Quantum walk with coherent multiple translations induces fast quantum gate operations

Yixiang Zhang; Xin Qiao; Luojia Wang; Yanyan He; Zhaohui Dong; Xianfeng Chen; Luqi Yuan

doi:10.1038/s41377-025-02106-3

Your Location：

Home >

Browse articles >

Quantum walk with coherent multiple translations induces fast quantum gate operations

Original Articles

- Quantum walk with coherent multiple translations induces fast quantum gate operations
- Quantum walk with coherent multiple translations induces fast quantum gate operations
- Light: Science & Applications 2026年15卷第1期页码：242-251
- Affiliations：
  
  1.State Key Laboratory of Photonics and Communications, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
  2.College of Physics and electronics Engineering, Northwest Normal University, Lanzhou 730070, China
  3.Collaborative Innovation Center of Light Manipulations and Applications, Shandong Normal University, Jinan 250358, China
  4.Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
- Author bio：
  
  Xin Qiao (qiaox@nwnu.edu.cn)
  Luqi Yuan (yuanluqi@sjtu.edu.cn)
- Funds：
- DOI：10.1038/s41377-025-02106-3
  中图分类号：
- 收稿：2025-06-08，
  
  修回：2025-09-24，
  
  录用：2025-10-22，
  
  网络出版：2026-01-01，
  
  纸质出版：2026-01-31
- Accepted：
Scan QR Code
Yixiang Zhang, Xin Qiao, Luojia Wang, 等. Quantum walk with coherent multiple translations induces fast quantum gate operations[J]. Light: Science & Applications, 2026,15(1):242-251.

Zhang, Y. X. et al. Quantum walk with coherent multiple translations induces fast quantum gate operations. Light: Science & Applications, 15, 242-251 (2026).
Yixiang Zhang, Xin Qiao, Luojia Wang, 等. Quantum walk with coherent multiple translations induces fast quantum gate operations[J]. Light: Science & Applications, 2026,15(1):242-251. DOI： 10.1038/s41377-025-02106-3.

Zhang, Y. X. et al. Quantum walk with coherent multiple translations induces fast quantum gate operations. Light: Science & Applications, 15, 242-251 (2026). DOI： 10.1038/s41377-025-02106-3.

摘要

Abstract

Quantum walks with one-dimensional translational symmetry are important for quantum algorithms

where the speed-up of the diffusion speed can be reached if long-range couplings are added. Our work studies a scheme of a ring under the strong resonant modulation that can support a discrete-time quantum walk including coherent multiple long-range translations in a natural way along the synthetic frequency dimension. These multiple translation paths are added in a coherent way

which makes the walker evolve under the topological band. Therein

not only the fast diffusion speed is expected

but more importantly

we find that single quantum gate operations can be performed in the quasi-momentum space. In particular

we show the arbitrary single-qubit state preparation and an example of CNOT two-qubit gate with only one time step

dramatically increasing quantum algorithms. Our study uses the modulated ring to provide fast quantum gate operations based on coherent multiple path quantum walk

which may provide unique designs for efficient quantum operations on photonic chips.

关键词

Keywords

references

Aharonov, Y., Davidovich, L. & Zagur y, N. Quantum random walks. Phys. Rev. A 48 , 1687–1690 (1993)..

Farhi, E. & Gutmann, S. Quantum computation & decision trees. Phys. Rev. A 58 , 915–928 (1998)..

Kempe, J. Quantum random walks: an introductory overview. Contemp. Phys. 44 , 307–327 (2003)..

Venegas-Andraca, S. E. Quantum walks: a comprehensive review. Quantum Inf. Process. 11 , 1015–1106 (2012)..

Shenvi, N., Kempe, J. & Whaley, K. B. Quantum random-walk search algorithm. Phys. Rev. A 67 , 052307 (2003)..

Ambainis, A. Quantum walks and their algorithmic applications. Int. J. Quantum Inf. 1 , 507–518 (2003)..

Ambainis, A. Quantum walk algorithm for element distinctness. SIAM J. Comput. 37 , 210–239 (2007)..

Chawla, P., Mangal, R. & Chandrashekar, C. M. Discrete-time quantum walk algorithm for ranking nodes on a network. Quantum Inf. Process. 19 , 158 (2020)..

Akmal, S. & Jin, C. Near-optimal quantum algorithms for string problems. in Proc. Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) (eds Naor, J. & Buchbinder, N. ) 2791–2832 (SIAM, 2022).

Oka, T. et al. Breakdown of an electric-field driven system: a mapping to a quantum walk. Phys. Rev. Lett. 94 , 100602 (2005)..

Chandrashekar, C. M. Disordered-quantum-walk-induced localization of a Bose-Einstein condensate. Phys. Rev. A 83 , 022320 (2011)..

Huerta Alderete, C. et al. Quantum walks and Dirac cellular automata on a programmable trapped-ion quantum computer. Nat. Commun. 11 , 3720 (2020)..

Kitagawa, T. et al. Exploring topological phases with quantum walks. Phys. Rev. A 82 , 033429 (2010)..

Obuse, H. & Kawakami, N. Topological phases and delocalization of quantum walks in random environments. Phys. Rev. B 84 , 195139 (2011)..

Cardano, F. et al. Statistical mom ents of quantum-walk dynamics reveal topological quantum transitions. Nat. Commun. 7 , 11439 (2016)..

Fan, X. Y. et al. Probing Weyl physics with one-dimensional sonic crystals. Phys. Rev. Lett. 122 , 136802 (2019)..

Boyers, E. et al. Exploring 2D synthetic quantum hall physics with a quasiperiodically driven qubit. Phys. Rev. Lett. 125 , 160505 (2020)..

Mittal, V. et al. Persistence of topological phases in non-Hermitian quantum walks. Sci. Rep. 11 , 10262 (2021)..

Lin, Q. et al. Topological phase transitions and mobility edges in non-Hermitian quasicrystals. Phys. Rev. Lett. 129 , 113601 (2022)..

Grudka, A. et al. Topological invariants in quantum walks. Phys. Rev. A 107 , 032201 (2023)..

Aharonov, D. et al. Quantum walks on graphs. in Proc. 33rd ACM Symposium on Theory of Computing , 50–59 (Association for Computing Machinery, 2001).

Ambainis, A. et al. O ne-dimensional quantum walks. in Proc. 33rd ACM Symposium on Theory of Computin g 37-49. (Association for Computing Machinery, 2001).

Grover, L. K. A fast quantum mechanical algorithm for database search. in Proc. 28th ACM Symposium on Theory of Computing , 212–219 (Association for Computing Machinery, 1996)..

Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79 , 325–328 (1997)..

Ambainis, A.,Kempe, J. & Rivosh, A. Coins make quantum walks faster. in Proc. 16th Annual ACM-SIAM Symposium on Discrete Algorithms 1099–1108 (Society for Industrial and Applied Mathematics, 2005)

Fenwick, K. L. et al. Photonic quantum walk with ultrafast time-bin encoding. Optica 11 , 1017–1023 (2024)..

Broome, M. A. et al. Discrete single-photon quantum walks with tunable decoherence. Phys. Rev. Lett. 104 , 153602 (2010)..

Cardano, F. et al. Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons. Nat. Commun. 8 , 15516 (2017)..

Nejadsattari, F. et al. Experimental realization of wave-packet dynamics in cyclic quantum walks. Optica 6 , 174–180 (2019)..

D'Errico, A. et al. Two-dimensional topological quantum walks in the momentum space of structured light. Optica 7 , 108–114 (2020)..

Di Colandrea, F. et al. Ultra-long quantum walks via spin–orbit photonics. Optica 10 , 324–331 (2023)..

Schreiber, A. et al. Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104 , 050502 (2010)..

Schreiber, A. et al. A 2D quantum walk simulation of two-particle dynamics. Science 336 , 55–58 (2012)..

Bagrets, D. et al. Probing the topological Anderson transition with quantum walks. Phys. Rev. Res. 3 , 023183 (2021)..

Held, P. et al. Driven Gaussian quantum walks. Phys. Rev. A 105 , 042210 (2022)..

Boutari, J. et al. Large scale quantum walks by means of optical fiber cavities. J. Opt. 18 , 094007 (2016)..

Sansoni, L. et al. Two-particle bosonic-fermionic quantum walk via integrated photonics. Phys. Rev. Lett. 108 , 010502 (2012)..

Gräfe, M. et al. Integrated photonic quantum walks. J. Opt. 18 , 103002 (2016)..

Childs, A. M. Universal computation by quantum walk. Phys. Rev. Lett. 102 , 180501 (2009)..

Lovett, N. B. et al. Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81 , 042330 (2010)..

Childs, A. M., Gosset, D. & Webb, Z. Universal computation by multiparticle quantum walk. Science 339 , 791–794 (2013)..

Singh, S. et al. Universal quantum computing using single-particle discrete-time quantum walk. Sci. Rep. 11 , 11551 (2021)..

Souza, R. C., Balthazar, W. F. & Huguenin, J. A. O. Universal quantum gates for path photonic qubit. Quantum Inf. Process. 21 , 68 (2022)..

Mandal, M., Goswami, I. & Mukhopadhyay, S. Implementation of programmable photonic one qubit quantum gates using intensity and phase encoding jointly. J. Opt. 52 , 145–153 (2023)..

Hu, Y. W. et al. Realization of high-dimensional frequency crystals in electro-optic microcombs. Optica 7 , 1189–1194 (2020)..

Fan, L. L. et al. Experimental realization of convolution processing in photonic synthetic frequency dimensions. Sci. Adv. 9 , eadi4956 (2023)..

Balčytis, A. et al. Synthetic dimension band structures on a Si CMOS photonic platform. Sci. Adv. 8 , eabk0468 (2022)..

Javid, U. A. et al. Chip-scale simulations in a quantum-correlated synthetic space. Nat. Photonics 17 , 883–890 (2023)..

Dinh, H. X. et al. Reconfigurable synthetic dimension frequency lattices in an integrated lithium niobate ring cavity. Commun. Phys. 7 , 185 (2024)..

Yuan, L. Q., Shi, Y. & Fan, S. H. Photonic gauge potential in a system with a synthetic frequency dimension. Opt. Lett. 41 , 741–744 (2016)..

Yuan, L. Q. & Fan, S. H. Bloch oscillation and unidirectional translation of frequency in a dynamically modulated ring resonator. Optica 3 , 1014–1018 (2016)..

Yuan, L. Q., Dutt, A. & Fan, S. H. Synthetic frequency dimensions in dynamically modulated ring resonators. APL Photonics 6 , 071102 (2021)..

Senanian, A. et al. Programmable large-scale simulation of bosonic transport in optical synthetic frequency lattices. Nat. Phys. 19 , 1333–1339 (2023)..

Cheng, D. L., Wang, K. & Fan, S. H. Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension. Phys. Rev. Lett. 130 , 083601 (2023)..

Cheng, D. L. et al. Non-Abelian lattice gauge fields in photonic synthetic frequency dimensions. Nature 637 , 52–56 (2025)..

Lin, Q., Yi, W. & Xue, P. Manipulating directional flow in a two-dimensional photonic quantum walk under a synthetic magnetic field. Nat. Commun. 14 , 6283 (2023)..

Buarque, A. R. C. et al. Discrete-time quantum walk dispersion control through long-range correlations. Phys. Rev. E 107 , 064139 (2023)..

Pang, Z. H. et al. Synthetic non-Abelian gauge fields for non-Hermitian systems. Phys. Rev. Lett. 132 , 043804 (2024)..

Kitagawa, T. Topological phenomena in quantum walks: elementary introduction to the physics of topological phases. Quantum Inf. Process. 11 , 1107–1148 (2012)..

Barone, S. R., Narcowich, M. A. & Narcowich, F. J. Floquet theory and applications. Phys. Rev. A 15 , 1109–1125 (1977)..

Dutt, A. et al. A single photonic cavity with two independent physical synthetic dimensions. Science 367 , 59–64 (2020)..

Spitzer, F. Principles of Random Walk (Springer Science & Business Media, 2001).

Mülken, O. & Blumen, A. Efficiency of quantum and classical transport on graphs. Phys. Rev. E 73 , 066117 (2006)..

Xu, X. P.Continuous-time quantum walks on one-dimensional regular networks. Phys. Rev. E 77 , 061127 (2008)..

Williams, C. P. Quantum gates. in Explorations in Quantum Computing 2nd edn (ed. Williams, C. P. ) 51–122 (Springer, 2011).

Shahwar, D. et al. On-chip polarization rotators using metasurface. ACS Omega 9 , 33055–33063 (2024)..

Chawla, P. et al. Multi-qubit quantum computing using discrete-time quantum walks on closed graphs. Sci. Rep. 13 , 12078 (2023)..

Sengupta, K. et al. Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk. Print at https://doi.org/10.48550/arXiv.2403.06665 https://doi.org/10.48550/arXiv.2403.06665 (2024).

Dutt, A. et al. Creating boundaries along a synthetic frequency dimension. Nat. Commun. 13 , 3377 (2022)..

Cheng, D. L. et al. Multi-dimensional band structure spectroscopy in the synthetic frequency dimension. Light Sci. Appl. 12 , 158 (2023)..

Englebert, N. et al. Bloch oscillations of coherently driven dissipative solitonsin a synthetic dimension. Nat. Phys. 19 , 1014–1021 (2023)..

Boes, A. et al. Lithium niobate photonics: unlocking the electromagnetic spectrum. Science 379 , eabj4396 (2023)..

Ye, R. et al. Construction ofvarious time-varying Hamiltonians on thin-film lithium niobate chip. Phys. Rev. Lett. 134 , 163802 (2025)..

Wang, Z. A. et al. On-chip photonic simulating band structures toward arbitrary-range coupled frequency lattices. Phys. Rev. Lett. 133 , 233805 (2024)..

Yuan, L. Q. et al. Synthetic space with arbitrary dimensions in a few rings undergoing dynamic modulation. Phys. Rev. B 97 , 104105 (2018)..

Qiao, X. et al. Topological degener acy breaking in synthetic frequency lattice by Floquet engineering. Nanophotonics 12 , 3807–3815 (2023)..

Li, G. Z. et al. Direct extraction of topological Zak phase with the synthetic dimension. Light Sci. Appl. 12 , 81 (2023)..

浏览量

Downloads

CSCD

文章被引用时，请邮件提醒。

Submit

工具集

关联资源

暂无数据