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

TL;DR

This paper demonstrates the simulation of a sparsified SYK model with 24 Majorana fermions on a trapped-ion quantum computer using a randomized algorithm, showcasing potential for larger-scale quantum simulations of chaotic systems.

Contribution

It introduces a novel randomized quantum algorithm, TETRIS, and an error mitigation technique for simulating the SYK model on noisy quantum hardware, enabling longer real-time dynamics observation.

Findings

Successful simulation of SYK model dynamics on trapped-ion hardware

Development of a scalable mirror-circuit benchmark for fidelity decay

Assessment of future resource requirements for larger SYK simulations

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.