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Holonomic quantum computation: a scalable adiabatic architecture

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Holonomic quantum computation: a scalable adiabatic architecture

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AbstractHolonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.Featured image: Robustness to loop-deforming errors (coloured paths) is given by the curvature of an underlying manifold (orange surface) which encodes how the computational subspace varies across the control manifold.Popular summaryQuantum systems are notoriously difficult to control, posing one of the central challenges on the path to a practical quantum computer. Broadly speaking, two types of errors can occur during a quantum computation: incoherent errors, arising from unwanted interactions with the environment; and coherent errors, stemming from imperfect control over the classical parameters that drive the computation on the physical hardware. Holonomic quantum computation offers a promising strategy for combating coherent errors. Holonomic gates depend only on the geometry of the control trajectory, on its overall shape, not the speed at which it is traversed. They are therefore instances of so-called geometric phases (in the simplest case, the famous Berry phase). The guiding intuition is that, because the gate depends only on the global shape of the control path, small local fluctuations should leave it unchanged. Yet the precise scope of this robustness has remained incompletely studied. In particular, errors that deform the shape of the control loop, rather than merely reparametrize it, call for a more careful analysis. In this work, we introduce a complete, scalable framework for holonomic quantum computation on cold-atom platforms based on the Rydberg interaction, with a universal set of single- and two-qubit gates realized through adiabatic geometric phases. As differential geometry tells us, robustness to loop-deforming errors is governed by the curvature of an underlying manifold which encodes how the computational subspace varies across the control manifold. In our protocols, control paths can be chosen to mostly run through regions of low curvature, where small deformations of the loop have negligible effect on the implemented gate. Beyond our proposed gates, we also hope that the geometric tools we introduce to analyse robustness will prove broadly useful for the design and evaluation of robust quantum gates across a range of physical platforms.► BibTeX data@article{Wassner2026holonomicquantum, doi = {10.22331/q-2026-04-23-2080}, url = {https://doi.org/10.22331/q-2026-04-23-2080}, title = {Holonomic quantum computation: a scalable adiabatic architecture}, author = {Wassner, Clara and Guaita, Tommaso and Eisert, Jens and Carrasco, Jose}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2080}, month = apr, year = {2026} }► References [1] Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler. Bounds for the adiabatic approximation with applications to quantum computation. Journal of Mathematical Physics, 48, 2007. 10.1063/1.2798382. https://doi.org/10.1063/1.2798382 [2] Jiang Zhang, Thi Ha Kyaw, Stefan Filipp, Leong-Chuan Kwek, Erik Sjöqvist, and Dianmin Tong. Geometric and holonomic quantum computation. Physics Reports, 1027: 1–53, 2023. 10.1016/j.physrep.2023.07.004. https://doi.org/10.1016/j.physrep.2023.07.004 [3] Michael V. Berry. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society A, 392: 45–57, 1984. 10.1098/rspa.1984.0023. https://doi.org/10.1098/rspa.1984.0023 [4] Frank Wilczek and Anthony Zee. Appearance of gauge structure in simple dynamical systems.

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Fast Quantum Gates for Neutral Atoms.

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URL http://www.jetp.ras.ru/cgi-bin/dn/e_020_05_1290.pdf. http://www.jetp.ras.ru/cgi-bin/dn/e_020_05_1290.pdfCited by[1] Jayant Rao, Jens Eisert, and Tommaso Guaita, "Stability of digital and analog quantum simulations under noise", arXiv:2510.08467, (2025). [2] Deepesh Singh, Ryan J. Marshman, Nathan Walk, Jens Eisert, Timothy C. Ralph, and Austin P. Lund, "Coherently mitigating boson samplers with stochastic errors", arXiv:2505.00102, (2025). [3] Anirudh Lanka, Juan Garcia-Nila, and Todd A. Brun, "Continuous measurement-based holonomic quantum computation", arXiv:2510.06725, (2025). [4] Anirudh Lanka, Juan Garcia-Nila, and Todd A. Brun, "Steering paths mid-flight for fault-tolerance in measurement-based holonomic gates", arXiv:2603.02552, (2026). The above citations are from SAO/NASA ADS (last updated successfully 2026-04-23 14:29:51). The list may be incomplete as not all publishers provide suitable and complete citation data.Could not fetch Crossref cited-by data during last attempt 2026-04-23 14:29:50: Could not fetch cited-by data for 10.22331/q-2026-04-23-2080 from Crossref. This is normal if the DOI was registered recently.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. AbstractHolonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.Featured image: Robustness to loop-deforming errors (coloured paths) is given by the curvature of an underlying manifold (orange surface) which encodes how the computational subspace varies across the control manifold.Popular summaryQuantum systems are notoriously difficult to control, posing one of the central challenges on the path to a practical quantum computer. Broadly speaking, two types of errors can occur during a quantum computation: incoherent errors, arising from unwanted interactions with the environment; and coherent errors, stemming from imperfect control over the classical parameters that drive the computation on the physical hardware. Holonomic quantum computation offers a promising strategy for combating coherent errors. Holonomic gates depend only on the geometry of the control trajectory, on its overall shape, not the speed at which it is traversed. They are therefore instances of so-called geometric phases (in the simplest case, the famous Berry phase). The guiding intuition is that, because the gate depends only on the global shape of the control path, small local fluctuations should leave it unchanged. Yet the precise scope of this robustness has remained incompletely studied. In particular, errors that deform the shape of the control loop, rather than merely reparametrize it, call for a more careful analysis. In this work, we introduce a complete, scalable framework for holonomic quantum computation on cold-atom platforms based on the Rydberg interaction, with a universal set of single- and two-qubit gates realized through adiabatic geometric phases. As differential geometry tells us, robustness to loop-deforming errors is governed by the curvature of an underlying manifold which encodes how the computational subspace varies across the control manifold. In our protocols, control paths can be chosen to mostly run through regions of low curvature, where small deformations of the loop have negligible effect on the implemented gate. Beyond our proposed gates, we also hope that the geometric tools we introduce to analyse robustness will prove broadly useful for the design and evaluation of robust quantum gates across a range of physical platforms.► BibTeX data@article{Wassner2026holonomicquantum, doi = {10.22331/q-2026-04-23-2080}, url = {https://doi.org/10.22331/q-2026-04-23-2080}, title = {Holonomic quantum computation: a scalable adiabatic architecture}, author = {Wassner, Clara and Guaita, Tommaso and Eisert, Jens and Carrasco, Jose}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2080}, month = apr, year = {2026} }► References [1] Sabine Jansen, Mary-Beth Ruskai, and Ruedi Seiler. Bounds for the adiabatic approximation with applications to quantum computation. Journal of Mathematical Physics, 48, 2007. 10.1063/1.2798382. https://doi.org/10.1063/1.2798382 [2] Jiang Zhang, Thi Ha Kyaw, Stefan Filipp, Leong-Chuan Kwek, Erik Sjöqvist, and Dianmin Tong. Geometric and holonomic quantum computation. Physics Reports, 1027: 1–53, 2023. 10.1016/j.physrep.2023.07.004. https://doi.org/10.1016/j.physrep.2023.07.004 [3] Michael V. Berry. Quantal phase factors accompanying adiabatic changes. Proceedings of the Royal Society A, 392: 45–57, 1984. 10.1098/rspa.1984.0023. https://doi.org/10.1098/rspa.1984.0023 [4] Frank Wilczek and Anthony Zee. Appearance of gauge structure in simple dynamical systems.

Quantum Information Processing, 10: 885, 2011. 10.1007/s11128-011-0303-5. https://doi.org/10.1007/s11128-011-0303-5 [34] Mikio Nakahara. Geometry, topology and physics.

Fast Quantum Gates for Neutral Atoms.

Physical Review Research, 5: 033052, 2023. 10.1103/PhysRevResearch.5.033052. https://doi.org/10.1103/PhysRevResearch.5.033052 [41] Qian Xu, J.

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Holonomic quantum computation: a scalable adiabatic architecture

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