Please wait a minute...
Chin. Phys. B, 2025, Vol. 34(11): 110302    DOI: 10.1088/1674-1056/ae00b0
RAPID COMMUNICATION Prev   Next  

Efficient characterization of the coupler spectrum via sideband driving in superconducting qubits

Jianwen Xu(徐建文)1,2,3,†, Ruonan Guo(郭若男)1,2,3,†, Wen Zheng(郑文)1,2,3,‡, Yu Zhang(张钰)1,2,3, Jie Zhao(赵杰)1,2,3, Zhiguo Huang(黄智国)4, Jingwei Wen(闻经纬)4, Runqing Zhang(张润清)4, Shaoxiong Li(李邵雄)1,2,3,5,6, Xinsheng Tan(谭新生)1,2,3,5,6, and Yang Yu(于扬)1,2,3,5,6,§
1 National Laboratory of Solid State Microstructures, School of Physics, Nanjing University, Nanjing 210093, China;
2 Shishan Laboratory, Nanjing University, Suzhou 215163, China;
3 Jiangsu Key Laboratory of Quantum Information Science and Technology, Nanjing University, Suzhou 215163, China;
4 China Mobile (Suzhou) Software Technology Company Limited, Suzhou 215163, China;
5 Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China;
6 Hefei National Laboratory, Hefei 230088, China
Abstract  Fabrication-friendly superconducting qubits continue to be a leading candidate for scalable quantum computing. Recent developments in tunable couplers have significantly advanced the progress toward practical quantum processors. However, high-performance quantum control, particularly two-qubit gates, depends on the delicate tuning of the coupler spectrum, as misalignment can lead to undesirable phenomena such as frequency crowding, which may cause errors including state leakage. Here, we propose an efficient method for characterizing the coupler spectrum through sideband drivings, obviating the need for additional components in current quantum processors. We demonstrate this technique experimentally by employing both continuous-wave and pulsed measurement protocols, successfully extracting the coupler spectrum. Furthermore, by utilizing the measured coupler spectrum, we calibrate the frequency dependence of the effective coupling strength between two qubits linked by the coupler. The proposed approach offers significant practical benefits, enabling the efficient characterization of the coupler spectrum in existing quantum architectures, thus paving the way for enhanced quantum control and scalability.
Keywords:  superconducting quantum circuits      tunable coupler      sideband driving  
Received:  02 July 2025      Revised:  15 August 2025      Accepted manuscript online:  29 August 2025
PACS:  03.67.Lx (Quantum computation architectures and implementations)  
  85.25.Dq (Superconducting quantum interference devices (SQUIDs))  
Fund: This work was partially supported by the Innovation Program for Quantum Science and Technology (Grant Nos. 2021ZD0301702 and 2024ZD0302000), the Natural Science Foundation of of Jiangsu Province (Grant No. BK20232002), the National Natural Science Foundation of China (Grant Nos. U21A20436 and 12074179), the Natural Science Foundation of Shandong Province (Grant No. ZR2023LZH002), and Nanjing University–China Mobile Communications Group Co., Ltd. Joint Institute.
Corresponding Authors:  Wen Zheng, Yang Yu     E-mail:  zhengwen@nju.edu.cn;yuyang@nju.edu.cn

Cite this article: 

Jianwen Xu(徐建文), Ruonan Guo(郭若男), Wen Zheng(郑文), Yu Zhang(张钰), Jie Zhao(赵杰), Zhiguo Huang(黄智国), Jingwei Wen(闻经纬), Runqing Zhang(张润清), Shaoxiong Li(李邵雄), Xinsheng Tan(谭新生), and Yang Yu(于扬) Efficient characterization of the coupler spectrum via sideband driving in superconducting qubits 2025 Chin. Phys. B 34 110302

[1] Yan F, Krantz P, Sung Y, Kjaergaard M, Campbell D L, Orlando T P, Gustavsson S and Oliver W D 2018 Phys. Rev. Appl. 10 054062
[2] Mundada P, Zhang G, Hazard T and Houck A 2019 Phys. Rev. Appl. 12 054023
[3] Li R, Kubo K, Ho Y, Yan Z, Nakamura Y and Goto H 2024 Phys. Rev. X 14 041050
[4] Xu Y, Chu J, Yuan J, Qiu J, Zhou Y, Zhang L, Tan X, Yu Y, Liu S, Li J, et al. 2020 Phys. Rev. Lett. 125 240503
[5] Sung Y, Ding L, Braumüller J, et al. 2021 Phys. Rev. X 11 021058
[6] Stehlik J, Zajac D M, Underwood D L, Phung T, Blair J, Carnevale S, Klaus D, Keefe G A, Carniol A, Kumph M, Steffen M and Dial O E 2021 Phys. Rev. Lett. 127 080505
[7] McKay D C, Filipp S, Mezzacapo A, Magesan E, Chow J M and Gambetta J M 2016 Phys. Rev. Appl. 6 064007
[8] Foxen B, Neill C, Dunsworth A, et al. 2020 Phys. Rev. Lett. 125 120504
[9] Chen Z, Liu W, Ma Y, Sun W, Wang R, Wang H, Xu H, Xue G, Yan H, Yang Z, Ding J, Gao Y, Li F, Zhang Y, Zhang Z, Jin Y, Yu H, Chen J and Yan F 2025 arXiv:2502.03612 [quant-ph]
[10] You J Q and Nori F 2011 Nature 474 589
[11] Krantz P, Kjaergaard M, Yan F, Orlando T P, Gustavsson S and Oliver W D 2019 Appl. Phys. Rev. 6 021318
[12] Blais A, Grimsmo A L, Girvin S M and Wallraff A 2021 Rev. Mod. Phys. 93 025005
[13] Arute F, Arya K, Babbush R, Bacon D, Bardin J C, Barends R, Biswas R, Boixo S, Brandao F G, Buell D A, et al. 2019 Nature 574 505
[14] Wu Y, BaoWS, Cao S, Chen F, Chen M C, Chen X, Chung T H, Deng H, Du Y, Fan D, et al. 2021 Phys. Rev. Lett. 127 180501
[15] Gao D, Fan D, Zha C, et al. 2025 Nature 638 920
[16] Ai G Q and Collaborators 2025 Nature 638 920
[17] Shor P W 1997 arXiv:quant-ph/9605011
[18] Jiang L, Taylor J M, Sørensen A S and Lukin M D 2007 Phys. Rev. A 76 062323
[19] Gambetta J M, Chow J M and Steffen M 2017 npj Quantum Inf. 3 2
[20] Bravyi S, Dial O, Gambetta J M, Gil D and Nazario Z 2022 J. Appl. Phys. 132 160902
[21] Ang J, Carini G, Chen Y, et al. 2022 (Preprint 2212.06167)
[22] Field M, Chen A Q, Scharmann B, Sete E A, Oruc F, Vu K, Kosenko V, Mutus J Y, Poletto S and Bestwick A 2024 Phys. Rev. Appl. 21 54063
[23] Preskill J 2018 Quantum 2 79
[24] Wang C, Li X, Xu H, Li Z,Wang J, Yang Z, Mi Z, Liang X, Su T, Yang C, Wang G, Wang W, Li Y, Chen M, Li C, Linghu K, Han J, Zhang Y, Feng Y, Song Y, Ma T, Zhang J, Wang R, Zhao P, Liu W, Xue G, Jin Y and Yu H 2022 npj Quantum Inf. 8 3
[25] Tong H M, Lai Y S and Wong C 2013 Advanced flip chip packaging Vol. 142 (Springer)
[26] Kosen S, Li H X, Rommel M, et al. 2022 Quantum Sci. Technol. 7 035018
[27] Koster N, Koblowski S, Bertenburg R, Heinen S and Wolff I 1989 Investigations on air bridges used for mmics in cpw technique 1989 19th European Microwave Conference (IEEE) pp. 666–671
[28] Chen Z, Megrant A, Kelly J, Barends R, Bochmann J, Chen Y, Chiaro B, Dunsworth A, Jeffrey E, Mutus J, et al. 2014 Appl. Phys. Lett. 104 052602
[29] Sun Y, Ding J, Xia X, Wang X, Xu J, Song S, Lan D, Zhao J and Yu Y 2022 Appl. Phys. Lett. 121 074001
[30] Gambino J P, Adderly S A and Knickerbocker J U 2015 Microelectron. Eng. 135 73
[31] Yost D R W, Schwartz M E, Mallek J, Rosenberg D, Stull C, Yoder J L, Calusine G, Cook M, Das R, Day A L, et al. 2020 npj Quantum Inf. 6 59
[32] Gong M, Wang S, Zha C, Chen M C, Huang H L, Wu Y, Zhu Q, Zhao Y, Li S, Guo S, et al. 2021 Science 372 948
[33] Chu J, He X, Zhou Y, Yuan J, Zhang L, Guo Q, Hai Y, Han Z, Hu C K, Huang W, et al. 2023 Nat. Phys. 19 126
[34] Zhang X, Jiang W, Deng J, Wang K, Chen J, Zhang P, Ren W, Dong H, Xu S, Gao Y, Jin F, Zhu X, Guo Q, Li H, Song C, Gorshkov A V, Iadecola T, Liu F, Gong Z X, Wang Z, Deng D L and Wang H 2022 Nature 607 468
[35] Xu S, Sun Z Z, Wang K, et al. 2023 Chin. Phys. Lett. 40 060301
[36] Fowler A G, Mariantoni M, Martinis J M and Cleland A N 2012 Phys. Rev. A 86 032324
[37] Cohen L Z, Kim I H, Bartlett S D and Brown B J 2022 Sci. Adv. 8 eabn1717
[38] Breuckmann N P and Eberhardt J N 2021 PRX Quantum 2 040101
[39] Bravyi S, Cross A W, Gambetta J M, Maslov D, Rall P and Yoder T J 2024 Nature 627 778
[40] Gidney C, Newman M, Brooks P and Jones C 2025 Nat. Commun. 16 4498
[41] Wang K, Lu Z, Zhang C, et al. 2025 arXiv:2505.09684 [quant-ph]
[42] Koch J, Yu T M, Gambetta J, Houck A A, Schuster D I, Majer J, Blais A, Devoret M H, Girvin S M and Schoelkopf R J 2007 Phys. Rev. A 76 042319
[43] Barends R, Kelly J, Megrant A, Sank D, Jeffrey E, Chen Y, Yin Y, Chiaro B, Mutus J, Neill C, O’Malley P, Roushan P, Wenner J, White T C, Cleland A N and Martinis J M 2013 Phys. Rev. Lett. 111 080502
[44] Zhao P, Zhang Y, Xue G, Jin Y and Yu H 2022 Appl. Phys. Lett. 121 32601
[45] Zhao C, He Y, Geng X, He K, Dai G, Liu J and Chen W 2023 Chin. Phys. Lett. 40 010301
[46] Mollenhauer M, Irfan A, Cao X, Mandal S and Pfaff W 2024 (Preprint 2407.16743)
[47] Song J, Yang S, Liu P, Xue G M, Mi Z Y, Zhang W G, Yan F, Jin Y R and Yu H F 2024 (Preprint 2407.20338)
[48] Deng X, ZhengW, Liao X, Zhou H, Ge Y, Zhao J, Lan D, Tan X, Zhang Y, Li S and Yu Y 2025 Phys. Rev. Lett. 134 020801
[49] Xiong H,Wang J, Song J, Yang J, Bao Z, Li Y, Mi Z Y, Zhang H, Yu H F, Song Y and Duan L 2025 (Preprint 2502.18902)
[50] Heya K, Phung T, Malekakhlagh M, Steiner R, Turchetti M, Shanks W, Mamin J, Lu W S, Kandel Y P, Sundaresan N and Orcutt J 2025 (Preprint 2502.15034)
[51] Xu J, Deng X, Zheng W, Yan W, Zhang T, Zhang Z, Huang W, Xia X, Liao X, Zhang Y, Zhao J, Li S, Tan X, Lan D and Yu Y 2025 arXiv:2506.14128 [quant-ph]
[52] Zhao P, Linghu K, Li Z, Xu P, Wang R, Xue G, Jin Y and Yu H 2022 PRX Quantum 3 020301
[53] Zhang Y, Zhang Y, Li S, Zheng W and Yu Y 2024 Chin. Phys. B 33 110306
[54] Wang R, Zhao P, Jin Y and Yu H 2022 Appl. Phys. Lett. 121 152602
[55] Li T M, Zhang J C, Chen B J, Huang K, Liu H T, Xiao Y X, Deng C L, Liang G H, Chen C T, Liu Y, Li H, Bao Z T, Zhao K, Xu Y, Li L, He Y, Liu Z H, Yu Y H, Zhou S Y, Liu Y J, Song X, Zheng D, Xiang Z, Shi Y H, Xu K and Fan H 2025 Phys. Rev. Appl. 23 024059
[56] Chu J and Yan F 2021 Phys. Rev. Appl. 16 054020
[57] Xu H, Liu W, Li Z, Han J, Zhang J, Linghu K, Li Y, Chen M, Yang Z, Wang J, Ma T, Xue G, Jin Y and Yu H 2021 Chin. Phys. B 30 044212
[58] Wallraff A, Schuster D I, Blais A, Gambetta J M, Schreier J, Frunzio L, Devoret M H, Girvin S M and Schoelkopf R J 2007 Phys. Rev. Lett. 99 050501
[59] Chen Z, Wang Y, Li T, Tian L, Qiu Y, Inomata K, Yoshihara F, Han S, Nori F, Tsai J S and You J Q 2017 Phys. Rev. A 96 012325
[60] Zhu Y Q, Zheng W, Zhu S L and Palumbo G 2021 Phys. Rev. B 104 205103
[61] Georgescu I M, Ashhab S and Nori F 2014 Rev. Mod. Phys. 86 153
[62] Zheng W, Xu J, Ma Z, Li Y, Dong Y, Zhang Y, Wang X, Sun G, Wu P, Zhao J, Li S, Lan D, Tan X and Yu Y 2022 Chin. Phys. Lett. 39 100202
[63] Sete E A, Chen A Q, Manenti R, Kulshreshtha S and Poletto S 2021 Phys. Rev. Appl. 15 064063
[64] Blais A, Gambetta J, Wallraff A, Schuster D I, Girvin S M, Devoret M H and Schoelkopf R J 2007 Phys. Rev. A 75 032329
[65] It is note that this red sideband process, including two detuned XY drivings inducing a coherent interaction in redefined subaspace fj0ei, j1gig, differs from the parametric modulation by using a lowfrequency parametric drive on the Z control (flux bias) line to achieve an effective exchange interaction.[69]
[66] Li D, Zheng W, Chu J, Yang X, Song S, Han Z, Dong Y, Wang Z, Yu X, Lan D, Zhao J, Li S, Tan X and Yu Y 2021 Appl. Phys. Lett. 118 104003
[67] ZhengW, Zhang Y, Dong Y, Xu J,Wang Z,Wang X, Li Y, Lan D, Zhao J, Li S, Tan X and Yu Y 2022 npj Quantum Inf. 8 9
[68] Vitanov N V, Rangelov A A, Shore B W and Bergmann K 2017 Rev. Mod. Phys. 89 015006
[69] Chu J, Li D, Yang X, Song S, Han Z, Yang Z, Dong Y, ZhengW,Wang Z, Yu X, Lan D, Tan X and Yu Y 2020 Phys. Rev. Appl. 13 064012
[1] A low-noise and high-stability DC source for superconducting quantum circuits
Daxiong Sun(孙大雄), Jiawei Zhang(张家蔚), Peisheng Huang(黄培生), Yubin Zhang(张玉斌), Zechen Guo(郭泽臣), Tingjin Chen(陈庭槿), Rui Wang(王睿), Xuandong Sun(孙炫东), Jiajian Zhang(张家健), Wenhui Huang(黄文辉), Jiawei Qiu(邱嘉威), Ji Chu(储继), Ziyu Tao(陶子予), Weijie Guo(郭伟杰), Xiayu Linpeng(林彭夏雨), Ji Jiang(蒋骥), Jingjing Niu(牛晶晶), Youpeng Zhong(钟有鹏), and Dapeng Yu(俞大鹏). Chin. Phys. B, 2025, 34(9): 090303.
[2] In-situ deposited anti-aging TiN capping layer for Nb superconducting quantum circuits
Hao-Ran Tao(陶浩然), Lei Du(杜磊), Liang-Liang Guo(郭亮亮), Yong Chen(陈勇), Hai-Feng Zhang(张海峰), Xiao-Yan Yang(杨小燕), Guo-Liang Xu(徐国良), Chi Zhang(张 驰), Zhi-Long Jia(贾志龙), Peng Duan(段鹏), and Guo-Ping Guo(郭国平). Chin. Phys. B, 2024, 33(9): 090310.
[3] Fast and perfect state transfer in superconducting circuit with tunable coupler
Chi Zhang(张驰), Tian-Le Wang(王天乐), Ze-An Zhao(赵泽安), Xiao-Yan Yang(杨小燕), Liang-Liang Guo(郭亮亮), Zhi-Long Jia(贾志龙), Peng Duan(段鹏), and Guo-Ping Guo(郭国平). Chin. Phys. B, 2023, 32(11): 110305.
[4] Interaction induced non-reciprocal three-level quantum transport
Sai Li(李赛), Tao Chen(陈涛), Jia Liu(刘佳), and Zheng-Yuan Xue(薛正远). Chin. Phys. B, 2021, 30(6): 060314.
[5] Realization of adiabatic and diabatic CZ gates in superconducting qubits coupled with a tunable coupler
Huikai Xu(徐晖凯), Weiyang Liu(刘伟洋), Zhiyuan Li(李志远), Jiaxiu Han(韩佳秀), Jingning Zhang(张静宁), Kehuan Linghu(令狐克寰), Yongchao Li(李永超), Mo Chen(陈墨), Zhen Yang(杨真), Junhua Wang(王骏华), Teng Ma(马腾), Guangming Xue(薛光明), Yirong Jin(金贻荣), and Haifeng Yu(于海峰). Chin. Phys. B, 2021, 30(4): 044212.
[6] Phase-controlled coherent population trapping in superconducting quantum circuits
Cheng Guang-Ling (程广玲), Wang Yi-Ping (王一平), Chen Ai-Xi (陈爱喜). Chin. Phys. B, 2015, 24(4): 044204.
[7] Structure formation of entanglement entropy in a system of two superconducting qubits coupled with an LC-resonator
Ge Guo-Qin(葛国勤), Qin Cui(覃翠), Yin Miao(尹淼), and Huang Yong-Hua(黄勇华). Chin. Phys. B, 2011, 20(8): 080304.
No Suggested Reading articles found!