Learning Quantum Gibbs States Locally and Efficiently

Learn quantum Gibbs states through a novel algorithm that achieves near-optimal sample and computational complexity for local Hamiltonians at arbitrary inverse temperatures. Explore how this 56-minute conference talk from the Simons Institute presents a breakthrough learning protocol that determines each local term of an n-qubit D-dimensional Hamiltonian to additive error ε with sample complexity scaling as e^{poly(β)} / β²ε² log(n). Discover the algorithm's use of parallelizable local quantum measurements within bounded lattice regions and near-linear-time classical post-processing, achieving complexity that is near optimal with respect to system size and error while being polynomially tight with respect to temperature. Examine the theoretical foundations built on the interplay between locality, the Kubo-Martin-Schwinger condition, and the operator Fourier transform at arbitrary temperatures. Understand how this approach addresses fundamental challenges in quantum learning theory and experimental sciences by providing provable algorithms that match the locality and simplicity found in classical cases. Learn about extensions to Hamiltonians with bounded interaction degree and their associated complexity scaling properties.