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Isolated zero mode in a quantum computer from a duality twist

Sutapa Samanta, Derek S. Wang, Armin Rahmani, and Aditi Mitra

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Researchers demonstrated the first quantum simulation of an isolated zero mode using an IBM quantum computer by engineering a duality twist defect in a transverse-field Ising chain. The mode exhibits infinite lifetime even in finite systems. The team used Floquet driving to create the defect, which acts as a domain wall between regions related by Kramers-Wannier duality. This marks the first experimental realization of such topological defects in a digital quantum device. Detection relied on measuring persistent autocorrelation functions with optimized sampling and error mitigation techniques. The zero mode’s stability was confirmed despite integrability-breaking perturbations. The work bridges theory and experiment in studying noninvertible generalized symmetries, which have implications for both condensed matter and high-energy physics. It validates quantum computers as tools for exotic physics exploration. This approach could enable broader investigations of topological defects and duality symmetries in quantum materials, advancing understanding of emergent quantum phenomena.

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AbstractInvestigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $\mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.Popular summaryIn this work, we use an IBM quantum computer to study an unusual and remarkably stable quantum mode created by a special kind of defect, known as a duality twist, in a periodically driven quantum spin chain. Crossing this defect transforms the system into a dual version of itself. We generate the mode through precise time-dependent control and detect it using measurements that reveal long-lived, persistent quantum behavior. Our results demonstrate how modern quantum devices can be used to explore exotic behaviors of quantum matter, particularly generalized symmetries that are of broad interest in both high-energy and condensed-matter physics.► BibTeX data@article{Samanta2025isolatedzeromodein, doi = {10.22331/q-2025-12-30-1957}, url = {https://doi.org/10.22331/q-2025-12-30-1957}, title = {Isolated zero mode in a quantum computer from a duality twist}, author = {Samanta, Sutapa and Wang, Derek S. and Rahmani, Armin and Mitra, Aditi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {9}, pages = {1957}, month = dec, year = {2025} }► References [1] Emilio Cobanera, Gerardo Ortiz, and Zohar Nussinov. ``The bond-algebraic approach to dualities''. Advances in Physics 60, 679–798 (2011). https://doi.org/10.1080/00018732.2011.619814 [2] Nathan Seiberg, T. Senthil, Chong Wang, and Edward Witten. ``A duality web in 2+1 dimensions and condensed matter physics''. Ann. Phys. 374, 395–433 (2016). https://doi.org/10.1016/j.aop.2016.08.007 [3] Andrés M. Somoza, Pablo Serna, and Adam Nahum. ``Self-dual criticality in three-dimensional $z_2$ gauge theory with matter''. Phys. Rev. X 11, 041008 (2021). https://doi.org/10.1103/PhysRevX.11.041008 [4] Laurens Lootens, Clement Delcamp, and Frank Verstraete. ``Dualities in one-dimensional quantum lattice models: Topological sectors''. PRX Quantum 5, 010338 (2024). https://doi.org/10.1103/PRXQuantum.5.010338 [5] Erik Verlinde. ``Fusion rules and modular transformations in 2d conformal field theory''. Nucl. Phys. B 300, 360–376 (1988). https://doi.org/10.1016/0550-3213(88)90603-7 [6] Lakshya Bhardwaj, Lea E. Bottini, Sakura Schäfer-Nameki, and Apoorv Tiwari. ``Non-invertible higher-categorical symmetries''. SciPost Phys. 14, 007 (2023). https://doi.org/10.21468/SciPostPhys.14.1.007 [7] David Aasen, Roger S K Mong, and Paul Fendley. ``Topological defects on the lattice: I. the ising model''. J. Phys. A: Math. Theor. 49, 354001 (2016). https://doi.org/10.1088/1751-8113/49/35/354001 [8] Ryan Thorngren and Yifan Wang. ``Fusion category symmetry. Part I. Anomaly in-flow and gapped phases''. JHEP 04, 132 (2024). arXiv:1912.02817. https://doi.org/10.1007/JHEP04(2024)132 arXiv:1912.02817 [9] David Aasen, Paul Fendley, and Roger SK Mong. ``Topological defects on the lattice: dualities and degeneracies'' (2020). url: doi.org/10.48550/arXiv.2008.08598. https://doi.org/10.48550/arXiv.2008.08598 [10] Liang Kong, Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang, and Hao Zheng. ``Algebraic higher symmetry and categorical symmetry: A holographic and entanglement view of symmetry''. Phys. Rev. Res. 2, 043086 (2020). https://doi.org/10.1103/PhysRevResearch.2.043086 [11] John McGreevy. ``Generalized symmetries in condensed matter''. Annual Review of Condensed Matter Physics 14, 57–82 (2023). https://doi.org/10.1146/annurev-conmatphys-040721-021029 [12] Davide Gaiotto, Anton Kapustin, Nathan Seiberg, and Brian Willett. ``Generalized global symmetries''. J.

High Energy Phys. 2015, 172 (2015). https://doi.org/10.1007/JHEP02(2015)172 [13] Davide Gaiotto, Ji Hoon Lee, and Jingxiang Wu. ``Integrable kondo problems''. J.

High Energy Phys. 2021 (2021). https://doi.org/10.1007/jhep04(2021)268 [14] Meng Cheng and Nathan Seiberg. ``Lieb-Schultz-Mattis, Luttinger, and 't Hooft - anomaly matching in lattice systems''. SciPost Phys. 15, 051 (2023). https://doi.org/10.21468/SciPostPhys.15.2.051 [15] Luisa Eck and Paul Fendley. ``From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects''. SciPost Phys. 16, 127 (2024). https://doi.org/10.21468/SciPostPhys.16.5.127 [16] John Preskill. ``Quantum Computing in the NISQ era and beyond''. Quantum 2, 79 (2018). https://doi.org/10.22331/q-2018-08-06-79 [17] H. A. Kramers and G. H. Wannier. ``Statistics of the two-dimensional ferromagnet. Part 1.''. Phys. Rev. 60, 252–262 (1941). https://doi.org/10.1103/PhysRev.60.252 [18] Mao Tian Tan, Yifan Wang, and Aditi Mitra. ``Topological defects in floquet circuits''. SciPost Physics 16 (2024). https://doi.org/10.21468/scipostphys.16.3.075 [19] Akash Sinha, Tinu Justin, Pramod Padmanabhan, and Vladimir Korepin. ``The yang–baxter integrability of the critical ising chain''. Journal of Statistical Mechanics: Theory and Experiment 2025, 103102 (2025). https://doi.org/10.1088/1742-5468/ae0690 [20] Hua-Chen Zhang and Germán Sierra. ``Kramers-wannier self-duality and non-invertible translation symmetry in quantum chains: a wave-function perspective''. Journal of High Energy Physics 2025, 157 (2025). https://doi.org/10.1007/JHEP05(2025)157 [21] John L. Cardy. ``Boundary conditions, fusion rules and the verlinde formula''. Nucl. Phys. B 324, 581–596 (1989). https://doi.org/10.1016/0550-3213(89)90521-X [22] G Schutz. ```duality twisted' boundary conditions in n-state potts models''. Journal of Physics A: Mathematical and General 26, 4555 (1993). https://doi.org/10.1088/0305-4470/26/18/021 [23] Masaki Oshikawa and Ian Affleck. ``Boundary conformal field theory approach to the critical two-dimensional ising model with a defect line''. Nuclear Physics B 495, 533–582 (1997). https://doi.org/10.1016/S0550-3213(97)00219-8 [24] V.B. Petkova and J.-B. Zuber. ``Generalised twisted partition functions''. Physics Letters B 504, 157–164 (2001). https://doi.org/10.1016/s0370-2693(01)00276-3 [25] Uwe Grimm. ``Spectrum of a duality twisted Ising quantum chain''. J. Phys. A 35, L25–L30 (2002). arXiv:hep-th/0111157. https://doi.org/10.1088/0305-4470/35/3/101 arXiv:hep-th/0111157 [26] Jürg Fröhlich, Jürgen Fuchs, Ingo Runkel, and Christoph Schweigert. ``Kramers-wannier duality from conformal defects''. Phys. Rev. Lett. 93, 070601 (2004). https://doi.org/10.1103/PhysRevLett.93.070601 [27] Chi-Ming Chang, Ying-Hsuan Lin, Shu-Heng Shao, Yifan Wang, and Xi Yin. ``Topological defect lines and renormalization group flows in two dimensions''. Journal of High Energy Physics 2019 (2019). https://doi.org/10.1007/jhep01(2019)026 [28] A. Y. Kitaev. ``Unpaired majorana fermions in quantum wires''. Phys.-Usp. 44 (2001). url: dx.doi.org/10.1070/1063-7869/44/10S/S29. https://doi.org/10.1070/1063-7869/44/10S/S29 [29] Paul Fendley. ``Strong zero modes and eigenstate phase transitions in the xyz/interacting majorana chain''. Journal of Physics A: Mathematical and Theoretical 49, 30LT01 (2016). https://doi.org/10.1088/1751-8113/49/30/30LT01 [30] Manisha Thakurathi, Aavishkar A. Patel, Diptiman Sen, and Amit Dutta. ``Floquet generation of majorana end modes and topological invariants''. Phys. Rev. B 88, 155133 (2013). https://doi.org/10.1103/PhysRevB.88.155133 [31] Daniel J. Yates, Fabian H. L. Essler, and Aditi Mitra. ``Almost strong ($0,{\pi}$) edge modes in clean interacting one-dimensional floquet systems''. Phys. Rev. B 99, 205419 (2019). https://doi.org/10.1103/PhysRevB.99.205419 [32] Aditi Mitra, Hsiu-Chung Yeh, Fei Yan, and Achim Rosch. ``Nonintegrable floquet ising model with duality twisted boundary conditions''. Phys. Rev. B 107, 245416 (2023). https://doi.org/10.1103/PhysRevB.107.245416 [33] Armin Rahmani, Kevin J. Sung, Harald Putterman, Pedram Roushan, Pouyan Ghaemi, and Zhang Jiang. ``Creating and manipulating a laughlin-type ${\nu}=1/3$ fractional quantum hall state on a quantum computer with linear depth circuits''. PRX Quantum 1, 020309 (2020). https://doi.org/10.1103/PRXQuantum.1.020309 [34] K. J. Satzinger et al. ``Realizing topologically ordered states on a quantum processor''. Science 374, 1237–1241 (2021). https://doi.org/10.1126/science.abi8378 [35] John P. T. Stenger, Nicholas T. Bronn, Daniel J. Egger, and David Pekker. ``Simulating the dynamics of braiding of majorana zero modes using an ibm quantum computer''. Phys. Rev. Res. 3, 033171 (2021). https://doi.org/10.1103/PhysRevResearch.3.033171 [36] Yu-Jie Liu, Kirill Shtengel, Adam Smith, and Frank Pollmann. ``Methods for simulating string-net states and anyons on a digital quantum computer''. PRX Quantum 3, 040315 (2022). https://doi.org/10.1103/PRXQuantum.3.040315 [37] Ammar Kirmani, Kieran Bull, Chang-Yu Hou, Vedika Saravanan, Samah Mohamed Saeed, Zlatko Papić, Armin Rahmani, and Pouyan Ghaemi. ``Probing geometric excitations of fractional quantum hall states on quantum computers''. Phys. Rev. Lett. 129, 056801 (2022). https://doi.org/10.1103/PhysRevLett.129.056801 [38] T. I. Andersen et al. ``Non-abelian braiding of graph vertices in a superconducting processor''. Nature 618, 264–269 (2023). https://doi.org/10.1038/s41586-023-05954-4 [39] Nikhil Harle, Oles Shtanko, and Ramis Movassagh. ``Observing and braiding topological majorana modes on programmable quantum simulators''. Nat. Comm. 14, 2286 (2023). https://doi.org/10.1038/s41467-023-37725-0 [40] Ammar Kirmani, Derek S. Wang, Pouyan Ghaemi, and Armin Rahmani. ``Braiding fractional quantum hall quasiholes on a superconducting quantum processor''. Phys. Rev. B 108, 064303 (2023). https://doi.org/10.1103/PhysRevB.108.064303 [41] X. Mi and et al. ``Noise-resilient edge modes on a chain of superconducting qubits''. Science 378, 785–790 (2022). https://doi.org/10.1126/science.abq5769 [42] Madhav Sinha, Fei Yan, Linnea Grans-Samuelsson, Ananda Roy, and Hubert Saleur. ``Lattice realizations of topological defects in the critical (1+1)-d three-state Potts model''. JHEP 07, 225 (2024). arXiv:2310.19703. https://doi.org/10.1007/JHEP07(2024)225 arXiv:2310.19703 [43] Nathan Seiberg, Sahand Seifnashri, and Shu-Heng Shao. ``Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space''. SciPost Phys. 16, 154 (2024). arXiv:2401.12281. https://doi.org/10.21468/SciPostPhys.16.6.154 arXiv:2401.12281 [44] Aswin Parayil Mana, Yabo Li, Hiroki Sukeno, and Tzu-Chieh Wei. ``Kennedy-Tasaki transformation and noninvertible symmetry in lattice models beyond one dimension''. Phys. Rev. B 109, 245129 (2024). arXiv:2402.09520. https://doi.org/10.1103/PhysRevB.109.245129 arXiv:2402.09520 [45] Arkya Chatterjee, Ömer M. Aksoy, and Xiao-Gang Wen. ``Quantum phases and transitions in spin chains with non-invertible symmetries''. SciPost Phys. 17, 115 (2024). https://doi.org/10.21468/SciPostPhys.17.4.115 [46] Da-Chuan Lu, Zhengdi Sun, and Yi-Zhuang You. ``Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems''. SciPost Phys. 17, 136 (2024). https://doi.org/10.21468/SciPostPhys.17.5.136 [47] Weiguang Cao, Linhao Li, and Masahito Yamazaki. ``Generating lattice non-invertible symmetries''. SciPost Phys. 17, 104 (2024). https://doi.org/10.21468/SciPostPhys.17.4.104 [48] Fei Yan, Robert Konik, and Aditi Mitra. ``Duality defect in a deformed transverse-field ising model''. Phys. Rev. Res. 7, 033198 (2025). https://doi.org/10.1103/ctxg-k3b6 [49] Markus Hauru, Glen Evenbly, Wen Wei Ho, Davide Gaiotto, and Guifre Vidal. ``Topological conformal defects with tensor networks''. Phys. Rev. B 94, 115125 (2016). https://doi.org/10.1103/PhysRevB.94.115125 [50] David Rogerson, Frank Pollmann, and Ananda Roy. ``Entanglement entropy and negativity in the ising model with defects''. Journal of High Energy Physics 2022 (2022). https://doi.org/10.1007/jhep06(2022)165 [51] Ananda Roy and Hubert Saleur. ``Entanglement entropy in the ising model with topological defects''. Phys. Rev. Lett. 128, 090603 (2022). https://doi.org/10.1103/PhysRevLett.128.090603 [52] Hsiu-Chung Yeh, Achim Rosch, and Aditi Mitra. ``Decay rates of almost strong modes in floquet spin chains beyond fermi's golden rule''. Phys. Rev. B 108, 075112 (2023). https://doi.org/10.1103/PhysRevB.108.075112 [53] Matthew B. Hastings and Jeongwan Haah. ``Dynamically Generated Logical Qubits''. Quantum 5, 564 (2021). https://doi.org/10.22331/q-2021-10-19-564 [54] Kaelyn J. Ferris, A. J. Rasmusson, Nicholas T. Bronn, and Olivia Lanes. ``Quantum Simulation on Noisy Superconducting Quantum Computers'' (2022). url: doi.org/10.48550/arXiv.2209.02795. https://doi.org/10.48550/arXiv.2209.02795 [55] Paul D. Nation, Hwajung Kang, Neereja Sundaresan, and Jay M. Gambetta. ``Scalable mitigation of measurement errors on quantum computers''. PRX Quantum 2, 040326 (2021). https://doi.org/10.1103/prxquantum.2.040326 [56] Ying Li and Simon C. Benjamin. ``Efficient variational quantum simulator incorporating active error minimization''. Phys. Rev. X 7, 021050 (2017). https://doi.org/10.1103/PhysRevX.7.021050 [57] Kristan Temme, Sergey Bravyi, and Jay M. Gambetta. ``Error mitigation for short-depth quantum circuits''. Phys. Rev. Lett. 119, 180509 (2017). https://doi.org/10.1103/PhysRevLett.119.180509 [58] Pedro Rivero, Friederike Metz, Areeq Hasan, Agata M. Brańczyk, and Caleb Johnson. ``Zero noise extrapolation prototype''. https://github.com/qiskit-community/prototype-zne (2022). https://github.com/qiskit-community/prototype-zneCited byCould not fetch Crossref cited-by data during last attempt 2025-12-30 08:39:06: Could not fetch cited-by data for 10.22331/q-2025-12-30-1957 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2025-12-30 08:39:07: No response from ADS or unable to decode the received json data when getting the list of citing works.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. AbstractInvestigating the interplay of dualities, generalized symmetries, and topological defects beyond theoretical models is an important challenge in condensed matter physics and quantum materials. A simple model exhibiting this physics is the transverse-field Ising model, which can host a topological defect that performs the Kramers-Wannier duality transformation. When acting on one point in space, this duality defect imposes the duality twisted boundary condition and binds a single zero mode. This zero mode is unusual as it lacks a localized partner in the same $\mathbb{Z}_2$ sector and has an infinite lifetime, even in finite systems. Using Floquet driving of a closed Ising chain with a duality defect, we generate this zero mode in a digital quantum computer. We detect the mode by measuring its associated persistent autocorrelation function using an efficient sampling protocol and a compound strategy for error mitigation. We also show that the zero mode resides at the domain wall between two regions related by a Kramers-Wannier duality transformation. Finally, we highlight the robustness of the isolated zero mode to integrability- and symmetry-breaking perturbations. Our findings provide a method for exploring exotic topological defects, associated with noninvertible generalized symmetries, in digitized quantum devices.Popular summaryIn this work, we use an IBM quantum computer to study an unusual and remarkably stable quantum mode created by a special kind of defect, known as a duality twist, in a periodically driven quantum spin chain. Crossing this defect transforms the system into a dual version of itself. We generate the mode through precise time-dependent control and detect it using measurements that reveal long-lived, persistent quantum behavior. Our results demonstrate how modern quantum devices can be used to explore exotic behaviors of quantum matter, particularly generalized symmetries that are of broad interest in both high-energy and condensed-matter physics.► BibTeX data@article{Samanta2025isolatedzeromodein, doi = {10.22331/q-2025-12-30-1957}, url = {https://doi.org/10.22331/q-2025-12-30-1957}, title = {Isolated zero mode in a quantum computer from a duality twist}, author = {Samanta, Sutapa and Wang, Derek S. and Rahmani, Armin and Mitra, Aditi}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {9}, pages = {1957}, month = dec, year = {2025} }► References [1] Emilio Cobanera, Gerardo Ortiz, and Zohar Nussinov. ``The bond-algebraic approach to dualities''. Advances in Physics 60, 679–798 (2011). https://doi.org/10.1080/00018732.2011.619814 [2] Nathan Seiberg, T. Senthil, Chong Wang, and Edward Witten. ``A duality web in 2+1 dimensions and condensed matter physics''. Ann. Phys. 374, 395–433 (2016). https://doi.org/10.1016/j.aop.2016.08.007 [3] Andrés M. Somoza, Pablo Serna, and Adam Nahum. ``Self-dual criticality in three-dimensional $z_2$ gauge theory with matter''. Phys. Rev. X 11, 041008 (2021). https://doi.org/10.1103/PhysRevX.11.041008 [4] Laurens Lootens, Clement Delcamp, and Frank Verstraete. ``Dualities in one-dimensional quantum lattice models: Topological sectors''. PRX Quantum 5, 010338 (2024). https://doi.org/10.1103/PRXQuantum.5.010338 [5] Erik Verlinde. ``Fusion rules and modular transformations in 2d conformal field theory''. Nucl. Phys. B 300, 360–376 (1988). https://doi.org/10.1016/0550-3213(88)90603-7 [6] Lakshya Bhardwaj, Lea E. Bottini, Sakura Schäfer-Nameki, and Apoorv Tiwari. ``Non-invertible higher-categorical symmetries''. SciPost Phys. 14, 007 (2023). https://doi.org/10.21468/SciPostPhys.14.1.007 [7] David Aasen, Roger S K Mong, and Paul Fendley. ``Topological defects on the lattice: I. the ising model''. J. Phys. A: Math. Theor. 49, 354001 (2016). https://doi.org/10.1088/1751-8113/49/35/354001 [8] Ryan Thorngren and Yifan Wang. ``Fusion category symmetry. Part I. Anomaly in-flow and gapped phases''. JHEP 04, 132 (2024). arXiv:1912.02817. https://doi.org/10.1007/JHEP04(2024)132 arXiv:1912.02817 [9] David Aasen, Paul Fendley, and Roger SK Mong. ``Topological defects on the lattice: dualities and degeneracies'' (2020). url: doi.org/10.48550/arXiv.2008.08598. https://doi.org/10.48550/arXiv.2008.08598 [10] Liang Kong, Tian Lan, Xiao-Gang Wen, Zhi-Hao Zhang, and Hao Zheng. ``Algebraic higher symmetry and categorical symmetry: A holographic and entanglement view of symmetry''. Phys. Rev. Res. 2, 043086 (2020). https://doi.org/10.1103/PhysRevResearch.2.043086 [11] John McGreevy. ``Generalized symmetries in condensed matter''. Annual Review of Condensed Matter Physics 14, 57–82 (2023). https://doi.org/10.1146/annurev-conmatphys-040721-021029 [12] Davide Gaiotto, Anton Kapustin, Nathan Seiberg, and Brian Willett. ``Generalized global symmetries''. J.

High Energy Phys. 2015, 172 (2015). https://doi.org/10.1007/JHEP02(2015)172 [13] Davide Gaiotto, Ji Hoon Lee, and Jingxiang Wu. ``Integrable kondo problems''. J.

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