Speaker: Sam Scalet, Cambridge University

Title: Algorithms from the Energy-Entropy Balance inequalities

Abstract: In the setting of local Hamiltonians on quantum spin lattices, we consider the problem of predicting expectation values of local observables in thermal states as well as its inverse problem of learning the Hamiltonian corresponding to a given Gibbs state through local measurements. We will introduce the Energy-Entropy Balance inequalities, which characterize ground and thermal states. As opposed to the equivalent KMS-condition, these constraints naturally allow for relaxations expressible in terms of local observables. Using these relaxed constraint systems, we arrive at a set of convex optimization and semidefinite programming algorithms for the prediction and learning problems. The resulting algorithms can be shown to have polynomial-time guarantees under additional assumptions on the Hamiltonian, give certificates on their outputs, and prove the decidability of a local observable problem.
This talk is based on arXiv:2311.18706 and arXiv:2410.23284.