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Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout


Quantum many-body systems subjected to unitary evolution with the addition of interspersed measurements exhibit a variety of dynamical phases that do not occur under pure unitary evolution. However, these systems remain challenging to investigate on near-term quantum hardware owing to the need for numerous ancilla qubits or repeated high-fidelity mid-circuit measurements, a capability that has only recently become available. Here we report the realization of a measurement-induced entanglement phase transition with a hybrid random circuit on up to 14 superconducting qubits with mid-circuit readout capability. We directly observe extensive and sub-extensive scaling of entanglement entropy in the volume- and area-law phases, respectively, by varying the rate of the measurements. We also demonstrate phenomenological critical behaviour by performing a data collapse of the measured entanglement entropy. Our work establishes the use of mid-circuit measurement as a powerful resource for quantum simulation on near-term quantum computers.

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Fig. 1: Measurement-induced entanglement transition using a hybrid random quantum circuit model.
Fig. 2: Entanglement crossover and system size scaling under projective measurements.
Fig. 3: Entanglement crossover under weak measurements.
Fig. 4: Phenomenological critical behaviour of the entanglement transition.

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Data availability

Data that support the findings of this study are publicly available via the Open Science Framework at

Code availability

Code used in this study is publicly available via the Open Science Framework at


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S.S. and A.J.M. were supported by the US Department of Energy under award no. DE-SC0019374. M.M. acknowledges J. Burks, D. McClure, S. Sheldon and M. Stypulkoski for help with access to, and use of, IBM Quantum devices. M.M. also acknowledges helpful discussions with L. Govia, E. Chen, and A. Kandala. The authors acknowledge the use of IBM Quantum services for this work.

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J.M.K., S.-N.S. and A.J.M. conceived and initiated the project. A.J.M. supervised the project. J.M.K. developed the quantum simulation codebase and ran experiments on emulators and quantum hardware. M.M. contributed to the codebase and ran experiments on quantum hardware. All authors contributed to the discussion of results and writing of the paper.

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Correspondence to Austin J. Minnich.

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Supplementary Notes 1–7, Figs. 1–11 and Tables 1–3.

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Koh, J.M., Sun, SN., Motta, M. et al. Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout. Nat. Phys. 19, 1314–1319 (2023).

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