Kerr-effect-based quantum logical gates in decoherence-free subspace

Fang-Fang Du; Gang Fan; Xue-Mei Ren

doi:10.22331/q-2024-05-13-1342

Kerr-effect-based quantum logical gates in decoherence-free subspace

Science and Technology on Electronic Test and Measurement Laboratory, North University of China, Taiyuan 030051, China

Published:	2024-05-13, volume 8, page 1342
Eprint:	arXiv:2306.05625v5
Doi:	https://doi.org/10.22331/q-2024-05-13-1342
Citation:	Quantum 8, 1342 (2024).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

The decoherence effect caused by the coupling between the system and the environment undoubtedly leads to the errors in efficient implementations of two (or three) qubit logical gates in quantum information processing. Fortunately, decoherence-free subspace (DFS) introduced can effectively decrease the influence of decoherence effect. In this paper, we propose some schemes for setting up a family of quantum control gates, including controlled-NOT (CNOT), Toffoli, and Fredkin gates for two or three logical qubits by means of cross-Kerr nonlinearities in DFS. These three logical gates require neither complicated quantum computational circuits nor auxiliary photons (or entangled states). The success probabilities of three logical gates are approximate 1 by performing the corresponding classical feed-forward operations based on the different measuring results of the X-homodyne detectors, and their fidelities are robust against the photon loss with the current technology. The proposed logical gates rely on only simple linear-optics elements, available single-qubit operations, and mature measurement methods, making our proposed gates be feasible and efficient in practical applications.

Featured image: Schematic diagram of the Toffoli gate in DFS based on cross-Kerr nonlinearities

► BibTeX data

@article{Du2024kerreffectbased,
  doi = {10.22331/q-2024-05-13-1342},
  url = {https://doi.org/10.22331/q-2024-05-13-1342},
  title = {Kerr-effect-based quantum logical gates in decoherence-free subspace},
  author = {Du, Fang-Fang and Fan, Gang and Ren, Xue-Mei},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1342},
  month = may,
  year = {2024}
}

► References

[1] Lov K. Grover Michael A. Nielsen, Isaac Chuang. ``Quantum computation and quantum information''. Am. J. Phys. 70, 558–559 (2002).
https://doi.org/10.1119/1.1463744

[2] Mingxia Huo and Ying Li. ``Error-resilient Monte Carlo quantum simulation of imaginary time''. Quantum 7, 916 (2023).
https://doi.org/10.22331/q-2023-02-09-916

[3] Masahito Hayashi and Yuxiang Yang. ``Efficient algorithms for quantum information bottleneck''. Quantum 7, 936 (2023).
https://doi.org/10.22331/q-2023-03-02-936

[4] XiuZhe Luo, JinGuo Liu, Pan Zhang, and Lei Wang. ``Yao.jl: Extensible, Efficient Framework for Quantum Algorithm Design''. Quantum 4, 341 (2020).
https://doi.org/10.22331/q-2020-10-11-341

[5] Xin Wang, Zhixin Song, and Youle Wang. ``Variational Quantum Singular Value Decomposition''. Quantum 5, 483 (2021).
https://doi.org/10.22331/q-2021-06-29-483

[6] G. L. Long and X. S. Liu. ``Theoretically efficient high-capacity quantum-key-distribution scheme''. Phys. Rev. A 65, 032302 (2002).
https://doi.org/10.1103/PhysRevA.65.032302

[7] Wei Zhang, Dong Sheng Ding, Yu Bo Sheng, Lan Zhou, Bao Sen Shi, and Guang Can Guo. ``Quantum secure direct communication with quantum memory''. Phys. Rev. Lett. 118, 220501 (2017).
https://doi.org/10.1103/PhysRevLett.118.220501

[8] Feng Zhu, Wei Zhang, Yu Bo Sheng, and Yi Dong Huang. ``Experimental long-distance quantum secure direct communication''. Sci. Bull. 62, 1519–1524 (2017).
https://doi.org/10.1016/j.scib.2017.10.023

[9] Fang-Fang Du, Yong-Ting Liu, Zhen-Rong Shi, Yu-Xi Liang, Jun Tang, and Jun Liu. ``Efficient hyperentanglement purification for three-photon systems with the fidelity-robust quantum gates and hyperentanglement link''. Opt. Express 27, 27046–27061 (2019).
https://doi.org/10.1364/OE.27.027046

[10] Tao Li and Gui Lu Long. ``Quantum secure direct communication based on single-photon bell-state measurement''. New J. Phys. 22, 063017 (2020).
https://doi.org/10.1088/1367-2630/ab8ab5

[11] Zixin Huang, Peter P. Rohde, Dominic W. Berry, Pieter Kok, Jonathan P. Dowling, and Cosmo Lupo. ``Photonic quantum data locking''. Quantum 5, 447 (2021).
https://doi.org/10.22331/q-2021-04-28-447

[12] Chuan Wang. ``Quantum secure direct communication: Intersection of communication and cryptography''. Fundam. Res. 1, 91–92 (2021).
https://doi.org/10.1016/j.fmre.2021.01.002

[13] Zhantong Qi, Yuanhua Li, Yiwen Huang, Juan Feng, Yuanlin Zheng, and Xianfeng Chen. ``A 15-user quantum secure direct communication network''. Light Sci. Appl. 10, 183 (2021).
https://doi.org/10.1038/s41377-021-00634-2

[14] G. L. Long and H. Zhang. ``Drastic increase of channel capacity in quantum secure direct communication using masking''. Sci. Bull. 66, 1267–1269 (2021).
https://doi.org/10.1016/j.scib.2021.04.016

[15] Yu Bo Sheng, Lan Zhou, and Gui Lu Long. ``One-step quantum secure direct communication''. Sci. Bull. 67, 367–374 (2022).
https://doi.org/10.1016/j.scib.2021.11.002

[16] Yue Ru Zhou, Qing Feng Zhang, Fei Fei Liu, Yu Hong Han, Yong Pan Gao, Ling Fan, Ru Zhang, and Cong Cao. ``Controllable nonreciprocal phonon laser in a hybrid photonic molecule based on directional quantum squeezing''. Opt. Express 32, 2786–2803 (2024).
https://doi.org/10.1364/OE.512280

[17] Peng Zhao, Meng Ying Yang, Sha Zhu, Lan Zhou, Wei Zhong, Ming Ming Du, and Yu Bo Sheng. ``Generation of hyperentangled state encoded in three degrees of freedom''. Sci. China Phys. Mech. 66, 100311 (2023).
https://doi.org/10.1007/s11433-023-2164-7

[18] Yun Feng Guo, Wei Zhong, Lan Zhou, and Yu Bo Sheng. ``Supersensitivity of kerr phase estimation with two-mode squeezed vacuum states''. Phys. Rev. A 105, 032609 (2022).
https://doi.org/10.1103/PhysRevA.105.032609

[19] Cong Cao, Yu-Hong Han, Li Zhang, Ling Fan, Yu-Wen Duan, and Ru Zhang. ``High-fidelity universal quantum controlled gates on electron-spin qubits in quantum dots inside single-sided optical microcavities''. Adv. Quantum Technol. 2, 1900081 (2019).
https://doi.org/10.1002/qute.201900081

[20] Cong Cao, Li Zhang, Yu Hong Han, Pan Pan Yin, Ling Fan, Yu Wen Duan, and Ru Zhang. ``Complete and faithful hyperentangled-bell-state analysis of photon systems using a failure-heralded and fidelity-robust quantum gate''. Opt. Express 28, 2857–2872 (2020).
https://doi.org/10.1364/OE.384360

[21] Yi Ming Wu, Gang Fan, and Fang Fang Du. ``Error-detected three-photon hyperparallel toffoli gate with state-selective reflection''. Front. Phys. 17, 51502 (2022).
https://doi.org/10.1007/s11467-022-1172-3

[22] Xiu Yu Zhang, Cong Cao, Yong Pan Gao, Ling Fan, Ru Zhang, and Chuan Wang. ``Generation and manipulation of phonon lasering in a two-drive cavity magnomechanical system''. New J. Phys. 25, 053039 (2023).
https://doi.org/10.1088/1367-2630/acd717

[23] Wen Qiang Liu and Hai Rui Wei. ``Optimal synthesis of the fredkin gate in a multilevel system''. New J. Phys. 22, 063026 (2020).
https://doi.org/10.1088/1367-2630/ab8e13

[24] Wen Qiang Liu, Hai Rui Wei, and Leong Chuan Kwek. ``Low-cost fredkin gate with auxiliary space''. Phys. Rev. Appl. 14, 054057 (2020).
https://doi.org/10.1103/PhysRevApplied.14.054057

[25] Jaromír Fiurášek. ``Linear optical fredkin gate based on partial-swap gate''. Phys. Rev. A 78, 032317 (2008).
https://doi.org/10.1103/PhysRevA.78.032317

[26] Fabio Dell’Anno, Silvio De Siena, and Fabrizio Illuminati. ``Multiphoton quantum optics and quantum state engineering''. Phys. Rep. 428, 53–168 (2006).
https://doi.org/10.1016/j.physrep.2006.01.004

[27] Gui-Long Jiang, Jun-Bin Yuan, Wen-Qiang Liu, and Hai-Rui Wei. ``Efficient and deterministic high-dimensional controlled-swap gates on hybrid linear optical systems with high fidelity''. Phys. Rev. Appl. 21, 014001 (2024).
https://doi.org/10.1103/PhysRevApplied.21.014001

[28] Kae Nemoto and W. J. Munro. ``Nearly deterministic linear optical controlled-not gate''. Phys. Rev. Lett. 93, 250502 (2004).
https://doi.org/10.1103/PhysRevLett.93.250502

[29] Qing Lin and Jian Li. ``Quantum control gates with weak cross-kerr nonlinearity''. Phys. Rev. A 79, 022301 (2009).
https://doi.org/10.1103/PhysRevA.79.022301

[30] Qing Lin and Bing He. ``Single-photon logic gates using minimal resources''. Phys. Rev. A 80, 042310 (2009).
https://doi.org/10.1103/PhysRevA.80.042310

[31] Li Dong, Sen Lin Wang, Cen Cui, Xue Geng, Qing Yang Li, Hai Kuan Dong, Xiao Ming Xiu, and Ya Jun Gao. ``Polarization toffoli gate assisted by multiple degrees of freedom''. Opt. Lett. 43, 4635–4638 (2018).
https://doi.org/10.1364/OL.43.004635

[32] Fang Fang Du, Gang Fan, Xue Mei Ren, and Ming Ma. ``Deterministic hyperparallel control gates with weak kerr effects''. Adv. Quantum Technol. 6, 2300201 (2023).
https://doi.org/10.1002/qute.202300201

[33] Hai Rui Wei and Fu Guo Deng. ``Compact quantum gates on electron-spin qubits assisted by diamond nitrogen-vacancy centers inside cavities''. Phys. Rev. A 88, 042323 (2013).
https://doi.org/10.1103/PhysRevA.88.042323

[34] Qing Ai, Peng-Bo Li, Wei Qin, Jie-Xing Zhao, C. P. Sun, and Franco Nori. ``The nv metamaterial: Tunable quantum hyperbolic metamaterial using nitrogen vacancy centers in diamond''. Phys. Rev. B 104, 014109 (2021).
https://doi.org/10.1103/PhysRevB.104.014109

[35] Fang Fang Du, Xue Mei Ren, Ming Ma, and Gang Fan. ``Qudit-based high-dimensional controlled-not gate''. Opt. Lett. 49, 1229 (2024).
https://doi.org/10.1364/ol.518336

[36] Hai Rui Wei and Fu Guo Deng. ``Universal quantum gates on electron-spin qubits with quantum dots inside single-side optical microcavities''. Opt. Express 22, 593–607 (2014).
https://doi.org/10.1364/OE.22.000593

[37] Hai Rui Wei, Yan Bei Zheng, Ming Hua, and Guo Fu Xu. ``Robust-fidelity hyperparallel controlled-phase-flip gate through microcavities''. Appl. Phys. Express 13, 082007 (2020).
https://doi.org/10.35848/1882-0786/aba64a

[38] Yu Hong Han, Cong Cao, Ling Fan, and Ru Zhang. ``Heralded high-fidelity quantum hyper-cnot gates assisted by charged quantum dots inside single-sided optical microcavities''. Opt. Express 29, 20045–20062 (2021).
https://doi.org/10.1364/OE.426325

[39] Guo Zhu Song, Jin Liang Guo, Qian Liu, Hai Rui Wei, and Gui Lu Long. ``Heralded quantum gates for hybrid systems via waveguide-mediated photon scattering''. Phys. Rev. A 104, 012608 (2021).
https://doi.org/10.1103/PhysRevA.104.012608

[40] Tao Li, Adam Miranowicz, Ke Yu Xia, and Franco Nori. ``Resource-efficient analyzer of bell and greenberger-horne-zeilinger states of multiphoton systems''. Phys. Rev. A 100, 052302 (2019).
https://doi.org/10.1103/PhysRevA.100.052302

[41] Guo Zhu Song, Ming Jie Tao, Jing Qiu, and Hai Rui Wei. ``Quantum entanglement creation based on quantum scattering in one-dimensional waveguides''. Phys. Rev. A 106, 032416 (2022).
https://doi.org/10.1103/PhysRevA.106.032416

[42] Fang Fang Du and Zhen Rong Shi. ``Robust hybrid hyper-controlled-not gates assisted by an input-output process of low-q cavities''. Opt. Express 27, 17493–17506 (2019).
https://doi.org/10.1364/OE.27.017493

[43] Fang Fang Du, Yi Ming Wu, and Gang Fan. ``Refined quantum gates for $\lambda$-type atom-photon hybrid systems''. Adv. Quantum Technol. 6, 2300090 (2023).
https://doi.org/10.1002/qute.202300090

[44] Frank Arute, Kunal Arya, Ryan Babbush, Dave Bacon, Joseph C Bardin, Rami Barends, Rupak Biswas, Sergio Boixo, Fernando GSL Brandao, David A Buell, et al. ``Quantum supremacy using a programmable superconducting processor''. Nature 574, 505–510 (2019).
https://doi.org/10.1038/s41586-019-1666-5

[45] Lu Ming Duan and Guang Can Guo. ``Preserving coherence in quantum computation by pairing quantum bits''. Phys. Rev. Lett. 79, 1953–1956 (1997).
https://doi.org/10.1103/PhysRevLett.79.1953

[46] Hua Wei, Wan Li Yang, Zhi Jiao Deng, and Mang Feng. ``Many-qubit network employing cavity qed in a decoherence-free subspace''. Phys. Rev. A 78, 014304 (2008).
https://doi.org/10.1103/PhysRevA.78.014304

[47] Z. J. Deng, M. Feng, and K. L. Gao. ``Preparation of entangled states of four remote atomic qubits in decoherence-free subspace''. Phys. Rev. A 75, 024302 (2007).
https://doi.org/10.1103/PhysRevA.75.024302

[48] Lei Chen, Xiao Ming Xiu, Li Dong, Shou Zhang, Shi Lei Su, Shu Chen, and Er Jun Liang. ``Conversion of knill–laflamme–milburn entanglement to greenberger–horne–zeilinger entanglement in decoherence-free subspace''. Ann. Phys. 534, 2100365 (2022).
https://doi.org/10.1002/andp.202100365

[49] Lei Chen, Xiao Ming Xiu, Li Dong, Nan Nan Liu, Cai Peng Shen, Shou Zhang, Shu Chen, and Shi Lei Su. ``Direct conversion of greenberger–horne–zeilinger state to knill–laflamme–milburn state in decoherence-free subspace''. Opt. Lett. 47, 2262–2265 (2022).
https://doi.org/10.1002/andp.202100365

[50] Fang Fang Du, Xue Mei Ren, Zhi Guo Fan, Ling Hui Li, Xin Shan Du, Ming Ma, Gang Fan, and Jing Guo. ``Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates''. Opt. Express 32, 1686 (2024).
https://doi.org/10.1364/oe.508088

[51] Yi Fan Qiao, Jia Qiang Chen, Xing Liang Dong, Bo Long Wang, Xin Lei Hei, Cai Peng Shen, Yuan Zhou, and Peng Bo Li. ``Generation of greenberger-horne-zeilinger states for silicon-vacancy centers using a decoherence-free subspace''. Phys. Rev. A 105, 032415 (2022).
https://doi.org/10.1103/PhysRevA.105.032415

[52] Hua Wei, ZhiJiao Deng, XiaoLong Zhang, and Mang Feng. ``Transfer and teleportation of quantum states encoded in decoherence-free subspace''. Phys. Rev. A 76, 054304 (2007).
https://doi.org/10.1103/PhysRevA.76.054304

[53] Alejandro Fonseca. ``High-dimensional quantum teleportation under noisy environments''. Phys. Rev. A 100, 062311 (2019).
https://doi.org/10.1103/PhysRevA.100.062311

[54] Xiao Xiao Hu, Fei Hao Zhang, Yan Song Li, and Gui Lu Long. ``Optimizing quantum gates within decoherence-free subspaces''. Phys. Rev. A 104, 062612 (2021).
https://doi.org/10.1103/PhysRevA.104.062612

[55] D. Bacon, J. Kempe, D. A. Lidar, and K. B. Whaley. ``Universal fault-tolerant quantum computation on decoherence-free subspaces''. Phys. Rev. Lett. 85, 1758–1761 (2000).
https://doi.org/10.1103/PhysRevLett.85.1758

[56] Qiong Chen and Mang Feng. ``Quantum-information processing in decoherence-free subspace with low-q cavities''. Phys. Rev. A 82, 052329 (2010).
https://doi.org/10.1103/PhysRevA.82.052329

[57] J. S. Pedernales, F. Cosco, and M. B. Plenio. ``Decoherence-free rotational degrees of freedom for quantum applications''. Phys. Rev. Lett. 125, 090501 (2020).
https://doi.org/10.1103/PhysRevLett.125.090501

[58] Arne Hamann, Pavel Sekatski, and Wolfgang Dür. ``Approximate decoherence free subspaces for distributed sensing''. Quantum Sci. Technol. 7, 025003 (2022).
https://doi.org/10.1088/2058-9565/ac44de

[59] Xin Wen Wang, Deng Yu Zhang, Shi Qing Tang, Li Jun Xie, Zhi Yong Wang, and Le Man Kuang. ``Photonic two-qubit parity gate with tiny cross–kerr nonlinearity''. Phys. Rev. A 85, 052326 (2012).
https://doi.org/10.1103/PhysRevA.85.052326

[60] Io Chun Hoi, Anton F. Kockum, Tauno Palomaki, Thomas M. Stace, Bixuan Fan, Lars Tornberg, Sankar R. Sathyamoorthy, Göran Johansson, Per Delsing, and C. M. Wilson. ``Giant cross–kerr effect for propagating microwaves induced by an artificial atom''. Phys. Rev. Lett. 111, 053601 (2013).
https://doi.org/10.1103/PhysRevLett.111.053601

[61] Pieter Kok, W. J. Munro, Kae Nemoto, T. C. Ralph, Jonathan P. Dowling, and G. J. Milburn. ``Linear optical quantum computing with photonic qubits''. Rev. Mod. Phys. 79, 135–174 (2007).
https://doi.org/10.1103/RevModPhys.79.135

[62] Michael Siomau, Ali A. Kamli, Sergey A. Moiseev, and Barry C. Sanders. ``Entanglement creation with negative index metamaterials''. Phys. Rev. A 85, 050303 (2012).
https://doi.org/10.1103/PhysRevA.85.050303

[63] Hanhee Paik, D. I. Schuster, Lev S. Bishop, G. Kirchmair, G. Catelani, A. P. Sears, B. R. Johnson, M. J. Reagor, L. Frunzio, L. I. Glazman, S. M. Girvin, M. H. Devoret, and R. J. Schoelkopf. ``Observation of high coherence in josephson junction qubits measured in a three-dimensional circuit qed architecture''. Phys. Rev. Lett. 107, 240501 (2011).
https://doi.org/10.1103/PhysRevLett.107.240501

[64] Gerhard Kirchmair, Brian Vlastakis, Zaki Leghtas, Simon E. Nigg, Hanhee Paik, Eran Ginossar, Mazyar Mirrahimi, Luigi Frunzio, S. M. Girvin, and R. J. Schoelkopf. ``Observation of quantum state collapse and revival due to the single-photon kerr effect''. Nature 495, 205–209 (2013).
https://doi.org/10.1038/nature11902

[65] M. D. Lukin and A. Imamoğlu. ``Nonlinear optics and quantum entanglement of ultraslow single photons''. Phys. Rev. Lett. 84, 1419–1422 (2000).
https://doi.org/10.1103/PhysRevLett.84.1419

[66] M. Bajcsy, A. S. Zibrov, and M. D. Lukin. ``Stationary pulses of light in an atomic medium''. Nature 426, 638–641 (2003).
https://doi.org/10.1038/nature02176

[67] Zeng Bin Wang, Karl Peter Marzlin, and Barry C. Sanders. ``Large cross-phase modulation between slow copropagating weak pulses in $^{87}\mathrm{Rb}$''. Phys. Rev. Lett. 97, 063901 (2006).
https://doi.org/10.1103/PhysRevLett.97.063901

[68] Yi Hsin Chen, Meng Jung Lee, Weilun Hung, Ying Cheng Chen, Yong Fan Chen, and Ite A. Yu. ``Demonstration of the interaction between two stopped light pulses''. Phys. Rev. Lett. 108, 173603 (2012).
https://doi.org/10.1103/PhysRevLett.108.173603

[69] Hyunseok Jeong. ``Quantum computation using weak nonlinearities: Robustness against decoherence''. Phys. Rev. A 73, 052320 (2006).
https://doi.org/10.1103/PhysRevA.73.052320

[70] Amir Feizpour, Xingxing Xing, and Aephraim M. Steinberg. ``Amplifying single-photon nonlinearity using weak measurements''. Phys. Rev. Lett. 107, 133603 (2011).
https://doi.org/10.1103/PhysRevLett.107.133603

[71] Seckin Sefi, Vishal Vaibhav, and Peter van Loock. ``Measurement induced optical kerr interaction''. Phys. Rev. A 88, 012303 (2013).
https://doi.org/10.1103/PhysRevA.88.012303

[72] Monika Bartkowiak, Lian Ao Wu, and Adam Miranowicz. ``Quantum circuits for amplification of kerr nonlinearity via quadrature squeezing''. J. Phys. B: At. Mol. Opt. Phys. 47, 145501 (2014).
https://doi.org/10.1088/0953-4075/47/14/145501

[73] Holger F Hofmann, Kunihiro Kojima, Shigeki Takeuchi, and Keiji Sasaki. ``Optimized phase switching using a single-atom nonlinearity''. J. Opt. B: Quantum Semiclass. Opt. 5, 218 (2003).
https://doi.org/10.1088/1464-4266/5/3/304

[74] Christoffer Wittmann, Ulrik L. Andersen, Masahiro Takeoka, Denis Sych, and Gerd Leuchs. ``Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector''. Phys. Rev. A 81, 062338 (2010).
https://doi.org/10.1103/PhysRevA.81.062338

[75] Li Dong, Jun Xi Wang, Qing Yang Li, Hong Zhi Shen, Hai Kuan Dong, Xiao Ming Xiu, Ya Jun Gao, and Choo Hiap Oh. ``Nearly deterministic preparation of the perfect $w$ state with weak cross-kerr nonlinearities''. Phys. Rev. A 93, 012308 (2016).
https://doi.org/10.1103/PhysRevA.93.012308

[76] Michael A. Nielsen and Isaac L. Chuang. ``Quantum computation and quantum information''. Cambridge University Press. (2010).
https://doi.org/10.1017/CBO9780511976667

Cited by

[1] Ling-Hui Li, Zhuo-Ya Bai, and Fang-Fang Du, "Robust-fidelity high-dimensional qudit-dependent entanglement creation for photon systems with balanced state-selective reflection", Optics & Laser Technology 195, 114549 (2026).

[2] Chang Gao, Fei-Fei Liu, Ze-Qiang Fan, Ling Fan, Ru Zhang, and Cong Cao, "Quantum-Squeezing-Engineered Third-Order Kerr Nonlinearity and Optical High-Order Sideband Comb in a Composite Resonator-Atom System", IEEE Journal of Selected Topics in Quantum Electronics 1 (2024).

[3] Fang-Fang Du, Yuan Yao, Ling-Hui Li, and Yang-Yang Wang, "Error-predicted interconversion for hybrid photon-spin entangled states", Laser Physics Letters 22 9, 095207 (2025).

[4] Fang‐Fang Du, Xin‐Shan Du, Zhuo‐Ya Bai, and Qiang Zhu, "High‐Fidelity Qudit‐Encoded High‐Dimensional Photonic Toffoli Gate Through Imperfect Photon Scattering", Advanced Quantum Technologies 8 11, e00350 (2025).

[5] Fang-Fang Du and Xue-Mei Ren, "A deterministic qudit-dependent high-dimensional photonic quantum gate with weak cross-kerr nonlinearity", Optics & Laser Technology 180, 111440 (2025).

[6] Hao Yuan, Guo-Zhu Pan, and Gang Zhang, "Asymmetric bidirectional quantum 2$$\Leftrightarrow $$3 qubit teleportation via seven-qubit entangled state", Quantum Information Processing 23 10, 351 (2024).

[7] Xue‐Mei Ren and Fang‐Fang Du, "High‐Dimensional Photonic Quantum Computing with a Measurement‐Free Auxiliary System", Advanced Quantum Technologies 7 11, 2400208 (2024).

[8] Ming Ma, Qiang Zhu, and Fang‐Fang Du, "Kerr‐Effect‐Based High‐Dimensional Entanglement Generation for Qudit Systems", Advanced Quantum Technologies 8 5, 2500010 (2025).

[9] Heng-Zhi Niu, Ling-Hui Li, Zhi-Guo Fan, and Fang-Fang Du, "Efficient interconversion between three-electron-spin W state and KLM state for silicon-vacancy system", Laser Physics 35 9, 095204 (2025).

[10] Fang-Fang Du, Xue-Mei Ren, and Jing Guo, "Error-heralded high-dimensional quantum gate with robust fidelity", Optics Express 32 18, 31633 (2024).

[11] Zhi‐Guo Fan, Zhuo‐Ya Bai, Qiu‐Lin Tan, and Fang‐Fang Du, "Computing‐Heightened Low‐Cost High‐Dimensional Controlled‐SUM Gates", Advanced Quantum Technologies 8 11, e00370 (2025).

[12] Fang-Fang Du, Hao-Lin Shi, and Ling-Hui Li, "Heralded robust-fidelity mutual conversions of Λ-type three-atom entangled states", Laser Physics Letters 22 9, 095203 (2025).

[13] Xiao-Xi Yao and Yusuf Turek, "Non-Gaussian state preparation and enhancement using weak-value amplification", npj Quantum Information 12 1, 30 (2026).

[14] Gang Fan, Heng‐Zhi Niu, Qiu‐Lin Tan, and Fang‐Fang Du, "A Computation‐Enhanced High‐Dimensional Quantum Gate for Silicon‐Vacancy Spins", Advanced Quantum Technologies 8 10, 2500167 (2025).

[15] Fang‐Fang Du, Xue‐Mei Ren, and Qiu‐Lin Tan, "A Computation‐Strengthened High‐Dimensional Three‐Qudit Toffoli Gate", Advanced Quantum Technologies 7 12, 2400313 (2024).

[16] Fang‐Fang Du, Ming Ma, and Wen‐Yao Liu, "Preparation of Arbitrary High‐Fidelity Decoherence‐Free States for a Four‐Qubit Hybrid System via Whispering‐Gallery‐Mode Microresonator", Annalen der Physik 537 5, 2400435 (2025).

[17] Fang‐Fang Du, Hao‐Lin Shi, Xue‐Shuo Deng, Cheng‐Yan Gao, and Qiu‐Lin Tan, "Deterministic Kerr‐Effect‐Based Mutual Conversions of Entangled States in Decoherence‐Free Subspace", Annalen der Physik 537 11, e00319 (2025).

[18] Fang‐Fang Du, Ming Ma, and Qiu‐lin Tan, "Error‐Heralded and Deterministic Interconversion Between W State and Greenberger–Horne–Zeilinger State with Faithful Quantum Gates in Decoherence‐Free‐Subspace", Advanced Quantum Technologies 7 12, 2400322 (2024).

[19] Fang-Fang 芳芳 Du 杜, Zhi-Guo 志国 Fan 范, Xue-Mei 雪梅 Ren 任, Ming 明 Ma 马, and Wen-Yao 文耀 Liu 刘, "Established conversions for hybrid entangled states assisted by error-predicted parity-discriminated devices", Chinese Physics B 34 1, 010303 (2025).

[20] Li Dong, Zi-Qing Yuan, Zi-Lin Zhao, Si-Ge Chen, Xin-Yi Zhang, Yan-Qiang Ji, Jiu-Ming Li, and Xiao-Ming Xiu, "Logic-qubit CNOT gates in decoherence-free subspaces assisted by the nitrogen-vacancy center", Optics Letters 50 3, 722 (2025).

[21] Fang-Fang Du, Ming Ma, Zhuo-Ya Bai, and Qiu-lin Tan, "Generation of arbitrary high-dimensional qudit-based entangled states", Physical Review A 111 3, 032604 (2025).

[22] Fang-Fang Du, Zhi-Guo Fan, Xue-Mei Ren, Ming Ma, and Wen-Yao Liu, "In-depth conversion of entangled states for electron-spin systems with error-avoiding parity-check gates", The European Physical Journal Plus 139 11, 1031 (2024).

[23] Jiaxin Ou, Yupeng Duan, and Yingjie Du, "Cross-Kerr nonlinearity and four-wave mixing in an N -type four-level coherent system", Physical Review A 112 1, 013534 (2025).

[24] Fang-Fang Du, Ling-Hui Li, Xue-Mei Ren, Yang-Yang Wang, and Wen-Yao Liu, "Error-rejecting entanglement purification and concentration for one-dimensional waveguide-emitter system", Laser Physics 34 11, 115203 (2024).

[25] Fang-Fang Du, Ming Ma, and Qiu-lin Tan, "Heralded interconversion between hyperentangled W state and hyperentangled KLM state assisted by nitrogen vacancy centers coupled with microresonators", Scientific Reports 15 1, 2505 (2025).

[26] Wen‐Xiu Zhang, Guo‐Zhu Song, and Hai‐Rui Wei, "The Simplified Quantum Circuits for Implementing Quantum Teleportation", Annalen der Physik 536 10, 2400231 (2024).

[27] She‑Xiang Jiang and Qi-Ke Zhang, "Multi-level hierarchical multi-hop quantum teleportation based on GHZ-Bell states", Physica Scripta 100 8, 085104 (2025).

[28] Zhi-Guo Fan, Xue-Shuo Deng, Qiu-Lin Tan, and Fang-Fang Du, "Linear-optics-based high-dimensional quantum gate with qudits", Optics Letters 50 18, 5771 (2025).

[29] Yousef Mafi, Ali Kookani, Hossein Aghababa, Masoud Barati, and Mohammadreza Kolahdouz, "Bidirectional quantum controlled teleportation in multi-hop networks: a generalized protocol for the arbitrary n-qubit state through the noisy channel", Quantum Information Processing 23 10, 350 (2024).

[30] Xin‐Shan Du, Qiu‐Lin Tan, and Fang‐Fang Du, "Error‐Detected Robust‐fidelity SWAP and (SWAP)1/m Gates for Quantum‐Dot Spins", Advanced Quantum Technologies 8 9, 2400619 (2025).

[31] David S. Simon, Christopher R. Schwarze, Anthony D. Manni, Abdoulaye Ndao, and Alexander V. Sergienko, "Deterministic linear-optical computing with symmetry-based qubits", Quantum Information Processing 25 5, 136 (2026).

[32] Fang-Fang Du, Zhi-Guo Fan, Zhuo-Ya Bai, and Qiu-Lin Tan, "Heralded fidelity-robust high-dimensional quantum computing", New Journal of Physics 27 7, 074102 (2025).

[33] Xue‐Mei Ren, Jing Guo, and Fang‐Fang Du, "Heralded and Complete Interconversion Between W State and Knill–Laflamme–Milburn State via State‐Selective Reflection with Robust Fidelity", Annalen der Physik 536 10, 2400215 (2024).

[34] Fang-Fang Du, Xin-Shan Du, Zhuo-Ya Bai, Qiang Zhu, and Qiu-Lin Tan, "Robust-fidelity high-dimensional controlled-controlled-SUM gate with qudits", EPJ Quantum Technology 12 1, 95 (2025).

[35] Ling‐Hui Li and Fang‐Fang Du, "Faithful Interconversions of Three‐Logic‐Qubit Entangled States Via Error‐Predicted Module in Decoherence‐Free Subspace", Advanced Quantum Technologies 8 10, 2500188 (2025).

[36] Fang-Fang Du, Ling-Hui Li, Xue-Mei Ren, Ming Ma, Yang-Yang Wang, and Wen-Yao Liu, "Heralded high-efficiency entanglement concentration of cluster states for photon systems with linear optics via time-delay effect", Laser Physics Letters 21 9, 095205 (2024).

[37] Xiao-Ming Xiu, Si-Ge Chen, Zi-Lin Zhao, Zi-Qing Yuan, Xin-Yi Zhang, and Li Dong, "High-fidelity n-qubit quantum controlled-not gates on quantum-dot spins", Optics Express 32 21, 37382 (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-11 23:34:02) and SAO/NASA ADS (last updated successfully 2026-08-11 23:34:03). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.