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Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator


A quantum simulator is a type of quantum computer that controls the interactions between quantum bits (or qubits) in a way that can be mapped to certain quantum many-body problems1,2. As it becomes possible to exert more control over larger numbers of qubits, such simulators will be able to tackle a wider range of problems, such as materials design and molecular modelling, with the ultimate limit being a universal quantum computer that can solve general classes of hard problems3. Here we use a quantum simulator composed of up to 53 qubits to study non-equilibrium dynamics in the transverse-field Ising model with long-range interactions. We observe a dynamical phase transition after a sudden change of the Hamiltonian, in a regime in which conventional statistical mechanics does not apply4. The qubits are represented by the spins of trapped ions, which can be prepared in various initial pure states. We apply a global long-range Ising interaction with controllable strength and range, and measure each individual qubit with an efficiency of nearly 99 per cent. Such high efficiency means that arbitrary many-body correlations between qubits can be measured in a single shot, enabling the dynamical phase transition to be probed directly and revealing computationally intractable features that rely on the long-range interactions and high connectivity between qubits.

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Figure 1: Illustration of the DPT from a quantum quench.
Figure 2: Real-time spin dynamics after a quantum quench of 16 spins in an Ising chain.
Figure 3: Two-body correlations.
Figure 4: Domain statistics and reconstructed single-shot images of 53 spins.


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We acknowledge discussions with M. Cetina, L. Duan, A. Polkovnikov, M. Heyl, M. Maghrebi, P. Titum and J. Iosue. This work is supported by the ARO and AFOSR Atomic and Molecular Physics Programs, the AFOSR MURI on Quantum Measurement and Verification, the IARPA LogiQ programme, the ARO MURI on Modular Quantum Systems, the ARL Center for Distributed Quantum Information, the NSF Quantum Information Science programme, and the NSF Physics Frontier Center at JQI. G.P. is supported by the IC Postdoctoral Research Fellowship Program.

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Authors and Affiliations



J.Z., G.P., P.W.H., A.K., P.B., H.K. and C.M. all contributed to experimental design, construction, data collection and analysis. Z.-X.G. and A.V.G. contributed to the theory for the experiment. All authors contributed to this manuscript.

Corresponding author

Correspondence to J. Zhang.

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Competing interests

C.M. is a founding scientist of ionQ, Inc.

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Reviewer Information Nature thanks C. Muschik and C. Roos for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Distributions of the largest domain size.

Statistics of the largest domain size in each experimental shot (200 experiments for each of the last 5 time steps). Considering only the largest domains of each shot eliminates the undesirable biasing towards small domain sizes that is present in Fig. 4a. Domain sizes are related to many-body correlators, with a domain size of N corresponding to an N-body correlator. Dashed lines are fits to a two-parameter Gamma distribution proportional to ex/βxα−1, with shape parameter α and scale parameter β.

Extended Data Figure 2 Domain size observable for 16 spins.

Mean maximum domain size as a function of the (Kac-normalized41) transverse field for 16 spins. Experimental data are analysed as for Fig. 4b. The dashed line is a numerical simulation of the Hamiltonian determined from the experimental parameters. Error bars, 1 s.d.

Extended Data Figure 3 Theoretical calculations of the correlations.

The spatially and long-time averaged correlation (defined in equation (4)), calculated as a function of for α = 0. The finite-N curves are calculated using exact diagonalization; the N = ∞ curve is calculated analytically from equation (4).

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Zhang, J., Pagano, G., Hess, P. et al. Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551, 601–604 (2017).

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