Abstract
Monitored many-body quantum systems can exhibit a measurement-induced phase transition (MIPT) between entangling and disentangling dynamical phases. Proposed approaches to study the MIPT experimentally typically rely on a classical decoding process, but the complexity of this decoding generally grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome this difficulty in the context of tree-shaped quantum circuits. We construct a hybrid circuit with Haar-random unitary operators, and we show that the MIPT can be detected without postselection using a simple decoding process whose complexity grows linearly with the number of qubits. The tree structure also enables a complete theoretical description of the MIPT and all its critical properties. We experimentally realize the MIPT on a trapped-ion quantum computer and show that the results are precisely described by theory without the need for error mitigation.
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Data availability
Data for this experiment is available at a public Zenodo repository60. We include the measurement outcomes and circuits we used for the experiment.
Code availability
Code for this experiment is available at a public Zenodo repository60. We include code to create the circuits and analyze the data, as well as code for classically simulating the order parameter.
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Acknowledgements
We thank Michael Foss-Feig for assistance with running our circuits on the Quantinuum quantum computers and for suggesting the weak measurement circuit construction in Fig. 3c. We thank Zihan Cheng and Matteo Ippoliti for useful discussions. This work was supported by the Ministère de l’Économie, de l’Innovation et de l’Énergie du Québec via its contributions to its Research Chair in Quantum Computing and to the AlgoLab at Institut quantique, Université de Sherbrooke. S.K. and J.C. were supported by a Natural Sciences and Engineering Research Council of Canada Discovery grant. This research used resources of the Oak Ridge Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC05-00OR22725.
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X.F. and J.C. contributed equally. X.F. and J.C. developed the code for the experiment and analyzed the results from numerical simulations and experiment. B.S. and S.K. supervised the project. All authors wrote the manuscript.
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Feng, X., Côté, J., Kourtis, S. et al. Postselection-free experimental observation of the measurement-induced phase transition in circuits with universal gates. Commun Phys (2026). https://doi.org/10.1038/s42005-025-02443-0
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DOI: https://doi.org/10.1038/s42005-025-02443-0
