Simulation of the homogeneous electron gas on quantum computers*

The homogeneous electron gas is an idealized system of infinitely many interacting electrons extending infinitely in space. It is a simple model for metals, and is thus an important system to physicists, chemists, and materials scientists. 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 and a variety of quantum simulators. Specifically, we will employ the variational quantum eigensolver (VQE) method to compute a variational approximation to the ground state of the HEG, comparing it to exact diagonalization approaches. We will discuss the performance of optimized symmetry-informed ansatzes and report on results obtained using different quantum computing platforms platforms (based on superconducting circuits, trapped-ions, and simulators).