First Measurement of Entanglement Dynamics in the SYK Model using Quantum Computers

Abstract: The Sachdev-Ye-Kitaev (SYK) model, fundamental to quantum chaos, many-body physics, and holographic duality, exhibits both maximal chaos and exact solvability, yet its entanglement entropy has never been measured experimentally. Here, we present the first measurement of entanglement entropy growth under the SYK Hamiltonian using IBM's superconducting quantum computer as a programmable quantum platform. We implement an optimized swap-based many-body interference protocol tailored for limited qubit connectivity to measure entanglement entropy. Additionally, we enhance the randomized measurement protocol for entropy measurement by expanding the unitary ensemble, which increases the circuit volume and pushes the capability of the near-term devices. However, we tackle this challenge by employing a quantum multi-programming strategy that parallelizes circuit execution. This work paves the way for exploring chaotic quantum dynamics and establishes scalable methods for investigating complex entanglement growth on current quantum platforms.