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Characterizing a non-equilibrium phase transition on a quantum computer


Quantum systems subject to driving and dissipation display distinctive non-equilibrium phenomena relevant to condensed matter, quantum optics, metrology and quantum error correction. An example is the emergence of phase transitions with uniquely quantum properties, which opposes the intuition that dissipation generally leads to classical behaviour. The quantum and non-equilibrium nature of such systems makes them hard to study with existing tools, such as those from equilibrium statistical mechanics, and represents a challenge for numerical simulations. Quantum computers, however, are well suited to simulating such systems, especially as hardware developments enable the controlled application of dissipative operations in a pristine quantum environment. Here we demonstrate a large-scale accurate quantum simulation of a non-equilibrium phase transition using a trapped-ion quantum computer. We simulate a quantum extension of the classical contact process that has been proposed as a description for driven gases of Rydberg atoms and has stimulated numerous attempts to determine the impact of quantum effects on the classical directed-percolation universality class. We use techniques such as qubit reuse and error avoidance based on real-time conditional logic to implement large instances of the model with 73 sites and up to 72 circuit layers and quantitatively determine the model’s critical properties. Our work demonstrates that today’s quantum computers are able to perform useful simulations of open quantum system dynamics and non-equilibrium phase transitions.

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Fig. 1: A driven-dissipative quantum circuit.
Fig. 2: Qubit reuse and real-time conditional logic.
Fig. 3: Experimental observation of critical scaling in a quantum computer.

Data availability

The data produced by the Quantinuum devices for this work are available online in Supplementary Information. Additional classical simulation results are available upon reasonable request.

Code availability

The code used to generate data for this work is available upon reasonable request.


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This work was made possible by a large group of people, and we would like to thank the entire Quantinuum team for their many contributions. The experiments reported in this paper were performed on the Quantinuum system model H1-1 quantum computer (, which is powered by Honeywell ion traps. Numerical calculations were performed using the ITensor library46. We thank S. Diehl, M. Buchold, K. Hemery, H. Dreyer, R. Haghshenas, N. Brown, C. Ryan-Anderson, M. DeCross, K. Mayer, C. Langlett, M. Lubasch, M. Wall, P. D. Blocher, I. Deutsch, M. Iqbal and V. Khemani for helpful discussions. This research was supported in part by the National Science Foundation under grant number PHY-1748958. A.C.P. was supported by Department of Energy DE-SC0022102 and the Alfred P. Sloan Foundation through a Sloan Research Fellowship. A.C.P. and S.G. performed this work in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. This research used resources of the Oak Ridge Leadership Computing Facility, which is a Department of Energy Office of Science User Facility supported under Contract DE-AC05-00OR22725.

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Authors and Affiliations



E.C., M.F.-F., D.H., A.C.P. and S.G. conceived the experiment. T.M.G., J.A.G., K.G., D.G., A. Hall, A. Hankin, M.M., T.M., B.N. and R.S. executed the experiment on the Quantinuum quantum computer. E.C. analysed the experimental data. E.C. and Z.C. performed numerical simulations. E.C., M.F.-F., Z.C., A.C.P., D.H. and S.G. wrote the paper and supplement. All authors edited the paper.

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Correspondence to Eli Chertkov.

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Nature Physics thanks Kenji Toyoda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–21, Discussion and Table 1.

Supplementary Data

The data presented in the main paper obtained from the H1-1 quantum computer and noise-less classical simulations.

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Chertkov, E., Cheng, Z., Potter, A.C. et al. Characterizing a non-equilibrium phase transition on a quantum computer. Nat. Phys. (2023).

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