Abstract: |
The problem of learning a quantum Hamiltonian from its Gibbs state is a central problem in the field of quantum information, with most attention given to the problem of learning local Hamiltonians. Work in recent years has established bounds on the measurements required to learn a local Hamiltonian, but bounds on the computational complexity are limited to special cases like high temperatures. No general algorithm has achieved a runtime complexity that is less than exponential in system size. In this talk I will discuss the special case of commuting 2-local Hamiltonians, for which we think that efficient learning algorithms exist, as this problem is closely linked to the classical Hamlitonian learning problem, for which efficient algorithms exist. I will present how an efficient learning algorithm may make use of the similarity between the quantum and classical problems, and discuss the challenges of using such an algorithm in the presence of statistical errors. |