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Holographic dynamics simulations with a trapped-ion quantum computer

Abstract

Quantum computers promise to efficiently simulate quantum dynamics, a classically intractable task central to fields ranging from chemistry to high-energy physics. Yet, quantum computational advantage has only been demonstrated for artificial tasks such as random circuit sampling, and hardware limitations and noise have limited experiments to qualitative studies of small-scale systems. Quantum processors capable of high-fidelity measurements and qubit reuse enable a recently proposed holographic technique that employs quantum tensor-network states, a class of states that efficiently compress quantum data, to simulate the evolution of infinitely long, entangled initial states using a small number of qubits. Here we benchmark this holographic technique in a trapped-ion quantum processor using 11 qubits to simulate the dynamics of an infinite entangled state. We observe the hallmarks of quantum chaos and light-cone propagation of correlations, and find excellent quantitative agreement with theoretical predictions for the infinite-size limit of the implemented model with minimal post-processing or error mitigation. These results show that quantum tensor-network methods, paired with state-of-the-art quantum processor capabilities, offer a viable route to practical quantum computational advantage on problems of direct interest to science and technology in the near term.

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Fig. 1: Holographic simulation of the kicked Ising model.
Fig. 2: Quantum computer used in this work.
Fig. 3: Experimental data.

Data availability

The raw data produced by the Quantinuum devices for this work are available in Supplementary Data 1.

Code availability

The code used to generate data for this work is available from the corresponding author upon reasonable request.

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Acknowledgements

This work was made possible by a large group of people, and the authors would like to thank the entire Quantinuum team for their many contributions. The experiments reported in this manuscript were performed on Quantinuum’s H1-1 and H1-2 system models, which are powered by Honeywell ion traps. We thank C. Baldwin for helpful discussions regarding the performance benchmarks on H1-1 and H1-2. We used the ITensor library32, written in Julia39, to perform the tensor-network contractions to generate the theory curves. Quantum circuits were prepared and simulated using the Qiskit library created by IBM40. A.C.P. was supported by NSF Convergence Accelerator Track C award 2040549.

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E.C., M.F.-F. and A.C.P. conceived the experiment. J.B., D.F., J.G., D.G., A.H., K.L., B.N. and R.S. executed the experiment on the Quantinuum quantum computer. E.C. performed the theoretical analysis and numerical simulations. E.C., M.F.-F. and A.C.P. analysed the experimental data. M.F.-F. and D.H. coordinated and supervised the project. E.C., M.F.-F., A.C.P. and D.H. wrote the manuscript and the Supplementary Information. All the authors edited the manuscript.

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Correspondence to Eli Chertkov.

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

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Supplementary Information

Supplementary Figs. 1–7, discussion and references.

Supplementary Data 1

Experimental data used to produce the figures in the manuscript.

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Chertkov, E., Bohnet, J., Francois, D. et al. Holographic dynamics simulations with a trapped-ion quantum computer. Nat. Phys. (2022). https://doi.org/10.1038/s41567-022-01689-7

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