Certificates of quantum many-body properties assisted by machine learning

Understand

Computationally intractable tasks are often encountered in physics and optimization.

• Such tasks often comprise a cost function to be optimized over a so-called feasible set, which is specified by a set of constraints.
• This may yield, in general, to difficult and non-convex optimization tasks.
• A number of standard methods are used to tackle such problems: variational approaches focus on parameterizing a subclass of solutions within the feasible set; in contrast, relaxation techniques have been proposed to approximate it from outside, thus complementing the variational approach by providing ultimate bounds to the global optimal solution.