Computing bandgaps of periodic materials with a quantum processor via tight-biding projection and subspace quantum diagonalization

State-of-the-art techniques in computational materials science often fail to capture many-body interactions of highly correlated, periodic quantum systems. In this contribution, we present a subspace quantum diagonalization workflow for simulating the electronic ground state energy of periodic materials, and for predicting their bandgaps. We obtain a fermionic Hamiltonian for solids by first projecting the electronic density obtained by density functional theory onto a localized basis set and then adding interaction parameters obtained by self-consistent field theory. We then use coefficients obtained by coupled-cluster calculation to initialize a quantum circuit for approximating the system’s ground state, avoiding a costly optimization of the circuit’s parameters. By sampling the circuit and classically diagonalizing the Hamiltonian in the subspace selected by the measured samples on the quantum device, we predict the bandgap energy of representative materials and obtain agreement with experimental results. Our non-variational approach limits the need for quantum-computational resources, and, therefore, offers a scalable pathway for utility-scale, quantum simulation of materials properties.