Recent progress of quantum control in solid-state single-spin systems

Li Ting-Wei; Rong Xing; Du Jiang-Feng

doi:10.7498/aps.71.20211808

Abstract

In the field of quantum physics, quantum control is essential. Precise and efficient quantum control is a prerequisite for the experimental research using quantum systems, and it is also the basis for applications such as in quantum computing and quantum sensing. As a solid-state spin system, the nitrogen-vacancy (NV) center in diamond has a long coherence time at room temperature. It can be initialized and read out by optical methods, and can achieve universal quantum control through the microwave field and radio frequency fields. It is an excellent experimental platform for studying quantum physics. In this review, we introduce the recent results of quantum control in NV center and discuss the following parts: 1) the physical properties of the NV center and the realization method of quantum control, 2) the decoherence mechanism of the NV center spin qubit, and 3) the application of single-spin quantum control and relevant research progress.

Keywords:

Authors and contacts

1.
CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
2.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Rong Xing, xrong@ustc.edu.cn

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References

[1]	Kastner M A 1992 Rev. Mod. Phys. 64 849 Google Scholar
[2]	Yoneda J, Takeda K, Otsuka T, Nakajima T, Delbecq M R, Allison G, Honda T, Kodera T, Oda S, Hoshi Y, Usami N, Itoh K M, Tarucha S 2018 Nat. Nanotechnol. 13 102 Google Scholar
[3]	Huang W, Yang C H, Chan K W, Tanttu T, Hensen B, Leon R C C, Fogarty M A, Hwang J C C, Hudson F E, Itoh K M, Morello A, Laucht A, Dzurak A S 2019 Nature 569 532 Google Scholar
[4]	Yang A, Steger M, Sekiguchi T, Thewalt M L W, Ladd T D, Itoh K M, Riemann H, Abrosimov N V, Becker P, Pohl H J 2009 Phys. Rev. Lett. 102 257401 Google Scholar
[5]	He Y, Gorman S K, Keith D, Kranz L, Keizer J G, Simmons M Y 2019 Nature 571 371 Google Scholar
[6]	Doherty M W, Manson N B, Delaney P, Jelezko F, Wrachtrup J, Hollenberg L C L 2013 Phys. Rep. 528 1 Google Scholar
[7]	Dobrovitski V V, Fuchs G D, Falk A L, Santori C, Awschalom D D 2013 Annu. Rev. Condens. Matter Phys. 4 23 Google Scholar
[8]	Rembold P, Oshnik N, Müller M M, Montangero S, Calarco T, Neu E 2020 AVS Quantum Sci. 2 024701 Google Scholar
[9]	伍旸 2020 博士学位论文 (合肥: 中国科学技术大学) Wu Y 2020 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[10]	Gali A, Fyta M, Kaxiras E 2008 Phys. Rev. B 77 155206 Google Scholar
[11]	Acosta V M, Jarmola A, Bauch E, Budker D 2010 Phys. Rev. B 82 201202 Google Scholar
[12]	Loubser J, van Wyk J 1978 Rep. Prog. Phys. 41 1201 Google Scholar
[13]	Manson N B, Harrison J P, Sellars M J 2006 Phys. Rev. B 74 104303 Google Scholar
[14]	Nizovtsev A P, Kilin S Y, Jelezko F, Popa I, Gruber A, Tietz C, Wrachtrup J 2003 Opt. Spectrosc. 94 848 Google Scholar
[15]	Van der Sar T, Wang Z H, Blok M S, Bernien H, Taminiau T H, Toyli D M, Lidar D A, Awschalom D D, Hanson R, Dobrovitski V V 2012 Nature 484 82 Google Scholar
[16]	Weil J A, Bolton J R 2007 Electron Paramagnetic Resonance: Elementary Theory and Practical Applications (Hoboken: John Wiley & Sons, Inc.)
[17]	Victor A C 1962 J. Chem. Phys. 36 1903 Google Scholar
[18]	Rong X, Geng J P, Shi F Z, Liu Y, Xu K B, Ma W C, Kong F, Jiang Z, Wu Y, Du J F 2015 Nat. Commun. 6 8748 Google Scholar
[19]	De Raedt H, Barbara B, Miyashita S, Michielsen K, Bertaina S, Gambarelli S 2012 Phys. Rev. B 85 014408 Google Scholar
[20]	Rong X, Geng J P, Wang Z X, Zhang Q, Ju C Y, Shi F Z, Duan C K, Du J F 2014 Phys. Rev. Lett. 112 050503 Google Scholar
[21]	Geng J P, Wu Y, Wang X T, Xu K B, Shi F Z, Xie Y J, Rong X, Du J F 2016 Phys. Rev. Lett. 117 170501 Google Scholar
[22]	Wu Y, Wang Y, Qin X, Rong X, Du J F 2019 Npj Quantum Inf. 5 1 Google Scholar
[23]	Wu Y, Liu W Q, Geng J P, Song X R, Ye X Y, Duan C K, Rong X, Du J F 2019 Science 364 878 Google Scholar
[24]	Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 82 2417 Google Scholar
[25]	Khodjasteh K, Lidar D A 2005 Phys. Rev. Lett. 95 180501
[26]	Uhrig G S 2007 Phys. Rev. Lett. 98 100504 Google Scholar
[27]	Du J F, Rong X, Zhao N, Wang Y, Yang J H, Liu R B 2009 Nature 461 1265 Google Scholar
[28]	De Lange G, Wang Z H, Riste D, Dobrovitski V V, Hanson R 2010 Science 330 60 Google Scholar
[29]	Naydenov B, Dolde F, Hall L T, Shin C, Fedder H, Hollenberg L C, Jelezko F, Wrachtrup J 2011 Phys. Rev. B 83 081201 Google Scholar
[30]	Liu G Q, Po H C, Du J, Liu R B, Pan X Y 2013 Nat. Commun. 4 2254
[31]	Zhang J F, Souza A M, Brandao F D, Suter D 2014 Phys. Rev. Lett. 112 050502 Google Scholar
[32]	Khodjasteh K, Viola L 2009 Phys. Rev. Lett. 102 080501 Google Scholar
[33]	Khodjasteh K, Lidar D A, Viola L 2010 Phys. Rev. Lett. 104 090501 Google Scholar
[34]	West J R, Lidar D A, Fong B H, Gyure M F 2010 Phys. Rev. Lett. 105 230503 Google Scholar
[35]	Kestner J P, Wang X, Bishop L S, Barnes E, Das Sarma S 2013 Phys. Rev. Lett. 110 140502
[36]	Wang X, Bishop L S, Kestner J P, Barnes E, Sun K, Dar Sarma S 2012 Nat. Commun. 3 997
[37]	Nielsen M A, Chuang I L 2000 Quantum Computing and Quantum Information (Cambridge: Cambridge University Press)
[38]	Wimperis S 1994 J. Magn. Reson. 109 221 Google Scholar
[39]	Ichikawa T, Bando M, Kondo Y, Nakahara M 2011 Phys. Rev. A 84 062311 Google Scholar
[40]	Bando M, Ichikawa T, Kondo Y, Nakahara M 2013 J. Phys. Soc. Japan 82 014004
[41]	Cummins H K, Llewellyn G, Jones J A 2003 Phys. Rev. A 67 042308 Google Scholar
[42]	Knill E, Leibfried D, Reichle R, Britton J, Blakestad R B, Jost J D, Langer C, Ozeri R, Seidelin S, Wineland D J 2008 Phys. Rev. A 77 012307 Google Scholar
[43]	Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324 Google Scholar
[44]	Zermelo E 1931 Z. Angew. Math. Mech. 11 114 Google Scholar
[45]	Wang X T, Allegra M, Jacobs K, Lloyd S, Lupo C, Mohseni M 2015 Phys. Rev. Lett. 114 170501 Google Scholar
[46]	Barends R, Kelly J, Megrant A, Veitia A, Sank D, Jeffrey E, White T C, Mutus J, Fowler A G, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth B, Neill C, O'Malley P, Roushan P, Vainsencher A, Wenner J, Korotkov A N, Cleland A N, Martinis J M 2014 Nature 508 500 Google Scholar
[47]	Nielsen M A, Chuang I L 1997 Phys. Rev. Lett. 79 321 Google Scholar
[48]	Kim J, Cheong Y, Lee J S, Lee S 2001 Phys. Rev. A 65 012302 Google Scholar
[49]	Vidal G, Masanes L, Cirac J I 2002 Phys. Rev. Lett. 88 047905 Google Scholar
[50]	Shende V V, Markov I L, Bullock S S 2004 Phys. Rev. A 69 062321
[51]	Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243 Google Scholar
[52]	Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401 Google Scholar
[53]	Bender C M 2007 Rep. Prog. Phys. 70 947 Google Scholar
[54]	Mostafazadeh A 2005 J. Math. Phys. 46 102108 Google Scholar
[55]	Dorey P, Dunning C, Lishman A, Tateo R 2009 J. Phys. A: Math. Theor. 42 465302
[56]	Gong J, Wang Q 2013 J. Phys. A: Math. Theor. 46 485302
[57]	Kunst F K, Edvardsson E, Budich J C, Bergholtz E J 2018 Phys. Rev. Lett. 121 026808 Google Scholar
[58]	Song F, Yao S Y, Wang Z 2019 Phys. Rev. Lett. 123 170401 Google Scholar
[59]	Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S, Ueda M 2018 Phys. Rev. X 8 031079
[60]	Özdemir Ş K, Rotter S, Nori F, Yang L 2019 Nat. Mater. 18 783 Google Scholar
[61]	Miri M-A, Alù A 2019 Science 363 eaar7709
[62]	Bender N, Factor S, Bodyfelt J D, Ramezani H, Christodoulides D N, Ellis F M, Kottos T 2013 Phys. Rev. Lett. 110 234101 Google Scholar
[63]	Assawaworrarit S, Yu X, Fan S 2017 Nature 546 387 Google Scholar
[64]	Choi Y, Hahn C, Yoon J W, Song S H 2018 Nat. Commun. 9 2182
[65]	Bittner S, Dietz B, Günther U, Harney H L, Miski-Oglu M, Richter A, Schäfer F 2012 Phys. Rev. Lett. 108 024101 Google Scholar
[66]	Bender C M, Berntson B K, Parker D, Samuel E 2013 Am. J. Phys. 81 173 Google Scholar
[67]	Zhu X F, Ramezani H, Shi C Z, Zhu J, Zhang X 2014 Phys. Rev. X 4 031042
[68]	Popa B I, Cummer S A 2014 Nat. Commun. 5 3398
[69]	Fleury R, Sounas D, Alù A 2015 Nat. Commun. 6 5905
[70]	Li J M, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L 2019 Nat. Commun. 10 855
[71]	Naghiloo M, Abbasi M, Joglekar Y N, Murch K W 2019 Nat. Phys. 15 1232 Google Scholar
[72]	Liu W Q, Wu Y, Duan C K, Rong X, Du J F 2021 Phys. Rev. Lett. 126 170506 Google Scholar
[73]	Lau H K, Clerk A A 2018 Nat. Commun. 9 4320
[74]	Chen C, Jin L, Liu R B 2019 New J. Phys. 21 083002 Google Scholar

Cited By

图 1 金刚石中NV色心结构图^[9]

Figure 1. Schematic atomic structure of the NV center in diamond^[9].

DownLoad: Full-Size Img PowerPoint

图 2 金刚石NV色心能级结构^[9]　(a) NV色心的基态、激发态和亚稳态; (b) NV色心基态的精细结构和¹⁴N核带来的超精细结构

Figure 2. Energy level diagram of the NV center in diamond^[9]: (a) Ground state, excited state and metastable state of the NV center; (b) fine structure and hyperfine structure (caused by ¹⁴N nuclear spin) of the NV center ground state.

DownLoad: Full-Size Img PowerPoint

图 3 NV色心电子自旋的退相位过程^[18]　(a) 电子自旋的自由感应衰减曲线, 插图为实验脉冲序列; (b) 准静态噪声$ \delta_0 $的分布$ P(\delta_0 $)

Figure 3. Dephasing process of the electron spin of the NV center^[18]: (a) FID of the electron spin, the inset is the experimental pulse sequence; (b) probability density distribution of $ \delta_0 $.

DownLoad: Full-Size Img PowerPoint

图 4 操控场噪声下NV色心的退相干^[18]　(a) 电子自旋的拉比振荡, 插图为实验脉冲序列; (b) 准静态操控场噪声$ \delta_1 $的分布$ P(\delta_1 $)

Figure 4. Decoherence of the NV center under control field noise^[18]: (a) Results of the nutation experiment for the electron spin, the inset is the experimental pulse sequence; (b) probability density distribution of $ \delta_1 $.

DownLoad: Full-Size Img PowerPoint

图 5 实验验证SUPCODE序列在实现量子逻辑门时对准静态环境噪声的抑制效果^[20]

Figure 5. Experimental demonstration of the robustness of SUPCODE against the noise stemming from the quasistatic fluctuation of Overhauser field^[20].

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图 6 级联5-piece SUPCODE序列实现的量子逻辑门保真度随序列时长的关系^[20]

Figure 6. Decay of the fidelity of 5-piece SUPCODEs^[20].

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图 7 实现量子逻辑门的各种脉冲序列及在噪声影响下的保真度^[18]　(a) 普通方波脉冲; (b) 5-piece SUPCODE脉冲序列; (c) BB1脉冲序列; (d) BB1inC脉冲序列

Figure 7. Pulse sequences for quantum gate and the fidelity under noises^[18]: (a) Plain pulse; (b) 5-piece SUPCODE pulse; (c) BB1 pulse; (d) BB1inC pulse.

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图 8 单比特量子逻辑门保真度的实验测量结果, 插图为四种脉冲序列对应的量子逻辑门的出错概率$ \varepsilon $^[18]

Figure 8. Average fidelity of single-qubit gates, where the inset shows the average error per gates of the pulses^[18].

DownLoad: Full-Size Img PowerPoint

图 9 测量CNOT门保真度的量子线路图(a)和实验结果(b)^[18]

Figure 9. Quantum circuit diagram (a) and experimental result (b) for measuring the fidelity of CNOT gates^[18].

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图 10 时间最优控制示意图^[21]

Figure 10. Schematic diagram of time optimal quantum control^[21].

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图 11 时间最优量子控制和欧拉转动实现单比特操控$ R(\hat{z}, \theta) $花费时间对比^[21]　(a) 转角$ \theta $分别为$ \pi/8 $, $ \pi/4 $, $ \pi/2 $和$ \pi $时, 实现单比特操控$ R(\hat{z}, \theta) $耗时对比; (b) 时间最优量子控制和欧拉转动下量子态的演化过程

Figure 11. Comparison on time costs for target gate operator $ R(\hat{z}, \theta) $ between the derived time-optimal control (TOC) and the Euler rotations^[21]: (a) Comparison of experimental gate time for $ \theta = \pi/8 $, $ \pi/4 $, $ \pi/2 $, and $ \pi $; (b) state evolutions during $ R(\hat{z}, \theta) $ with TOC and Euler rotation.

DownLoad: Full-Size Img PowerPoint

图 12 初态为(a) $ |0, 1\rangle $和 (b) $ |0, 0\rangle $时量子态在两比特时间最优控制下的演化^[21]

Figure 12. State trajectories under the two-qubit controlled-U gate by TOC with initial states (a) $ |0, 1\rangle $ and (b) $ |0, 0\rangle $^[21].

DownLoad: Full-Size Img PowerPoint

图 13 普适可编程量子逻辑线路^[22]

Figure 13. Universal programmable quantum logic circuit^[22].

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图 14 单比特门对应的脉冲^[22]

Figure 14. Realization of the single-qubit gate^[22].

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图 15 金刚石NV色心体系中实现PT对称哈密顿量的量子线路图^[23]

Figure 15. Quantum circuit of the experiment of constructing a PT symmetric Hamiltonian in a NV center^[23].

DownLoad: Full-Size Img PowerPoint

图 16 量子态在PT对称哈密顿量$ H_{PT} $下的演化^[23]　(a) $ r $ = 0, 厄米哈密顿量; (b) $ r $ = 0.6, PT对称非破缺; (c) $ r $ = 1.0, 奇异点; (d) $ r $ = 1.4, PT对称破缺时的情况

Figure 16. State evolution under $ H_{PT} $^[23]. Experimental dynamics of renormalized population $ P_0 $ when $ r $ = 0 (a), $ r $ = 0.6 (b), $ r $ = 1.0 (c), and $ r $ = 1.4 (d).

DownLoad: Full-Size Img PowerPoint

表 1 不同量子逻辑门序列下末态保真度的偏差随${\delta_0}/{\omega_1}$的阶数关系^[20]

Table 1. Infidelity of quantum gate for different pulses as a function of ${\delta_0}/{\omega_1}$^[20].

脉冲序列	末态保真度偏差
普通方波脉冲	$0.5(\delta_0/\omega_1)^2+O(\delta_0/\omega_1)^4$
3-piece SUPCODE脉冲	$11.1(\delta_0/\omega_1)^4+O(\delta_0/\omega_1)^6$
5-piece SUPCODE脉冲	$64.1(\delta_0/\omega_1)^6+O(\delta_0/\omega_1)^8$

DownLoad: CSV

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[1]	Kastner M A 1992 Rev. Mod. Phys. 64 849 Google Scholar
[2]	Yoneda J, Takeda K, Otsuka T, Nakajima T, Delbecq M R, Allison G, Honda T, Kodera T, Oda S, Hoshi Y, Usami N, Itoh K M, Tarucha S 2018 Nat. Nanotechnol. 13 102 Google Scholar
[3]	Huang W, Yang C H, Chan K W, Tanttu T, Hensen B, Leon R C C, Fogarty M A, Hwang J C C, Hudson F E, Itoh K M, Morello A, Laucht A, Dzurak A S 2019 Nature 569 532 Google Scholar
[4]	Yang A, Steger M, Sekiguchi T, Thewalt M L W, Ladd T D, Itoh K M, Riemann H, Abrosimov N V, Becker P, Pohl H J 2009 Phys. Rev. Lett. 102 257401 Google Scholar
[5]	He Y, Gorman S K, Keith D, Kranz L, Keizer J G, Simmons M Y 2019 Nature 571 371 Google Scholar
[6]	Doherty M W, Manson N B, Delaney P, Jelezko F, Wrachtrup J, Hollenberg L C L 2013 Phys. Rep. 528 1 Google Scholar
[7]	Dobrovitski V V, Fuchs G D, Falk A L, Santori C, Awschalom D D 2013 Annu. Rev. Condens. Matter Phys. 4 23 Google Scholar
[8]	Rembold P, Oshnik N, Müller M M, Montangero S, Calarco T, Neu E 2020 AVS Quantum Sci. 2 024701 Google Scholar
[9]	伍旸 2020 博士学位论文 (合肥: 中国科学技术大学) Wu Y 2020 Ph. D. Dissertation (Hefei: University of Science and Technology of China) (in Chinese)
[10]	Gali A, Fyta M, Kaxiras E 2008 Phys. Rev. B 77 155206 Google Scholar
[11]	Acosta V M, Jarmola A, Bauch E, Budker D 2010 Phys. Rev. B 82 201202 Google Scholar
[12]	Loubser J, van Wyk J 1978 Rep. Prog. Phys. 41 1201 Google Scholar
[13]	Manson N B, Harrison J P, Sellars M J 2006 Phys. Rev. B 74 104303 Google Scholar
[14]	Nizovtsev A P, Kilin S Y, Jelezko F, Popa I, Gruber A, Tietz C, Wrachtrup J 2003 Opt. Spectrosc. 94 848 Google Scholar
[15]	Van der Sar T, Wang Z H, Blok M S, Bernien H, Taminiau T H, Toyli D M, Lidar D A, Awschalom D D, Hanson R, Dobrovitski V V 2012 Nature 484 82 Google Scholar
[16]	Weil J A, Bolton J R 2007 Electron Paramagnetic Resonance: Elementary Theory and Practical Applications (Hoboken: John Wiley & Sons, Inc.)
[17]	Victor A C 1962 J. Chem. Phys. 36 1903 Google Scholar
[18]	Rong X, Geng J P, Shi F Z, Liu Y, Xu K B, Ma W C, Kong F, Jiang Z, Wu Y, Du J F 2015 Nat. Commun. 6 8748 Google Scholar
[19]	De Raedt H, Barbara B, Miyashita S, Michielsen K, Bertaina S, Gambarelli S 2012 Phys. Rev. B 85 014408 Google Scholar
[20]	Rong X, Geng J P, Wang Z X, Zhang Q, Ju C Y, Shi F Z, Duan C K, Du J F 2014 Phys. Rev. Lett. 112 050503 Google Scholar
[21]	Geng J P, Wu Y, Wang X T, Xu K B, Shi F Z, Xie Y J, Rong X, Du J F 2016 Phys. Rev. Lett. 117 170501 Google Scholar
[22]	Wu Y, Wang Y, Qin X, Rong X, Du J F 2019 Npj Quantum Inf. 5 1 Google Scholar
[23]	Wu Y, Liu W Q, Geng J P, Song X R, Ye X Y, Duan C K, Rong X, Du J F 2019 Science 364 878 Google Scholar
[24]	Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 82 2417 Google Scholar
[25]	Khodjasteh K, Lidar D A 2005 Phys. Rev. Lett. 95 180501
[26]	Uhrig G S 2007 Phys. Rev. Lett. 98 100504 Google Scholar
[27]	Du J F, Rong X, Zhao N, Wang Y, Yang J H, Liu R B 2009 Nature 461 1265 Google Scholar
[28]	De Lange G, Wang Z H, Riste D, Dobrovitski V V, Hanson R 2010 Science 330 60 Google Scholar
[29]	Naydenov B, Dolde F, Hall L T, Shin C, Fedder H, Hollenberg L C, Jelezko F, Wrachtrup J 2011 Phys. Rev. B 83 081201 Google Scholar
[30]	Liu G Q, Po H C, Du J, Liu R B, Pan X Y 2013 Nat. Commun. 4 2254
[31]	Zhang J F, Souza A M, Brandao F D, Suter D 2014 Phys. Rev. Lett. 112 050502 Google Scholar
[32]	Khodjasteh K, Viola L 2009 Phys. Rev. Lett. 102 080501 Google Scholar
[33]	Khodjasteh K, Lidar D A, Viola L 2010 Phys. Rev. Lett. 104 090501 Google Scholar
[34]	West J R, Lidar D A, Fong B H, Gyure M F 2010 Phys. Rev. Lett. 105 230503 Google Scholar
[35]	Kestner J P, Wang X, Bishop L S, Barnes E, Das Sarma S 2013 Phys. Rev. Lett. 110 140502
[36]	Wang X, Bishop L S, Kestner J P, Barnes E, Sun K, Dar Sarma S 2012 Nat. Commun. 3 997
[37]	Nielsen M A, Chuang I L 2000 Quantum Computing and Quantum Information (Cambridge: Cambridge University Press)
[38]	Wimperis S 1994 J. Magn. Reson. 109 221 Google Scholar
[39]	Ichikawa T, Bando M, Kondo Y, Nakahara M 2011 Phys. Rev. A 84 062311 Google Scholar
[40]	Bando M, Ichikawa T, Kondo Y, Nakahara M 2013 J. Phys. Soc. Japan 82 014004
[41]	Cummins H K, Llewellyn G, Jones J A 2003 Phys. Rev. A 67 042308 Google Scholar
[42]	Knill E, Leibfried D, Reichle R, Britton J, Blakestad R B, Jost J D, Langer C, Ozeri R, Seidelin S, Wineland D J 2008 Phys. Rev. A 77 012307 Google Scholar
[43]	Fowler A G, Mariantoni M, Martinis J M, Cleland A N 2012 Phys. Rev. A 86 032324 Google Scholar
[44]	Zermelo E 1931 Z. Angew. Math. Mech. 11 114 Google Scholar
[45]	Wang X T, Allegra M, Jacobs K, Lloyd S, Lupo C, Mohseni M 2015 Phys. Rev. Lett. 114 170501 Google Scholar
[46]	Barends R, Kelly J, Megrant A, Veitia A, Sank D, Jeffrey E, White T C, Mutus J, Fowler A G, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth B, Neill C, O'Malley P, Roushan P, Vainsencher A, Wenner J, Korotkov A N, Cleland A N, Martinis J M 2014 Nature 508 500 Google Scholar
[47]	Nielsen M A, Chuang I L 1997 Phys. Rev. Lett. 79 321 Google Scholar
[48]	Kim J, Cheong Y, Lee J S, Lee S 2001 Phys. Rev. A 65 012302 Google Scholar
[49]	Vidal G, Masanes L, Cirac J I 2002 Phys. Rev. Lett. 88 047905 Google Scholar
[50]	Shende V V, Markov I L, Bullock S S 2004 Phys. Rev. A 69 062321
[51]	Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243 Google Scholar
[52]	Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 89 270401 Google Scholar
[53]	Bender C M 2007 Rep. Prog. Phys. 70 947 Google Scholar
[54]	Mostafazadeh A 2005 J. Math. Phys. 46 102108 Google Scholar
[55]	Dorey P, Dunning C, Lishman A, Tateo R 2009 J. Phys. A: Math. Theor. 42 465302
[56]	Gong J, Wang Q 2013 J. Phys. A: Math. Theor. 46 485302
[57]	Kunst F K, Edvardsson E, Budich J C, Bergholtz E J 2018 Phys. Rev. Lett. 121 026808 Google Scholar
[58]	Song F, Yao S Y, Wang Z 2019 Phys. Rev. Lett. 123 170401 Google Scholar
[59]	Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S, Ueda M 2018 Phys. Rev. X 8 031079
[60]	Özdemir Ş K, Rotter S, Nori F, Yang L 2019 Nat. Mater. 18 783 Google Scholar
[61]	Miri M-A, Alù A 2019 Science 363 eaar7709
[62]	Bender N, Factor S, Bodyfelt J D, Ramezani H, Christodoulides D N, Ellis F M, Kottos T 2013 Phys. Rev. Lett. 110 234101 Google Scholar
[63]	Assawaworrarit S, Yu X, Fan S 2017 Nature 546 387 Google Scholar
[64]	Choi Y, Hahn C, Yoon J W, Song S H 2018 Nat. Commun. 9 2182
[65]	Bittner S, Dietz B, Günther U, Harney H L, Miski-Oglu M, Richter A, Schäfer F 2012 Phys. Rev. Lett. 108 024101 Google Scholar
[66]	Bender C M, Berntson B K, Parker D, Samuel E 2013 Am. J. Phys. 81 173 Google Scholar
[67]	Zhu X F, Ramezani H, Shi C Z, Zhu J, Zhang X 2014 Phys. Rev. X 4 031042
[68]	Popa B I, Cummer S A 2014 Nat. Commun. 5 3398
[69]	Fleury R, Sounas D, Alù A 2015 Nat. Commun. 6 5905
[70]	Li J M, Harter A K, Liu J, de Melo L, Joglekar Y N, Luo L 2019 Nat. Commun. 10 855
[71]	Naghiloo M, Abbasi M, Joglekar Y N, Murch K W 2019 Nat. Phys. 15 1232 Google Scholar
[72]	Liu W Q, Wu Y, Duan C K, Rong X, Du J F 2021 Phys. Rev. Lett. 126 170506 Google Scholar
[73]	Lau H K, Clerk A A 2018 Nat. Commun. 9 4320
[74]	Chen C, Jin L, Liu R B 2019 New J. Phys. 21 083002 Google Scholar

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Vol. 71, Issue 6 - 2022-03-20

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