Hamiltonian learning for 300 trapped ion qubits with long-range couplings
Shian Guo, Yukai Wu, J. Ye, Lin Zhang, Y. Wang, Wentao Lian, Rui Yao, Yulin Xu, Chi Zhang, Yuling Xu, B. Qi, Pan‐Yu Hou, Li He, Z.-C. Zhou, Luming Duan · Science Advances · 2025
Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for any quantitative applications of a quantum simulator, remains an outstanding challenge due to the fast increasing time cost with the qubit number and the lack of high-fidelity universal gate operations in the noisy intermediate-scale quantum era. Here, we demonstrate the Hamiltonian learning of a two-dimensional ion trap quantum simulator with 300 qubits. We use global manipulations and single-qubit-resolved state detection to efficiently learn the all-to-all-coupled Ising model Hamiltonian, with the required quantum resources scaling at most linearly with the qubit number. We further demonstrate a physically guided learning scheme with the quantum sample complexity independent of system sizes by carefully fitting the anharmonic trap potential. Our work paves the way for wide applications of large-scale ion trap quantum simulators.