Investigating the properties of the Homogeneous Electron Gas on small-scale quantum computers

The homogeneous electron gas is an idealized system of infinitely many interacting electrons extending infinitely in space. It is an important system to physicists, chemists, and materials scientists to understand properties of large slabs of matter in 2 and 3 dimensions, and as a simple model for metals. In this talk, we will report on the opportunities and limits of many-body calculations of the homogeneous electron gas (HEG) when performed on small-scale quantum computers. In particular, we will employ the variational quantum eigensolver (VQE) method to compute a variational approximation to the ground state of the HEG, comparing it to results calculated using standard classical Quantum Monte Carlo approaches. We will discuss the performance and limitations of choosing different basis types, and ansatzes, and report on results obtained using two different platforms (based on superconducting circuits as well as trapped-ions).