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Measurement-induced quantum phases realized in a trapped-ion quantum computer


Many-body open quantum systems balance internal dynamics against decoherence and measurements induced by interactions with an environment1,2. Quantum circuits composed of random unitary gates with interspersed projective measurements represent a minimal model to study the balance between unitary dynamics and measurement processes3,4,5. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerant threshold6. Here we explore this purification transition with random quantum circuits implemented on a trapped-ion quantum computer. We probe the pure phase, where the system is rapidly projected to a pure state conditioned on the measurement outcomes, and the mixed or coding phase, where the initial state becomes partially encoded into a quantum error correcting codespace that keeps the memory of initial conditions for long times6,7. We find experimental evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition emerge.

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Fig. 1: Model and purification dynamics.
Fig. 2: Phase diagram and scaling limit of average purification dynamics.
Fig. 3: Experimental observation of phases and simulated critical behaviour.

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All data is available in the manuscript or the Supplementary Information.


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We acknowledge fruitful discussions with E. Altman, S. Choi, A. Deshpande, S. Diehl, B. Fefferman, S. Gopalakrishnan, M. Ippoliti, V. Khemani, A. Nahum, J. Pixley, O. Shtanko and A. Zabalo, and the contributions of M. Goldman, K. Beck, J. Amini, K. Hudek and J. Mizrahi to the experimental set-up. This work is supported by the ARO through the IARPA LogiQ programme, the NSF STAQ programme, the AFOSR MURIs on Dissipation Engineering in Open Quantum Systems and Quantum Measurement/Verification and Quantum Interactive Protocols, the ARO MURI on Modular Quantum Circuits, the DoE Quantum Systems Accelerator, the DoE ASCR Accelerated Research in Quantum Computing programme (award no. DE-SC0020312) and the National Science Foundation (QLCI grant no. OMA-2120757). L.E. is also funded by NSF award no. DMR-1747426. This work was performed at the University of Maryland with no material support from IonQ.

Author information

Authors and Affiliations



C.N. collected the data. C.N. and P.N analysed the data. C.N., P.N. and M.J.G. wrote the manuscript and designed figures. M.C. and C.M. led construction of the experimental apparatus with contributions from C.N., D.Z., A.R., L.E. and D.B. Theory support was provided by P.N., M.J.G., A.V.G. and D.A.H. C.M., M.J.G. and D.A.H. supervised the project. All authors discussed the results and contributed to the manuscript.

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Correspondence to Crystal Noel.

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Nature Physics thanks Yi-Zhuang You and Tobias Schaetz for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Scrambling Unitary.

Example of a scrambling unitary on a system with L = 6 qubits. Each single-qubit gate C refers to a random single-qubit Clifford gate. The XX gates have an implied rotation angle of π/4.

Extended Data Fig. 2 Feedback Truth Table.

Truth table for outcomes of measurement ancillae and reference qubit for a circuit.

Extended Data Fig. 3 Feedback Circuit.

Feedback circuit corresponding to example circuit #45 described in Methods.

Extended Data Fig. 4 Histogram of Experimental Data for S_C.

All raw outcomes of SC in study of phases (main text Fig. 3a). The legend indicates the simulated expected outcome for that circuit. The bin size is .033 and SC = . 93 (dashed line) is used as a threshold for all the data.

Extended Data Fig. 5 Comparison of Theory and Experiment.

(a) Raw average of all circuit outcomes without thresholding applied. (b) Thresholded data with extended simulations showing expected behaviour up to L=32.

Extended Data Fig. 6 Analysis Method to Extract Critical Data.

(a) Late time decay of 〈SQ〉 showing the exponential decay regime used to extract the decay rate τ. Here, we took (P, Px) = (0.15, 0.7) near the critical point. (b) Scaling of τ vs L for different values of Px at P = 0.15. We can estimate Pxc and extract z by looking for the inflection point in this family of curves and fitting the slope.

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Supplementary Information

Supplementary Discussion and Supplementary Figs. 1 and 2.

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Noel, C., Niroula, P., Zhu, D. et al. Measurement-induced quantum phases realized in a trapped-ion quantum computer. Nat. Phys. 18, 760–764 (2022).

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