Computing band gaps of periodic materials via sample-based quantum diagonalization

A key objective of computational solid state physics is to predict electronic properties of periodic materials. However, electronic structure simulations based on density functional theory fail to predict experimental results if correlations are not properly accounted for. Here, we report a sample-based quantum diagonalization workflow for simulating electronic states of periodic materials, and for predicting their band gaps. To that end, we devise a general lattice Hamiltonian representation in which material-specific, electronic interaction parameters are obtained self-consistently. Two exemplar, wide-gap materials - hafnium dioxide and zirconium dioxide - are expressed as quantum circuits that leverage the lattice representation with a materials-specific parametrization. We sample the quantum circuits on a state-of-the-art, superconducting quantum processor and diagonalize the lattice Hamiltonian in the reduced configuration subspaces with standard techniques. Our method outperforms select quantum-chemical benchmarks as well as approaches based on density functional theory, the standard reference in materials simulation of solids. Importantly, the quantum-computed band gap predictions for the two dielectrics agree with independent lab experiments. In essence, quantum-classical hybrid simulation workflows on pre-fault tolerant quantum computers produce useful, experimentally verifiable property predictions in applied materials science.