Scalable quantum simulator with an extended gate set in giant atoms

Guangze Chen; Anton Frisk Kockum

doi:10.22331/q-2026-01-30-1992

Scalable quantum simulator with an extended gate set in giant atoms

Guangze Chen and Anton Frisk Kockum

Department of Microtechnology and Nanoscience, Chalmers University of Technology, 41296 Gothenburg, Sweden

Published:	2026-01-30, volume 10, page 1992
Editor:	Angelo Carollo
Eprint:	arXiv:2503.04537v3
Doi:	https://doi.org/10.22331/q-2026-01-30-1992
Citation:	Quantum 10, 1992 (2026).

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Abstract

Quantum computation and quantum simulation require a versatile gate set to optimize circuit compilation for practical applications. However, existing platforms are often limited to specific gate types or rely on parametric couplers to extend their gate set, which compromises scalability. Here, we propose a scalable quantum simulator with an extended gate set based on giant-atom three-level systems, which can be implemented with superconducting circuits. Unlike conventional small atoms, giant atoms couple to the environment at multiple points, introducing interference effects that allow exceptional tunability of their interactions. By leveraging this tunability, our setup supports both CZ and iSWAP gates through simple frequency adjustments, eliminating the need for parametric couplers. This dual-gate capability enhances circuit efficiency, reducing the overhead for quantum simulation. As a demonstration, we showcase the simulation of spin dynamics in dissipative Heisenberg XXZ spin chains, highlighting the setup's ability to tackle complex open quantum many-body dynamics. Finally, we discuss how a two-dimensional extension of our system could enable fault-tolerant quantum computation, paving the way for a universal quantum processor.

Featured image: Artistic sketch of a giant-atom-based scalable quantum simulator, and how iSWAP and CZ gates can be performed on this simulator by simple frequency tuning.

PresentatioN Quantum simulation of open quantum many-body systems with giant atoms by Guangze Chen and Anton Frisk Kockum

Popular summary

Building scalable quantum simulators requires not only increasing qubit numbers, but also realizing the right kinds of interactions at the hardware level. Many existing platforms provide only a limited set of native two-qubit gates, forcing simulations to rely on long gate sequences that increase circuit depth and sensitivity to noise.

We propose a quantum-simulation architecture based on giant atoms: artificial atoms that couple to a waveguide at multiple, spatially separated points. Owing to interference effects inherent to this multi-point coupling, giant atoms offer additional control over qubit–qubit interactions. We show that this enables a richer native gate set without added hardware complexity.

In particular, our scheme realizes both iSWAP and controlled-phase gates within the same device through simple frequency tuning. Access to both interaction types substantially reduces circuit depth compared to architectures restricted to a single gate, improving simulation efficiency and robustness.

Beyond coherent control, the giant-atom platform allows engineered dissipation via interference-controlled decay rates, enabling natural simulations of open quantum systems. We demonstrate this capability by simulating a dissipative XXZ spin chain, a paradigmatic model of non-equilibrium many-body physics.

Finally, we discuss extensions to two-dimensional layouts compatible with surface-code error correction. Overall, our work shows how the spatial structure of giant atoms can be exploited to achieve scalable, versatile quantum simulation with minimal hardware overhead.

► BibTeX data

@article{Chen2026scalablequantum,
  doi = {10.22331/q-2026-01-30-1992},
  url = {https://doi.org/10.22331/q-2026-01-30-1992},
  title = {Scalable quantum simulator with an extended gate set in giant atoms},
  author = {Chen, Guangze and Kockum, Anton Frisk},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {10},
  pages = {1992},
  month = jan,
  year = {2026}
}

► References

[1] I. M. Georgescu, S. Ashhab, and Franco Nori. ``Quantum simulation''. Reviews of Modern Physics 86, 153–185 (2014).
https://doi.org/10.1103/RevModPhys.86.153

[2] Ehud Altman et al. ``Quantum Simulators: Architectures and Opportunities''. PRX Quantum 2, 017003 (2021).
https://doi.org/10.1103/PRXQuantum.2.017003

[3] Benedikt Fauseweh. ``Quantum many-body simulations on digital quantum computers: State-of-the-art and future challenges''. Nature Communications 15, 2123 (2024).
https://doi.org/10.1038/s41467-024-46402-9

[4] Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter. ``Elementary gates for quantum computation''. Physical Review A 52, 3457–3467 (1995).
https://doi.org/10.1103/PhysRevA.52.3457

[5] Karen Wintersperger, Florian Dommert, Thomas Ehmer, Andrey Hoursanov, Johannes Klepsch, Wolfgang Mauerer, Georg Reuber, Thomas Strohm, Ming Yin, and Sebastian Luber. ``Neutral atom quantum computing hardware: performance and end-user perspective''. EPJ Quantum Technology 10, 32 (2023).
https://doi.org/10.1140/epjqt/s40507-023-00190-1

[6] Thomas Strohm, Karen Wintersperger, Florian Dommert, Daniel Basilewitsch, Georg Reuber, Andrey Hoursanov, Thomas Ehmer, Davide Vodola, and Sebastian Luber. ``Ion-Based Quantum Computing Hardware: Performance and End-User Perspective'' (2024). arXiv:2405.11450.
arXiv:2405.11450

[7] Frank Leymann and Johanna Barzen. ``The bitter truth about gate-based quantum algorithms in the NISQ era''. Quantum Science and Technology 5, 044007 (2020).
https://doi.org/10.1088/2058-9565/abae7d

[8] Justin Kalloor, Mathias Weiden, Ed Younis, John Kubiatowicz, Bert De Jong, and Costin Iancu. ``Quantum Hardware Roofline: Evaluating the Impact of Gate Expressivity on Quantum Processor Design'' (2024). arXiv:2403.00132.
arXiv:2403.00132

[9] Yan Ge, Wu Wenjie, Chen Yuheng, Pan Kaisen, Lu Xudong, Zhou Zixiang, Wang Yuhan, Wang Ruocheng, and Yan Junchi. ``Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects'' (2024). arXiv:2407.00736.
arXiv:2407.00736

[10] Christian Križan, Janka Biznárová, Liangyu Chen, Emil Hogedal, Amr Osman, Christopher W Warren, Sandoko Kosen, Hang-Xi Li, Tahereh Abad, Anuj Aggarwal, Marco Caputo, Jorge Fernández-Pendás, Akshay Gaikwad, Leif Grönberg, Andreas Nylander, Robert Rehammar, Marcus Rommel, Olga I Yuzephovich, Anton Frisk Kockum, Joonas Govenius, Giovanna Tancredi, and Jonas Bylander. ``Quantum swap gate realized with cz and iswap gates in a superconducting architecture''. New Journal of Physics 27, 074507 (2025).
https://doi.org/10.1088/1367-2630/adeba7

[11] Deanna M. Abrams, Nicolas Didier, Blake R. Johnson, Marcus P. da Silva, and Colm A. Ryan. ``Implementation of xy entangling gates with a single calibrated pulse''. Nature Electronics 3, 744–750 (2020).
https://doi.org/10.1038/s41928-020-00498-1

[12] M. Ganzhorn, G. Salis, D. J. Egger, A. Fuhrer, M. Mergenthaler, C. Müller, P. Müller, S. Paredes, M. Pechal, M. Werninghaus, and S. Filipp. ``Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform''. Physical Review Research 2, 033447 (2020).
https://doi.org/10.1103/PhysRevResearch.2.033447

[13] Eyob A. Sete, Nicolas Didier, Angela Q. Chen, Shobhan Kulshreshtha, Riccardo Manenti, and Stefano Poletto. ``Parametric-Resonance Entangling Gates with a Tunable Coupler''. Physical Review Applied 16, 024050 (2021).
https://doi.org/10.1103/PhysRevApplied.16.024050

[14] Rigetti QCS. ``Aspen-m-3 quantum processor'' (2023).

[15] R. Barends, C. M. Quintana, A. G. Petukhov, Yu Chen, D. Kafri, K. Kechedzhi, R. Collins, O. Naaman, S. Boixo, F. Arute, K. Arya, D. Buell, B. Burkett, Z. Chen, B. Chiaro, A. Dunsworth, B. Foxen, A. Fowler, C. Gidney, M. Giustina, R. Graff, T. Huang, E. Jeffrey, J. Kelly, P. V. Klimov, F. Kostritsa, D. Landhuis, E. Lucero, M. McEwen, A. Megrant, X. Mi, J. Mutus, M. Neeley, C. Neill, E. Ostby, P. Roushan, D. Sank, K. J. Satzinger, A. Vainsencher, T. White, J. Yao, P. Yeh, A. Zalcman, H. Neven, V. N. Smelyanskiy, and John M. Martinis. ``Diabatic gates for frequency-tunable superconducting qubits''. Physical Review Letters 123, 210501 (2019).
https://doi.org/10.1103/PhysRevLett.123.210501

[16] Atsushi Noguchi, Alto Osada, Shumpei Masuda, Shingo Kono, Kentaro Heya, Samuel Piotr Wolski, Hiroki Takahashi, Takanori Sugiyama, Dany Lachance-Quirion, and Yasunobu Nakamura. ``Fast parametric two-qubit gates with suppressed residual interaction using the second-order nonlinearity of a cubic transmon''. Physical Review A 102, 062408 (2020).
https://doi.org/10.1103/PhysRevA.102.062408

[17] Eyob A. Sete, Nicolas Didier, Angela Q. Chen, Shobhan Kulshreshtha, Riccardo Manenti, and Stefano Poletto. ``Parametric-resonance entangling gates with a tunable coupler''. Physical Review Applied 16, 024050 (2021).
https://doi.org/10.1103/PhysRevApplied.16.024050

[18] S. A. Caldwell, N. Didier, C. A. Ryan, E. A. Sete, A. Hudson, P. Karalekas, R. Manenti, M. P. da Silva, R. Sinclair, E. Acala, N. Alidoust, J. Angeles, A. Bestwick, M. Block, B. Bloom, A. Bradley, C. Bui, L. Capelluto, R. Chilcott, J. Cordova, G. Crossman, M. Curtis, S. Deshpande, T. El Bouayadi, D. Girshovich, S. Hong, K. Kuang, M. Lenihan, T. Manning, A. Marchenkov, J. Marshall, R. Maydra, Y. Mohan, W. O'Brien, C. Osborn, J. Otterbach, A. Papageorge, J.-P. Paquette, M. Pelstring, A. Polloreno, G. Prawiroatmodjo, V. Rawat, M. Reagor, R. Renzas, N. Rubin, D. Russell, M. Rust, D. Scarabelli, M. Scheer, M. Selvanayagam, R. Smith, A. Staley, M. Suska, N. Tezak, D. C. Thompson, T.-W. To, M. Vahidpour, N. Vodrahalli, T. Whyland, K. Yadav, W. Zeng, and C. Rigetti. ``Parametrically activated entangling gates using transmon qubits''. Physical Review Applied 10, 034050 (2018).
https://doi.org/10.1103/PhysRevApplied.10.034050

[19] Nathan Lacroix, Christoph Hellings, Christian Kraglund Andersen, Agustin Di Paolo, Ants Remm, Stefania Lazar, Sebastian Krinner, Graham J. Norris, Mihai Gabureac, Johannes Heinsoo, Alexandre Blais, Christopher Eichler, and Andreas Wallraff. ``Improving the Performance of Deep Quantum Optimization Algorithms with Continuous Gate Sets''. PRX Quantum 1, 110304 (2020).
https://doi.org/10.1103/PRXQuantum.1.020304

[20] Youngkyu Sung, Leon Ding, Jochen Braumüller, Antti Vepsäläinen, Bharath Kannan, Morten Kjaergaard, Ami Greene, Gabriel O. Samach, Chris McNally, David Kim, Alexander Melville, Bethany M. Niedzielski, Mollie E. Schwartz, Jonilyn L. Yoder, Terry P. Orlando, Simon Gustavsson, and William D. Oliver. ``Realization of High-Fidelity CZ and ZZ-Free iSWAP Gates with a Tunable Coupler''. Physical Review X 11, 021058 (2021).
https://doi.org/10.1103/PhysRevX.11.021058

[21] Helin Zhang, Chunyang Ding, D.K. Weiss, Ziwen Huang, Yuwei Ma, Charles Guinn, Sara Sussman, Sai Pavan Chitta, Danyang Chen, Andrew A. Houck, Jens Koch, and David I. Schuster. ``Tunable Inductive Coupler for High-Fidelity Gates Between Fluxonium Qubits''. PRX Quantum 5, 020326 (2024).
https://doi.org/10.1103/PRXQuantum.5.020326

[22] Zhen Chen, Weiyang Liu, Yanjun Ma, Weijie Sun, Ruixia Wang, He Wang, Huikai Xu, Guangming Xue, Haisheng Yan, Zhen Yang, Jiayu Ding, Yang Gao, Feiyu Li, Yujia Zhang, Zikang Zhang, Yirong Jin, Haifeng Yu, Jianxin Chen, and Fei Yan. ``Efficient implementation of arbitrary two-qubit gates using unified control''. Nature Physics 21, 1489–1496 (2025).
https://doi.org/10.1038/s41567-025-02990-x

[23] Tian-Ming Li, Jia-Chi Zhang, Bing-Jie Chen, Kaixuan Huang, Hao-Tian Liu, Yong-Xi Xiao, Cheng-Lin Deng, Gui-Han Liang, Chi-Tong Chen, Yu Liu, Hao Li, Zhen-Ting Bao, Kui Zhao, Yueshan Xu, Li Li, Yang He, Zheng-He Liu, Yi-Han Yu, Si-Yun Zhou, Yan-Jun Liu, Xiaohui Song, Dongning Zheng, Zhongcheng Xiang, Yun-Hao Shi, Kai Xu, and Heng Fan. ``High-precision pulse calibration of tunable couplers for high-fidelity two-qubit gates in superconducting quantum processors''. Physical Review Applied 23, 024059 (2025).
https://doi.org/10.1103/PhysRevApplied.23.024059

[24] Hao-Tian Liu, Bing-Jie Chen, Jia-Chi Zhang, Yong-Xi Xiao, Tian-Ming Li, Kaixuan Huang, Ziting Wang, Hao Li, Kui Zhao, Yueshan Xu, Cheng-Lin Deng, Gui-Han Liang, Zheng-He Liu, Si-Yun Zhou, Cai-Ping Fang, Xiaohui Song, Zhongcheng Xiang, Dongning Zheng, Yun-Hao Shi, Kai Xu, and Heng Fan. ``Direct implementation of high-fidelity three-qubit gates for superconducting processor with tunable couplers''. Physical Review Letters 135, 050602 (2025).
https://doi.org/10.1103/lvb9-pfr3

[25] K. X. Wei, E. Magesan, I. Lauer, S. Srinivasan, D. F. Bogorin, S. Carnevale, G. A. Keefe, Y. Kim, D. Klaus, W. Landers, N. Sundaresan, C. Wang, E. J. Zhang, M. Steffen, O. E. Dial, D. C. McKay, and A. Kandala. ``Hamiltonian Engineering with Multicolor Drives for Fast Entangling Gates and Quantum Crosstalk Cancellation''. Physical Review Letters 129, 060501 (2022).
https://doi.org/10.1103/PhysRevLett.129.060501

[26] Long B. Nguyen, Yosep Kim, Akel Hashim, Noah Goss, Brian Marinelli, Bibek Bhandari, Debmalya Das, Ravi K. Naik, John Mark Kreikebaum, Andrew N. Jordan, David I. Santiago, and Irfan Siddiqi. ``Programmable Heisenberg interactions between Floquet qubits''. Nature Physics 20, 240–246 (2024).
https://doi.org/10.1038/s41567-023-02326-7

[27] K. X. Wei, E. Magesan, I. Lauer, S. Srinivasan, D. F. Bogorin, S. Carnevale, G. A. Keefe, Y. Kim, D. Klaus, W. Landers, N. Sundaresan, C. Wang, E. J. Zhang, M. Steffen, O. E. Dial, D. C. McKay, and A. Kandala. ``Hamiltonian engineering with multicolor drives for fast entangling gates and quantum crosstalk cancellation''. Physical Review Letters 129, 060501 (2022).
https://doi.org/10.1103/PhysRevLett.129.060501

[28] Helin Zhang, Chunyang Ding, D.K. Weiss, Ziwen Huang, Yuwei Ma, Charles Guinn, Sara Sussman, Sai Pavan Chitta, Danyang Chen, Andrew A. Houck, Jens Koch, and David I. Schuster. ``Tunable inductive coupler for high-fidelity gates between fluxonium qubits''. PRX Quantum 5, 020326 (2024).
https://doi.org/10.1103/PRXQuantum.5.020326

[29] Simon J. Evered, Dolev Bluvstein, Marcin Kalinowski, Sepehr Ebadi, Tom Manovitz, Hengyun Zhou, Sophie H. Li, Alexandra A. Geim, Tout T. Wang, Nishad Maskara, Harry Levine, Giulia Semeghini, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin. ``High-fidelity parallel entangling gates on a neutral-atom quantum computer''. Nature 622, 268–272 (2023).
https://doi.org/10.1038/s41586-023-06481-y

[30] B. Foxen, C. Neill, A. Dunsworth, P. Roushan, B. Chiaro, A. Megrant, J. Kelly, Zijun Chen, K. Satzinger, R. Barends, F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, S. Boixo, D. Buell, B. Burkett, Yu Chen, R. Collins, E. Farhi, A. Fowler, C. Gidney, M. Giustina, R. Graff, M. Harrigan, T. Huang, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, P. Klimov, A. Korotkov, F. Kostritsa, D. Landhuis, E. Lucero, J. McClean, M. McEwen, X. Mi, M. Mohseni, J. Y. Mutus, O. Naaman, M. Neeley, M. Niu, A. Petukhov, C. Quintana, N. Rubin, D. Sank, V. Smelyanskiy, A. Vainsencher, T. C. White, Z. Yao, P. Yeh, A. Zalcman, H. Neven, and J. M. Martinis. ``Demonstrating a continuous set of two-qubit gates for near-term quantum algorithms''. Physical Review Letters 125, 120504 (2020).
https://doi.org/10.1103/PhysRevLett.125.120504

[31] Ken Xuan Wei, Isaac Lauer, Emily Pritchett, William Shanks, David C. McKay, and Ali Javadi-Abhari. ``Native two-qubit gates in fixed-coupling, fixed-frequency transmons beyond cross-resonance interaction''. PRX Quantum 5, 020338 (2024).
https://doi.org/10.1103/PRXQuantum.5.020338

[32] A. F. Kockum. ``Quantum Optics with Giant Atoms - the First Five Years''. In International Symposium on Mathematics, Quantum Theory, and Cryptography (Mathematics for Industry, vol 33). Pages 125–146. Springer (2021).
https://doi.org/10.1007/978-981-15-5191-8_12

[33] Anton Frisk Kockum, Per Delsing, and Göran Johansson. ``Designing frequency-dependent relaxation rates and Lamb shifts for a giant artificial atom''. Physical Review A 90, 013837 (2014).
https://doi.org/10.1103/PhysRevA.90.013837

[34] L. Guo, A. L. Grimsmo, A. F. Kockum, M. Pletyukhov, and G. Johansson. ``Giant acoustic atom: A single quantum system with a deterministic time delay''. Physical Review A 95, 053821 (2017).
https://doi.org/10.1103/PhysRevA.95.053821

[35] Anton Frisk Kockum, Göran Johansson, and Franco Nori. ``Decoherence-Free Interaction between Giant Atoms in Waveguide Quantum Electrodynamics''. Physical Review Letters 120, 140404 (2018).
https://doi.org/10.1103/PhysRevLett.120.140404

[36] A González-Tudela, C Sánchez Muñoz, and J I Cirac. ``Engineering and Harnessing Giant Atoms in High-Dimensional Baths: A Proposal for Implementation with Cold Atoms''. Physical Review Letters 122, 203603 (2019).
https://doi.org/10.1103/PhysRevLett.122.203603

[37] Lingzhen Guo, Anton Frisk Kockum, Florian Marquardt, and Göran Johansson. ``Oscillating bound states for a giant atom''. Physical Review Research 2, 043014 (2020).
https://doi.org/10.1103/PhysRevResearch.2.043014

[38] P. O. Guimond, B. Vermersch, M. L. Juan, A. Sharafiev, G. Kirchmair, and P. Zoller. ``A unidirectional on-chip photonic interface for superconducting circuits''. npj Quantum Information 6, 32 (2020).
https://doi.org/10.1038/s41534-020-0261-9

[39] A. Ask, Y.-L. L. Fang, and A. F. Kockum. ``Synthesizing electromagnetically induced transparency without a control field in waveguide QED using small and giant atoms'' (2020). arXiv:2011.15077.
arXiv:2011.15077

[40] Dario Cilluffo, Angelo Carollo, Salvatore Lorenzo, Jonathan A Gross, G Massimo Palma, and Francesco Ciccarello. ``Collisional picture of quantum optics with giant emitters''. Physical Review Research 2, 043070 (2020).
https://doi.org/10.1103/PhysRevResearch.2.043070

[41] Xin Wang, Tao Liu, Anton Frisk Kockum, Hong-Rong Li, and Franco Nori. ``Tunable Chiral Bound States with Giant Atoms''. Physical Review Letters 126, 043602 (2021).
https://doi.org/10.1103/PhysRevLett.126.043602

[42] Lei Du and Yong Li. ``Single-photon frequency conversion via a giant $\Lambda$-type atom''. Physical Review A 104, 023712 (2021).
https://doi.org/10.1103/PhysRevA.104.023712

[43] Ariadna Soro and Anton Frisk Kockum. ``Chiral quantum optics with giant atoms''. Physical Review A 105, 023712 (2022).
https://doi.org/10.1103/PhysRevA.105.023712

[44] Xin Wang and Hong-rong Li. ``Chiral quantum network with giant atoms''. Quantum Science and Technology 7, 035007 (2022).
https://doi.org/10.1088/2058-9565/ac6a04

[45] Lei Du, Yan Zhang, Jin Hui Wu, Anton Frisk Kockum, and Yong Li. ``Giant Atoms in a Synthetic Frequency Dimension''. Physical Review Letters 128, 223602 (2022).
https://doi.org/10.1103/PhysRevLett.128.223602

[46] Lei Du, Yao-Tong Chen, Yan Zhang, and Yong Li. ``Giant atoms with time-dependent couplings''. Physical Review Research 4, 023198 (2022).
https://doi.org/10.1103/PhysRevResearch.4.023198

[47] Sergi Terradas-Briansó, Carlos A. González-Gutiérrez, Franco Nori, Luis Martín-Moreno, and David Zueco. ``Ultrastrong waveguide QED with giant atoms''. Physical Review A 106, 063717 (2022).
https://doi.org/10.1103/PhysRevA.106.063717

[48] Ariadna Soro, Carlos Sánchez Muñoz, and Anton Frisk Kockum. ``Interaction between giant atoms in a one-dimensional structured environment''. Physical Review A 107, 013710 (2023).
https://doi.org/10.1103/PhysRevA.107.013710

[49] Lei Du, Lingzhen Guo, Yan Zhang, and Anton Frisk Kockum. ``Giant emitters in a structured bath with non-Hermitian skin effect''. Physical Review Research 5, L042040 (2023).
https://doi.org/10.1103/PhysRevResearch.5.L042040

[50] Emil Raaholt Ingelsten, Anton Frisk Kockum, and Ariadna Soro. ``Avoiding decoherence with giant atoms in a two-dimensional structured environment''. Physical Review Research 6, 043222 (2024).
https://doi.org/10.1103/PhysRevResearch.6.043222

[51] Luca Leonforte, Xuejian Sun, Davide Valenti, Bernardo Spagnolo, Fabrizio Illuminati, Angelo Carollo, and Francesco Ciccarello. ``Quantum optics with giant atoms in a structured photonic bath''. Quantum Science and Technology 10, 015057 (2025).
https://doi.org/10.1088/2058-9565/ada08d

[52] Xin Wang, Huai-Bing Zhu, Tao Liu, and Franco Nori. ``Realizing quantum optics in structured environments with giant atoms''. Physical Review Research 6, 013279 (2024).
https://doi.org/10.1103/PhysRevResearch.6.013279

[53] Federico Roccati and Dario Cilluffo. ``Controlling Markovianity with Chiral Giant Atoms''. Physical Review Letters 133, 063603 (2024).
https://doi.org/10.1103/PhysRevLett.133.063603

[54] Rui-Yang Gong, Zi-Yu He, Cheng-He Yu, Ge-Fei Zhang, Franco Nori, and Ze-Liang Xiang. ``Tunable quantum router with giant atoms, implementing quantum gates, teleportation, non-reciprocity, and circulators'' (2024). arXiv:2411.19307.
arXiv:2411.19307

[55] Lei Du and Anton Frisk Kockum. ``Unconventional and robust light-matter interactions based on the non-Hermitian skin effect''. Physical Review Research 7, 013140 (2025).
https://doi.org/10.1103/PhysRevResearch.7.013140

[56] Martin V Gustafsson, Thomas Aref, Anton Frisk Kockum, Maria K Ekström, Göran Johansson, and Per Delsing. ``Propagating phonons coupled to an artificial atom''. Science 346, 207–211 (2014).
https://doi.org/10.1126/science.1257219

[57] R Manenti, A F Kockum, A Patterson, T Behrle, J Rahamim, G Tancredi, F Nori, and P J Leek. ``Circuit quantum acoustodynamics with surface acoustic waves''. Nature Communications 8, 975 (2017).
https://doi.org/10.1038/s41467-017-01063-9

[58] K J Satzinger, Y P Zhong, H.-S. Chang, G A Peairs, A Bienfait, M.-H. Chou, A Y Cleland, C R Conner, É Dumur, J Grebel, I Gutierrez, B H November, R G Povey, S J Whiteley, D D Awschalom, D I Schuster, and A N Cleland. ``Quantum control of surface acoustic-wave phonons''. Nature 563, 661 (2018).
https://doi.org/10.1038/s41586-018-0719-5

[59] A Bienfait, K J Satzinger, Y P Zhong, H.-S. Chang, M.-H. Chou, C R Conner, É Dumur, J Grebel, G A Peairs, R G Povey, and A N Cleland. ``Phonon-mediated quantum state transfer and remote qubit entanglement''. Science 364, 368 (2019).
https://doi.org/10.1126/science.aaw8415

[60] Gustav Andersson, Baladitya Suri, Lingzhen Guo, Thomas Aref, and Per Delsing. ``Non-exponential decay of a giant artificial atom''. Nature Physics 15, 1123–1127 (2019).
https://doi.org/10.1038/s41567-019-0605-6

[61] Bharath Kannan, Max J. Ruckriegel, Daniel L. Campbell, Anton Frisk Kockum, Jochen Braumüller, David K. Kim, Morten Kjaergaard, Philip Krantz, Alexander Melville, Bethany M. Niedzielski, Antti Vepsäläinen, Roni Winik, Jonilyn L. Yoder, Franco Nori, Terry P. Orlando, Simon Gustavsson, and William D. Oliver. ``Waveguide quantum electrodynamics with superconducting artificial giant atoms''. Nature 583, 775–779 (2020).
https://doi.org/10.1038/s41586-020-2529-9

[62] A Bienfait, Y P Zhong, H.-S. Chang, M.-H. Chou, C R Conner, É Dumur, J Grebel, G A Peairs, R G Povey, K J Satzinger, and A N Cleland. ``Quantum Erasure Using Entangled Surface Acoustic Phonons''. Physical Review X 10, 021055 (2020).
https://doi.org/10.1103/PhysRevX.10.021055

[63] G Andersson, M K Ekström, and P Delsing. ``Electromagnetically Induced Acoustic Transparency with a Superconducting Circuit''. Physical Review Letters 124, 240402 (2020).
https://doi.org/10.1103/PhysRevLett.124.240402

[64] A. M. Vadiraj, Andreas Ask, T. G. McConkey, I. Nsanzineza, C. W. Sandbo Chang, Anton Frisk Kockum, and C. M. Wilson. ``Engineering the level structure of a giant artificial atom in waveguide quantum electrodynamics''. Physical Review A 103, 023710 (2021).
https://doi.org/10.1103/PhysRevA.103.023710

[65] Zi Qi Wang, Yi Pu Wang, Jiguang Yao, Rui Chang Shen, Wei Jiang Wu, Jie Qian, Jie Li, Shi Yao Zhu, and J. Q. You. ``Giant spin ensembles in waveguide magnonics''. Nature Communications 13, 7580 (2022).
https://doi.org/10.1038/s41467-022-35174-9

[66] Chaitali Joshi, Frank Yang, and Mohammad Mirhosseini. ``Resonance Fluorescence of a Chiral Artificial Atom''. Physical Review X 13, 021039 (2023).
https://doi.org/10.1103/PhysRevX.13.021039

[67] Jingjing Hu, Dengfeng Li, Yufan Qie, Zelong Yin, Anton Frisk Kockum, Franco Nori, and Shuoming An. ``Engineering the Environment of a Superconducting Qubit with an Artificial Giant Atom'' (2024). arXiv:2410.15377.
arXiv:2410.15377

[68] Guangze Chen and Anton Frisk Kockum. ``Simulating open quantum systems with giant atoms''. Quantum Science and Technology 10, 025028 (2025).
https://doi.org/10.1088/2058-9565/adb2bd

[69] A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland. ``Surface codes: Towards practical large-scale quantum computation''. Physical Review A 86, 032324 (2012).
https://doi.org/10.1103/PhysRevA.86.032324

[70] X. Mi et al. ``Stable quantum-correlated many-body states through engineered dissipation''. Science 383, 1332–1337 (2024).
https://doi.org/10.1126/science.adh9932

[71] E. Rosenberg et al. ``Dynamics of magnetization at infinite temperature in a Heisenberg spin chain''. Science 384, 48–53 (2024).
https://doi.org/10.1126/science.adi7877

[72] T Prosen. ``Open $XXZ$ Spin Chain: Nonequilibrium Steady State and a Strict Bound on Ballistic Transport''. Physical Review Letters 106, 217206 (2011).
https://doi.org/10.1103/PhysRevLett.106.217206

[73] Marko Žnidarič. ``Spin Transport in a One-Dimensional Anisotropic Heisenberg Model''. Physical Review Letters 106, 220601 (2011).
https://doi.org/10.1103/PhysRevLett.106.220601

[74] J. Koch, T. M. Yu, J. Gambetta, A. A. Houck, D. I. Schuster, J. Majer, A. Blais, M. H. Devoret, S. M. Girvin, and R. J. Schoelkopf. ``Charge-insensitive qubit design derived from the Cooper pair box''. Physical Review A 76, 042319 (2007).
https://doi.org/10.1103/PhysRevA.76.042319

[75] Alexei Gilchrist, Nathan K. Langford, and Michael A. Nielsen. ``Distance measures to compare real and ideal quantum processes''. Physical Review A 71, 062310 (2005).
https://doi.org/10.1103/PhysRevA.71.062310

[76] Man-Duen Choi. ``Completely positive linear maps on complex matrices''. Linear Algebra and its Applications 10, 285–290 (1975).
https://doi.org/10.1016/0024-3795(75)90075-0

[77] Tahereh Abad, Jorge Fernández-Pendás, Anton Frisk Kockum, and Göran Johansson. ``Universal Fidelity Reduction of Quantum Operations from Weak Dissipation''. Physical Review Letters 129, 150504 (2022).
https://doi.org/10.1103/PhysRevLett.129.150504

[78] Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I.-J. Wang, Simon Gustavsson, and William D. Oliver. ``Superconducting qubits: Current state of play''. Annual Review of Condensed Matter Physics 11, 369–395 (2020).
https://doi.org/10.1146/annurev-conmatphys-031119-050605

[79] Alexander P. M. Place, Lila V. H. Rodgers, Pranav Mundada, Basil M. Smitham, Mattias Fitzpatrick, Zhaoqi Leng, Anjali Premkumar, Jacob Bryon, Andrei Vrajitoarea, Sara Sussman, Guangming Cheng, Trisha Madhavan, Harshvardhan K. Babla, Xuan Hoang Le, Youqi Gang, Berthold Jäck, András Gyenis, Nan Yao, Robert J. Cava, Nathalie P. de Leon, and Andrew A. Houck. ``New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds''. Nature Communications 12, 1779 (2021).
https://doi.org/10.1038/s41467-021-22030-5

[80] Aaron Somoroff, Quentin Ficheux, Raymond A. Mencia, Haonan Xiong, Roman Kuzmin, and Vladimir E. Manucharyan. ``Millisecond Coherence in a Superconducting Qubit''. Physical Review Letters 130, 267001 (2023).
https://doi.org/10.1103/PhysRevLett.130.267001

[81] Youngseok Kim, Andrew Eddins, Sajant Anand, Ken Xuan Wei, Ewout van den Berg, Sami Rosenblatt, Hasan Nayfeh, Yantao Wu, Michael Zaletel, Kristan Temme, and Abhinav Kandala. ``Evidence for the utility of quantum computing before fault tolerance''. Nature 618, 500 (2023).
https://doi.org/10.1038/s41586-023-06096-3

[82] Janka Biznárová, Amr Osman, Emil Rehnman, Lert Chayanun, Christian Križan, Per Malmberg, Marcus Rommel, Christopher Warren, Per Delsing, August Yurgens, Jonas Bylander, and Anita Fadavi Roudsari. ``Mitigation of interfacial dielectric loss in aluminum-on-silicon superconducting qubits''. npj Quantum Information 10, 78 (2024).
https://doi.org/10.1038/s41534-024-00868-z

[83] Shingo Kono, Jiahe Pan, Mahdi Chegnizadeh, Xuxin Wang, Amir Youssefi, Marco Scigliuzzo, and Tobias J. Kippenberg. ``Mechanically induced correlated errors on superconducting qubits with relaxation times exceeding 0.4 ms''. Nature Communications 15, 3950 (2024).
https://doi.org/10.1038/s41467-024-48230-3

[84] Mustafa Bal et al. ``Systematic improvements in transmon qubit coherence enabled by niobium surface encapsulation''. npj Quantum Information 10, 43 (2024).
https://doi.org/10.1038/s41534-024-00840-x

[85] F. W. Strauch, P. R. Johnson, A. J. Dragt, C. J. Lobb, J. R. Anderson, and F. C. Wellstood. ``Quantum Logic Gates for Coupled Superconducting Phase Qubits''. Physical Review Letters 91, 167005 (2003).
https://doi.org/10.1103/PhysRevLett.91.167005

[86] Tahereh Abad, Yoni Schattner, Anton Frisk Kockum, and Göran Johansson. ``Impact of decoherence on the fidelity of quantum gates leaving the computational subspace''. Quantum 9, 1684 (2025).
https://doi.org/10.22331/q-2025-04-03-1684

[87] The average gate fidelity of a two-qubit CZ gate is $F_{\text{ave, CZ}}\approx1-0.8\Gamma_\text{ex}\tau-1.15\Gamma_\phi\tau$, where $\tau$ is the gate time Abad2025 and we have assumed that the two qubits have the same decay and dephasing rates. For two qubits coupled with interaction strength $g$, the gate time is $\tau=\pi/(\sqrt{2}g)$. Combining these equations, we find that it agrees with the equation in the main text up to a second-order correction.

[88] Eli Chertkov, Zihan Cheng, Andrew C. Potter, Sarang Gopalakrishnan, Thomas M. Gatterman, Justin A. Gerber, Kevin Gilmore, Dan Gresh, Alex Hall, Aaron Hankin, Mitchell Matheny, Tanner Mengle, David Hayes, Brian Neyenhuis, Russell Stutz, and Michael Foss-Feig. ``Characterizing a non-equilibrium phase transition on a quantum computer''. Nature Physics 19, 1799–1804 (2023).
https://doi.org/10.1038/s41567-023-02199-w

[89] Federico Carollo, Edward Gillman, Hendrik Weimer, and Igor Lesanovsky. ``Critical Behavior of the Quantum Contact Process in One Dimension''. Physical Review Letters 123, 100604 (2019).
https://doi.org/10.1103/PhysRevLett.123.100604

[90] Matteo Marcuzzi, Michael Buchhold, Sebastian Diehl, and Igor Lesanovsky. ``Absorbing State Phase Transition with Competing Quantum and Classical Fluctuations''. Physical Review Letters 116, 245701 (2016).
https://doi.org/10.1103/PhysRevLett.116.245701

[91] Masuo Suzuki. ``Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations''. Physics Letters A 146, 319–323 (1990).
https://doi.org/10.1016/0375-9601(90)90962-N

[92] M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert. ``Dissipative Quantum Church-Turing Theorem''. Physical Review Letters 107, 120501 (2011).
https://doi.org/10.1103/PhysRevLett.107.120501

[93] Alexandre Blais, Arne L. Grimsmo, S. M. Girvin, and Andreas Wallraff. ``Circuit quantum electrodynamics''. Reviews of Modern Physics 93, 025005 (2021).
https://doi.org/10.1103/RevModPhys.93.025005

[94] Michele C. Collodo, Johannes Herrmann, Nathan Lacroix, Christian Kraglund Andersen, Ants Remm, Stefania Lazar, Jean-Claude Besse, Theo Walter, Andreas Wallraff, and Christopher Eichler. ``Implementation of Conditional Phase Gates Based on Tunable $ZZ$ Interactions''. Physical Review Letters 125, 240502 (2020).
https://doi.org/10.1103/PhysRevLett.125.240502

[95] Amr Osman, Jorge Fernández-Pendás, Christopher Warren, Sandoko Kosen, Marco Scigliuzzo, Anton Frisk Kockum, Giovanna Tancredi, Anita Fadavi Roudsari, and Jonas Bylander. ``Mitigation of frequency collisions in superconducting quantum processors''. Physical Review Research 5, 043001 (2023).
https://doi.org/10.1103/PhysRevResearch.5.043001

[96] Sandoko Kosen, Hang-xi Li, Marcus Rommel, Robert Rehammar, Marco Caputo, Leif Grönberg, Jorge Fernández-Pendás, Anton Frisk Kockum, Janka Biznárová, Liangyu Chen, Christian Križan, Andreas Nylander, Amr Osman, Anita Fadavi Roudsari, Daryoush Shiri, Giovanna Tancredi, Joonas Govenius, and Jonas Bylander. ``Signal Crosstalk in a Flip-Chip Quantum Processor''. PRX Quantum 5, 030350 (2024).
https://doi.org/10.1103/PRXQuantum.5.030350

[97] Christian Kraglund Andersen, Ants Remm, Stefania Lazar, Sebastian Krinner, Nathan Lacroix, Graham J. Norris, Mihai Gabureac, Christopher Eichler, and Andreas Wallraff. ``Repeated quantum error detection in a surface code''. Nature Physics 16, 875–880 (2020).
https://doi.org/10.1038/s41567-020-0920-y

[98] Rajeev Acharya et al. ``Suppressing quantum errors by scaling a surface code logical qubit''. Nature 614, 676–681 (2023).
https://doi.org/10.1038/s41586-022-05434-1

[99] X. Gu, A. F. Kockum, A. Miranowicz, Y.-X. Liu, and F. Nori. ``Microwave photonics with superconducting quantum circuits''. Physics Reports 718–719, 1–102 (2017).
https://doi.org/10.1016/j.physrep.2017.10.002

[100] Neereja M. Sundaresan, Yanbing Liu, Darius Sadri, László J. Szőcs, Devin L. Underwood, Moein Malekakhlagh, Hakan E. Türeci, and Andrew A. Houck. ``Beyond Strong Coupling in a Multimode Cavity''. Physical Review X 5, 021035 (2015).
https://doi.org/10.1103/PhysRevX.5.021035

[101] Simon Storz, Josua Schär, Anatoly Kulikov, Paul Magnard, Philipp Kurpiers, Janis Lütolf, Theo Walter, Adrian Copetudo, Kevin Reuer, Abdulkadir Akin, Jean-Claude Besse, Mihai Gabureac, Graham J. Norris, Andrés Rosario, Ferran Martin, José Martinez, Waldimar Amaya, Morgan W. Mitchell, Carlos Abellan, Jean-Daniel Bancal, Nicolas Sangouard, Baptiste Royer, Alexandre Blais, and Andreas Wallraff. ``Loophole-free Bell inequality violation with superconducting circuits''. Nature 617, 265–270 (2023).
https://doi.org/10.1038/s41586-023-05885-0

[102] Xiu Gu, Jorge Fernández-Pendás, Pontus Vikstål, Tahereh Abad, Christopher Warren, Andreas Bengtsson, Giovanna Tancredi, Vitaly Shumeiko, Jonas Bylander, Göran Johansson, and Anton Frisk Kockum. ``Fast Multiqubit Gates through Simultaneous Two-Qubit Gates''. PRX Quantum 2, 040348 (2021).
https://doi.org/10.1103/PRXQuantum.2.040348

[103] Christopher W. Warren, Jorge Fernández-Pendás, Shahnawaz Ahmed, Tahereh Abad, Andreas Bengtsson, Janka Biznárová, Kamanasish Debnath, Xiu Gu, Christian Križan, Amr Osman, Anita Fadavi Roudsari, Per Delsing, Göran Johansson, Anton Frisk Kockum, Giovanna Tancredi, and Jonas Bylander. ``Extensive characterization and implementation of a family of three-qubit gates at the coherence limit''. npj Quantum Information 9, 44 (2023).
https://doi.org/10.1038/s41534-023-00711-x

[104] J.R. Johansson, P.D. Nation, and Franco Nori. ``QuTiP: An open-source Python framework for the dynamics of open quantum systems''. Computer Physics Communications 183, 1760–1772 (2012).
https://doi.org/10.1016/j.cpc.2012.02.021

[105] J.R. Johansson, P.D. Nation, and Franco Nori. ``QuTiP 2: A Python framework for the dynamics of open quantum systems''. Computer Physics Communications 184, 1234–1240 (2013).
https://doi.org/10.1016/j.cpc.2012.11.019

[106] Neill Lambert, Eric Giguère, Paul Menczel, Boxi Li, Patrick Hopf, Gerardo Suárez, Marc Gali, Jake Lishman, Rushiraj Gadhvi, Rochisha Agarwal, Asier Galicia, Nathan Shammah, Paul Nation, J.R. Johansson, Shahnawaz Ahmed, Simon Cross, Alexander Pitchford, and Franco Nori. ``Qutip 5: The quantum toolbox in python''. Physics Reports 1153, 1–62 (2026).
https://doi.org/10.1016/j.physrep.2025.10.001

Cited by

[1] Tomás Levy-Yeyati, Tomás Ramos, and Alejandro González-Tudela, "Engineering giant transmon molecules as mediators of conditional two-photon gates", Physical Review Applied 25 5, 054060 (2026).

[2] Guangze Chen and Anton Frisk Kockum, "Efficient three-qubit gates with giant atoms", arXiv:2510.04545, (2025).

[3] Santiago F. Caballero-Benitez, "Quantum Correlations and Entanglement in Generalized Dicke-Ising Models", arXiv:2603.13693, (2026).

[4] Walter Rieck, Anton Frisk Kockum, and Guangze Chen, "Doublon bound states in the continuum through giant atoms", arXiv:2511.18212, (2025).

[5] Walter Rieck, Ariadna Soro, Anton Frisk Kockum, and Guangze Chen, "Controlled-Z gates with giant atoms in structured waveguides", arXiv:2603.26345, (2026).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-17 17:47:32) and SAO/NASA ADS (last updated successfully 2026-08-17 17:47:39). The list may be incomplete as not all publishers provide suitable and complete citation data.

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