Optimizing Strongly Interacting Fermionic Hamiltonians

Understand

The fundamental problem in much of physics and quantum chemistry is to optimize a low-degree polynomial in certain anticommuting variables.

• Being a quantum mechanical problem, in many cases we do not know an efficient classical witness to the optimum, or even to an approximation of the optimum.
• One prominent exception is when the optimum is described by a so-called "Gaussian state", also called a free fermion state.
• In this work we are interested in the complexity of this optimization problem when no good Gaussian state exists.