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  • Perspective
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Simulating topological order on quantum processors

Nature Reviews Physics (2026)Cite this article

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Abstract

It is an ongoing quest to realize topologically ordered quantum states on different platforms including condensed matter systems, quantum simulators and digital quantum processors. Unlike conventional states characterized by their local order, these exotic states are characterized by their non-local entanglement. The consequences of topological order can be as profound as they are surprising, ranging from the emergence of fractionalized anyonic excitations to potentially providing a scalable platform for quantum error correction. This deep connection to quantum computing naturally motivates the realization and study of topologically ordered quantum states on quantum processors. However, owing to the non-local nature of these states, their study presents a challenge for near-term quantum devices. This Perspective aims to review the recent progress towards the experimental realization of topologically ordered quantum states, their potential applications and promising directions of future research.

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Fig. 1: Preparation of symmetry-protected topological states on quantum computers.
Fig. 2: Characterizing SPT order on quantum computers.
Fig. 3: Preparing topological order on quantum processors.
Fig. 4: Characterizing topological order.

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Acknowledgements

A.G.-S. was supported by the UK Research and Innovation (UKRI) under the UK Government’s Horizon Europe funding guarantee (grant no. EP/Y036069/1). M.K. and F.P. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy-EXC-2111-390814868, TRR 360 — 492547816, FOR 5522 (project-id 499180199), and DFG grants no. KN1254/1-2 and no. KN1254/2-1, the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 851161), the European Union (grant agreement no. 101169765) and the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.

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  1. School of Physics and Astronomy, University of Nottingham, Nottingham, UK

    Adam Gammon-Smith

  2. Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham, UK

    Adam Gammon-Smith

  3. Technical University of Munich, TUM School of Natural Sciences, Physics Department, Garching, Germany

    Michael Knap & Frank Pollmann

  4. Munich Center for Quantum Science and Technology (MCQST), München, Germany

    Michael Knap & Frank Pollmann

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Gammon-Smith, A., Knap, M. & Pollmann, F. Simulating topological order on quantum processors. Nat Rev Phys (2026). https://doi.org/10.1038/s42254-025-00911-8

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