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arXiv:2507.07530 · npj Quantum Information

Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer

Etienne Granet, Yuta Kikuchi, Henrik Dreyer, Enrico Rinaldi

Published Feb 23, 2026• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41534-026-01206-1

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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.
A bstract The Sachdev-Ye-Kitaev (SYK) model is a system of N Majorana fermions with random interactions and strongly chaotic dynamics, which at low energy admits a holographically dual description as two-dimensional Jackiw-Teitelboim gravity. Hence the SYK model provides a toy model of quantum gravity that might be feasible to simulate with near-term quantum hardware. Motivated by the goal of reducing the resources needed for such a simulation, we study a sparsified version of the SYK model, in which interaction terms are deleted with probability 1 −p . Specifically, we compute numerically the spectral form factor (SFF, the Fourier transform of the Hamiltonian’s eigenvalue pair correlation function) and the nearest-neighbor eigenvalue gap ratio r (characterizing the distribution of gaps between consecutive eigenvalues). We find that when p is greater than a transition value p 1 , which scales as 1/ N 3 , both the SFF and r match the values attained by the full unsparsified model and with expectations from random matrix theory (RMT). But for p < p 1 , deviations from unsparsified SYK and RMT occur, indicating a breakdown of holography in the highly sparsified regime. Below an even smaller value p 2 , which also scales as 1/ N 3 , even the spacing of consecutive eigenvalues differs from RMT values, signaling a complete breakdown of spectral rigidity. Our results cast doubt on the holographic interpretation of very highly sparsified SYK models obtained via machine learning using teleportation infidelity as a loss function.
We study the Sachdev-Ye-Kitaev (SYK) model---an important toy model for quantum gravity on IBM's superconducting qubit quantum computers. By using a graph-coloring algorithm to minimize the number of commuting clusters of terms in the qubitized Hamiltonian, we find the gate complexity of the time evolution using the first-order product formula for NNN Majorana fermions is $\mathcal{O}({N}^{5}{J}^{2}{t}^{2}/\ensuremath{\epsilon})$ where JJJ is the dimensionful coupling parameter, ttt is the evolution time, and $\ensuremath{\epsilon}$ is the desired precision. With this improved resource requirement, we perform the time evolution for N=6N=6N=6, 8 with maximum two-qubit circuit depth and gate count of 343. We perform different error mitigation schemes on the noisy hardware results and find good agreement with the exact diagonalization results on classical computers and noiseless simulators. In particular, we compute vacuum return probability after time ttt and out-of-time order correlators which is a standard observable of quantifying the chaotic nature of quantum systems.
The ground state of random Hamiltonians with all-to-all interactions such as the quantum Sherrington-Kirkpatrick (SK) model and the Sachdev-Ye-Kitaev (SYK) model follow volume-law entanglement and are expected to be hard to model using tensor networks. In recent years, some progress has been made to push the limit of classical methods using neural quantum states. However, it remains an open question whether there exist quantum algorithms that could offer a quantum advantage over the state-of-the-art classical methods in simulating random Hamiltonians. In this work, we show that one such algorithm, TETRIS-ADAPT-VQE, can construct accurate ground states for dense and sparse SYK models containing up to N=20N=20N=20 Majorana fermions achieving fidelities ≥99.3%\geq 99.3\%≥99.3% and for the quantum SK model with up to L=18L=18L=18 sites achieving fidelities ≥99.9998%\geq 99.9998\%≥99.9998%. We find that while the preparation of ground states is efficient (in terms of operator pool size and circuit depth) for the SK model, it is not efficient for either dense or moderately sparse SYK models.
Quantum computers are expected to be vital for exploring complex dynamics in many-body quantum systems. Thus, validating established results on current quantum computers is essential for evaluating their future utility. Hence, we investigate the entanglement entropy of the Sachdev-Ye-Kitaev (SYK) model, a paradigmatic model of quantum chaos, many-body physics, and holographic duality, in current IBM’s superconducting quantum computers. We implement optimized swap-based many-body interference protocol and randomized measurement protocol tailored for IBM quantum computers’ limited qubit connectivity. Additionally, we employ quantum multi-programming that parallelizes circuit execution to improve the results obtained by the randomized measurement protocol. Finally, by incorporating the quantum error mitigation techniques into our implementation of the entropy measurement protocols on IBM quantum hardware, we show that the current noisy quantum computer can yield results aligned with theoretical expectations, therefore affirming its capability to explore chaotic quantum dynamics in complex quantum systems. • Measurement of the real-time dynamics of the entanglement entropy (second Rényi entropy) in the SYK Model using IBM’s superconducting quantum computers. • Implementation of the optimized SWAP-based many-body interference protocol designed for limited qubit connectivity to measure the entanglement entropy using IBM’s superconducting quantum computers. • Using quantum multi-programming to parallelize circuit execution to improve the randomized measurement protocol in determining the entanglement entropy.
We study the preparation of thermal states of the dense and sparse Sachdev-Ye-Kitaev (SYK) model using a variational quantum algorithm for 6≤N≤126 \le N \le 126≤N≤12 Majorana fermions over a wide range of temperatures. Utilizing IBM's 127-qubit quantum processor, we perform benchmark computations for the dense SYK model with N=6N = 6N=6, showing good agreement with exact results. The preparation of thermal states of a non-local random Hamiltonian with all-to-all coupling using the simulator and quantum hardware represents a significant step toward future computations of thermal out-of-time order correlators in quantum many-body systems.
Abstract The Sachdev-Ye-Kitaev (SYK) model incorporates rich physics, ranging from exotic non-Fermi liquid states without quasiparticle excitations, to holographic duality and quantum chaos. However, its experimental realization remains a daunting challenge due to various unnatural ingredients of the SYK Hamiltonian such as its strong randomness and fully nonlocal fermion interaction. At present, constructing such a nonlocal Hamiltonian and exploring its dynamics is best through digital quantum simulation, where state-of-the-art techniques can already handle a moderate number of qubits. Here, we demonstrate a first step towards simulation of the SYK model on a nuclear-spin-chain simulator. We observed the fermion paring instability of the non-Fermi liquid state and the chaotic-nonchaotic transition at simulated temperatures, as was predicted by previous theories. As the realization of the SYK model in practice, our experiment opens a new avenue towards investigating the key features of non-Fermi liquid states, as well as the quantum chaotic systems and the AdS/CFT duality.