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Generation of genuine entanglement up to 51 superconducting qubits


Scalable generation of genuine multipartite entanglement with an increasing number of qubits is important for both fundamental interest and practical use in quantum-information technologies1,2. On the one hand, multipartite entanglement shows a strong contradiction between the prediction of quantum mechanics and local realization and can be used for the study of quantum-to-classical transition3,4. On the other hand, realizing large-scale entanglement is a benchmark for the quality and controllability of the quantum system and is essential for realizing universal quantum computing5,6,7,8. However, scalable generation of genuine multipartite entanglement on a state-of-the-art quantum device can be challenging, requiring accurate quantum gates and efficient verification protocols. Here we show a scalable approach for preparing and verifying intermediate-scale genuine entanglement on a 66-qubit superconducting quantum processor. We used high-fidelity parallel quantum gates and optimized the fidelitites of parallel single- and two-qubit gates to be 99.91% and 99.05%, respectively. With efficient randomized fidelity estimation9, we realized 51-qubit one-dimensional and 30-qubit two-dimensional cluster states and achieved fidelities of 0.637 ± 0.030 and 0.671 ± 0.006, respectively. On the basis of high-fidelity cluster states, we further show a proof-of-principle realization of measurement-based variational quantum eigensolver10 for perturbed planar codes. Our work provides a feasible approach for preparing and verifying entanglement with a few hundred qubits, enabling medium-scale quantum computing with superconducting quantum systems.

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Fig. 1: Generation and verification of cluster states.
Fig. 2: Performance of the quantum processor.
Fig. 3: Generation and verification of genuine 1D and 2D cluster states.
Fig. 4: A proof-of-principle implementation of MBVQE for perturbed planar codes.

Data availability

The data shown in this paper are available from the corresponding authors upon reasonable request.

Code availability

The code for this paper is available from the corresponding authors upon reasonable request.


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We thank the USTC Center for Micro- and Nanoscale Research and Fabrication for supporting the sample fabrication and the QuantumCTek for supporting the fabrication and maintenance of room-temperature electronics. This research was supported by the Innovation Program for Quantum Science and Technology (grant no. 2021ZD0300200), Shanghai Municipal Science and Technology Major Project (grant no. 2019SHZDZX01), Anhui Initiative in Quantum Information Technologies and the Chinese Academy of Sciences. H.R. acknowledges support from Natural Science Foundation of Shandong Province (grant no. ZR202209080019). H.-L.H. acknowledges support from the Youth Talent Lifting Project (grant no. 2020-JCJQ-QT-030), National Natural Science Foundation of China (grant nos 12274464 and 11905294), China Postdoctoral Science Foundation and the Open Research Fund from State Key Laboratory of High Performance Computing of China (grant no. 201901-01). M.G. was supported by Shanghai Rising-Star Program (grant no. 23QA1410000) and the Youth Innovation Promotion Association of CAS (grant no. 2022460). X.Y. acknowledges support from the National Natural Science Foundation of China (no. 12175003) and the High-Performance Computing Platform of Peking University.

Author information

Authors and Affiliations



X.Z. and J.-W.P. conceived the research. X.Y., B.W., M.G., F.C., S.C., H.-L.H. and C.-Y.L. designed the experiment. S.C., F.C., S.G., H.Q., Y.W. and M.G. performed the measurements. X.Y., B.W., F.C., S.C. and M.G. analysed the results. Q.Z., Y.Y., C.Y., F.C. and S.L. designed the processor. S.C., Y.L., K.Z., S.G., H.Q., T.-H.C., H.R., H.D. and Y.-H.H. fabricated the processor. M.G., S.W., C.Z., Y.Z., S.L., C.Y., J.Y., D.F., D.W. and H.S. contributed to the construction of the ultracold and low-noise measurement system. J.L., Y.X., F.L., C.G., L.S., N.L. and C.-Z.P. developed the room-temperature electronics. All authors contributed to the discussion of the results and drafting of the manuscript. X.Z. and J.-W.P. supervised the whole project.

Corresponding authors

Correspondence to Xiao Yuan, Xiaobo Zhu or Jian-Wei Pan.

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Nature thanks Otfried Gühne and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 The correction of coupler flux pulse distortion.

a. The waveform sequences are used to measure the effect of distortion. We apply a square wave pulse to the coupler, after a variable delay time, and measure the phase of the qubit using the Ramsey experiment. b. Qubit phase as a function of the delay time, with and without distortion corrections.

Extended Data Fig. 2 Parallel CZ gates optimization process.

a. The state leakage to \(\left|20\right\rangle \) with a CZ gate. b. The conditional phase of a CZ gate. c. The cost function for initial value selection. The red point is the value chosen for the next optimization. d. The SPB sequence fidelity of the random circuit instances at different interaction frequencies. The magenta line represents the qubit’s current detuning. All these optimization procedures can be realized in parallel.

Extended Data Fig. 3 The performance of the quantum processor after calibration.

a. The single-qubit gate, readout, and CZ gate error for the generation of 1D cluster state. b. The single-qubit gate, readout, and CZ gate error for the generation of the 2D cluster state. c. The single-qubit gate, readout, and CZ gate error for the experiment of MBVQE.

Extended Data Fig. 4 Correlations of qubit pairs for all of the flip errors.

a. The covariance of all of the flip errors of the qubit pairs having the same device as 51-qubit 1D cluster state. b. The covariance of all of the flip errors of the qubit pairs having the same device as 30-qubit 2D cluster state, where \(ij\to \bar{i}\bar{j}\) denotes the covariance of two qubits with input state \(\left|ij\right\rangle \) and output state \(\left|(1-i)(1-j)\right\rangle \).

Extended Data Fig. 5 The whole iteration process of energy estimation.

Different colors represent different λ values. The first 10 points in every lambda regime are random ancillary states and the last point is the final state.

Extended Data Fig. 6 Simulation of the MBVQE algorithm under different error models.

(a) Ground state energy estimation and (b) Order parameter Z1. ‘Simulated_0’ denotes the ideal case where no error happens; ‘Simulated_1’ denotes the simulation with gate error to be depolarizing error, where error rate equals 0.002/0.01 for single/two-qubit gates; ‘Simulated_2’ denotes the simulation with depolarizing error (same error as Simulated_1) and measurement noise where error rate equals 0.05 for the first three ancillas qubits; ‘Simulated’ denotes the simulation with all of the errors in ‘Simulated_2’ and additional measurement noise for the rest four qubits. As a benchmark, we also plot the theoretical value for ground state energy, the first excited state energy, and the order parameter Z1. The simulation result leverage 20,000 repetitions of measurements for each circuit and measurement setting.

Supplementary information

Supplementary Information

This file contains Supplementary Sections 1–8, including Supplementary Figs 1–12 and Supplementary Tables 1–6 – see Contents page for details.

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Cao, S., Wu, B., Chen, F. et al. Generation of genuine entanglement up to 51 superconducting qubits. Nature 619, 738–742 (2023).

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