hermitian microresonator arrays. Phys. Rev. Appl., 2020, 13(6): 064015 https://doi.org/10.1103/PhysRevApplied.13.064015
57	H. Harder T., Sun M., A. Egorov O., Vakulchyk I., Beierlein J., Gagel P., Emmerling M., Schneider C., Peschel U., G. Savenko I., Klembt S., Höfling S.. Coherent topological polariton laser. ACS Photonics, 2021, 8(5): 1377 https://doi.org/10.1021/acsphotonics.0c01958
58	Ezawa M.. Nonlinear non-Hermitian higher-order topological laser. Phys. Rev. Res., 2022, 4(1): 013195 https://doi.org/10.1103/PhysRevResearch.4.013195
59	Longhi S.. Topological pumping of edge states via adiabatic passage. Phys. Rev. B, 2019, 99(15): 155150 https://doi.org/10.1103/PhysRevB.99.155150
60	M. D’Angelis F., A. Pinheiro F., Guéry-Odelin D., Longhi S., Impens F.. Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with next-to-nearest-neighbor interactions. Phys. Rev. Res., 2020, 2(3): 033475 https://doi.org/10.1103/PhysRevResearch.2.033475
61	Brouzos I., Kiorpelidis I., K. Diakonos F., Theocharis G.. Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain. Phys. Rev. B, 2020, 102(17): 174312 https://doi.org/10.1103/PhysRevB.102.174312
62	E. Palaiodimopoulos N., Brouzos I., K. Diakonos F., Theocharis G.. Fast and robust quantum state transfer via a topological chain. Phys. Rev. A, 2021, 103(5): 052409 https://doi.org/10.1103/PhysRevA.103.052409
63	Hu S., Ke Y., Lee C.. Topological quantum transport and spatial entanglement distribution via a disordered bulk channel. Phys. Rev. A, 2020, 101(5): 052323 https://doi.org/10.1103/PhysRevA.101.052323
64	Guéry-Odelin D., Ruschhaupt A., Kiely A., Torrontegui E., Martínez-Garaot S., G. Muga J.. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 2019, 91(4): 045001 https://doi.org/10.1103/RevModPhys.91.045001
65	Schmidt S., Koch J.. Circuit QED lattices: Towards quantum simulation with superconducting circuits. Ann. Phys., 2013, 525(6): 395 https://doi.org/10.1002/andp.201200261
66	Frunzio L., Wallraff A., Schuster D., Majer J., Schoelkopf R.. Fabrication and characterization of superconducting circuit QED devices for quantum computation. IEEE Trans. Appl. Supercond., 2005, 15(2): 860 https://doi.org/10.1109/TASC.2005.850084
67	L. Underwood D., E. Shanks W., Koch J., A. Houck A.. Low-disorder microwave cavity lattices for quantum simulation with photons. Phys. Rev. A, 2012, 86(2): 023837 https://doi.org/10.1103/PhysRevA.86.023837
68	Peropadre B., Forn-Díaz P., Solano E., J. García-Ripoll J.. Switchable ultrastrong coupling in circuit QED. Phys. Rev. Lett., 2010, 105(2): 023601 https://doi.org/10.1103/PhysRevLett.105.023601
69	DiCarlo L., M. Chow J., M. Gambetta J., S. Bishop L., R. Johnson B., I. Schuster D., Majer J., Blais A., Frunzio L., M. Girvin S., J. Schoelkopf R.. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature, 2009, 460(7252): 240 https://doi.org/10.1038/nature08121
70	Gu X., F. Kockum A., Miranowicz A., X. Liu Y., Nori F.. Microwave photonics with superconducting quantum circuits. Phys. Rep., 2017, 1: 718 https://doi.org/10.1016/j.physrep.2017.10.002
71	He Y., Wang Y., Yan Z.. A tunable superconducting LC-resonator with a variable superconducting electrode capacitor bank for application in wireless power transfer. Supercond. Sci. Technol., 2019, 32(12): 12LT02 https://doi.org/10.1088/1361-6668/ab4c1d
72	S. Allman M., Altomare F., D. Whittaker J., Cicak K., Li D., Sirois A., Strong J., D. Teufel J., W. Simmonds R.. RF-squid-mediated coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. Phys. Rev. Lett., 2010, 104: 177004 https://doi.org/10.1103/PhysRevLett.104.177004
73	S. Allman M., D. Whittaker J., Castellanos-Beltran M., Cicak K., da Silva F., P. DeFeo M., Lecocq F., Sirois A., D. Teufel J., Aumentado J., W. Simmonds R.. Tunable resonant and nonresonant interactions between a phase qubit and LC resonator. Phys. Rev. Lett., 2014, 112(12): 123601 https://doi.org/10.1103/PhysRevLett.112.123601
74	Wulschner F., Goetz J., R. Koessel F., Hoffmann E., Baust A., Eder P., Fischer M., Haeberlein M., J. Schwarz M., Pernpeintner M., Xie E., Zhong L., W. Zollitsch C., Peropadre B., G. Ripoll J.-J., Solano E., G. Fedorov K., P. Menzel E., Deppe F., Marx A., Gross R.. Tunable coupling of transmission-line microwave resonators mediated by an RF squid. EPJ Quantum Technol., 2016, 3: 8 https://doi.org/10.1140/epjqt/s40507-016-0048-2
75	Blais A., S. Huang R., Wallraff A., M. Girvin S., J. Schoelkopf R.. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A, 2004, 69(6): 062320 https://doi.org/10.1103/PhysRevA.69.062320
76	Clarke J., K. Wilhelm F.. Superconducting quantum bits. Nature, 2008, 453(7198): 1031 https://doi.org/10.1038/nature07128
77	Q. You J., Nori F.. Atomic physics and quantum optics using superconducting circuits. Nature, 2005, 474: 589 https://doi.org/10.1038/nature10122

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