Holographic dynamics simulations with a trapped-ion quantum computer

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. The simulation of quantum dynamics is a challenging task to solve with classical resources. An experiment with a trapped-ion quantum processor now shows the efficient simulation of the evolution of large-scale many-body quantum systems.