Showing how quantum simulators can explore otherwise inaccessible phenomena
A Colloquium in Reviews of Modern Physics provides an introduction to the field of quantum simulation of exotic geometries without a real-world counterpart. The review highlights unique opportunities offered by different platforms and discusses the novel physical phenomena that can be addressed with them.
Many important problems in physics, especially in fields like low-temperature physics and many-body physics, remain poorly understood because the underlying quantum mechanics is vastly complex. To address these challenges, scientists are turning to quantum simulation, a technique that allows researchers to manipulate and observe the behavior of a well-controlled quantum system in the lab, in order to learn about quantum systems that are otherwise inaccessible.
Quantum simulation was born to tackle real-world systems of interest, such as electronic materials, superconductors and complex molecules. However, physicists soon realized that quantum simulators might go beyond the mere imitation of existing systems. This opened a new research line: using quantum simulators to explore systems without real-world counterparts. Concepts that might seem to arise from science fiction, such as synthetic quantum matter, higher-dimensional spaces leading to an “augmented quantum reality”, analog black holes, suddenly became the object of scientific research.
Recently, a team of researchers led by Tobias Grass from Donostia International Physics Center in San Sebastián, with the participation of ICFO and ICREA Prof. Maciej Lewenstein, as well as researchers from ETH Zurich, Université de Lyon and TU Dortmund University, has published a Colloquium in Reviews of Modern Physics where they provide a comprehensive overview of these exotic quantum simulators. They cover various platforms, namely those based on atoms, electrons and photons, highlighting both their strengths and limitations. The paper also discusses how these platforms can enable scientists investigate phenomena across a wide range of fields, from condensed matter physics to cosmology.
According to the authors, one exciting possibility is the use of quantum simulators to create synthetic quantum matter with exotic geometries that lead to localization phenomena. In this scenario, the wavefunction of a particle or group of particles, which usually spreads out across a wide spatial area, becomes localized due to the confining geometry. This synthetic quantum matter can also host topological phases – exotic states of matter defined by entanglement patterns, rather than atomic arrangement and mobility – making it ideal for detailed study with quantum simulators. These simulators can also be used to explore cosmological models involving curved spacetimes, and even to simulate the physics of black holes, such as the Unruh effect and Hawking radiation. While these phenomena are incredibly faint and challenging to observe with astronomical techniques, quantum simulators could make them detectable in the lab.
Looking ahead, the researchers note: “Given the complexities in simulating these systems classically, quantum simulators may develop their full potential, opening the door to deep questions of quantum many-body physics. Our review shows that the basis for future explorations of the interacting world of fractals, quasicrystals, and curved and higher-dimensional spaces has been set.”
Reference:
Tobias Grass, Dario Bercioux, Utso Bhattacharya, Maciej Lewenstein, Hai Son Nguyen, and Christof Weitenberg, Colloquium: Synthetic quantum matter in nonstandard geometries, Rev. Mod. Phys. 97, 011001 (2025).
DOI: https://doi.org/10.1103/RevModPhys.97.011001
Caption:
The figure shows an artist’s conception of a fractal geometry known as Sierpiński gasket. This fractal geometry emerges by a self-similar construction of smaller and smaller triangles. As reviewed in the Colloquium, modern quantum simulators can synthetically generate such setups and explore the interplay of quantum mechanics and exotic geometry, giving rise to rich features such as non-standard localization and topological properties. Created with Microsoft AI image generator, by Tobias Grass.
Acknowledgements:
T. G. and D. B. acknowledge fruitful discussions with Geza Giedke. D. B. acknowledges the support of the Spanish MICINN-AEI through Project No. PID2020–120614GB-I00 (ENACT), the Transnational Common Laboratory Quantum ChemPhys, and the Department of Education of the Basque Government through Project No. PIBA_2023_1_0007 (STRAINER). T. G. and D. B. acknowledge the financial support received from the IKUR Strategy under the collaboration agreement between the Ikerbasque Foundation and DIPC on behalf of the Department of Education of the Basque Government, and by the Gipuzkoa Provincial Council within Project No. QUAN-000021-01. T. G. acknowledges funding from the Department of Education of the Basque Government through Project No. PIBA_2023_1_0021 (TENINT) and from the Agencia Estatal de Investigación (AEI) through Proyectos de Generación de Conocimiento No. PID2022-142308NA-I00 (EXQUSMI). This work has been produced with the support of a 2023 Leonardo Grant for Researchers in Physics from the BBVA Foundation. H. S. N. is funded by the French National Research Agency (ANR) under the project README (Project No. ANR-22-CE09-0036-01). The work of C.W. is funded by the Cluster of Excellence “CUI: Advanced Imaging of Matter” of the Deutsche Forschungsgemeinschaft (DFG)—EXC 2056 —Project No. 390715994 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. 802701.
U. B. is also grateful for the financial support of the IBM Quantum Researcher Program. M. L. acknowledges ERC AdG NOQIA; MCIN/AEI [PGC2018-0910.13039/501100011033, CEX2019-000910-S/10.13039/501100011033, Plan National FIDEUA PID2019–106901GB-I00, and the Plan National STAMEENA PID2022-139099NB-I00 project funded by MCIN/AEI/10.13039/501100011033 and by the “European Union NextGenerationEU/PRTR” (PRTR-C17.I1), FPI]; QuantERA MAQS (Grant No. PCI2019-111828-2); QuantERA DYNAMITE (Grant No. PCI2022-132919; QuantERA II Programme, cofunded by the European Union’s Horizon 2020 program under Grant Agreement No. 101017733), the Ministry of Economic Affairs and Digital Transformation of the Spanish Government through the QUANTUM ENIA project call–Quantum Spain project, and the European Union through the Recovery, Transformation, and Resilience Plan–NextGenerationEU within the framework of the Digital Spain 2026 Agenda; Fundació Cellex; Fundació Mir-Puig; Generalitat de Catalunya (European Social Fund FEDER and CERCA program, AGAUR Grant No. 2021 SGR 01452, and QuantumCAT Grant No. U16-011424, cofunded by the ERDF Operational Program of Catalonia 2014–2020); Barcelona Supercomputing Center MareNostrum (FI-2023-1-0013);EUQuantumFlagship (PASQuanS2.1, 101113690);EU Horizon 2020 FET-OPEN OPTOlogic (Grant No. 899794); EU Horizon Europe Program (Grant Agreement No. 101080086–NeQST); the ICFO Internal “QuantumGaudi” project; the European Union’s Horizon 2020 program under the Marie Skłodowska-Curie Grant Agreement No. 847648; and “La Caixa,” Junior Leaders fellowships, “La Caixa,” Foundation (ID No. 100010434): CF/BQ/PR23/11980043.