Abstract
The Sachdev-Ye-Kitaev (SYK) model describes a strongly correlated quantum system that shows a strong signature of quantum chaos. Due to its chaotic nature, the simulation of real-time dynamics becomes quickly intractable by means of classical numerics, and thus, quantum simulation is deemed to be an attractive alternative. Nevertheless, quantum simulations of the SYK model on noisy quantum processors are severely limited by the complexity of its Hamiltonian. In this work, we simulate the real-time dynamics of a sparsified version of the SYK model with 24 Majorana fermions on a trapped-ion quantum processor. We adopt a randomized quantum algorithm, TETRIS, and develop an error mitigation technique tailored to the algorithm. Leveraging the hardware’s high-fidelity quantum operations and all-to-all connectivity of the qubits, we successfully calculate the Loschmidt amplitude for sufficiently long times so that its decay is observed. Based on the experimental and further numerical results, we assess the future possibility of larger-scale simulations of the SYK model by estimating the required quantum resources. Moreover, we present a scalable mirror-circuit benchmark based on the randomized SYK Hamiltonian and the TETRIS algorithm, which we argue provides a better estimate of the decay of fidelity for local observables than standard mirror-circuits.
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Acknowledgements
The experimental data reported in this work were produced by the Quantinuum H1-1 quantum computer, Powered by Honeywell, on February 6-18, 2025. E.G. acknowledges support by the Bavarian Ministry of Economic Aff airs, Regional Development and Energy (StMWi) under project Bench-QC (DIK0425/01). Y.K. thanks Juan Pedersen for useful discussions. We thank Matthew DeCross and Christopher Self for reading the paper and providing feedback.
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Y.K. and E.R. initiated the idea to use the stochastic algorithm for simulating the SYK model, did the background research and scaling and resource estimate. E.G. implemented the numerical analysis, the hardware experiments and made the figures. E.G. and H.D. developed the noise mitigation technique. All authors contributed to discussing the results and improving the hardware protocol. All authors contributing to writing the manuscript.
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H.D. is a shareholder of Quantinuum.
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Granet, E., Kikuchi, Y., Dreyer, H. et al. Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer. npj Quantum Inf (2026). https://doi.org/10.1038/s41534-026-01206-1
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DOI: https://doi.org/10.1038/s41534-026-01206-1
