A Variational Quantum Eigensolver Based on the Measurement Scheme Tailored to Multiband Tight-Binding Simulations

We propose a cost-efficient measurement scheme of the variational quantum eigensolver (VQE) for atomistic simulations of electronic structures based on a tight-binding (TB) theory. Leveraging the lattice geometry of a material domain, the sparse TB Hamiltonian is constructed in a bottom-up manner and is represented as a linear combination of the standard-basis (SB) operators. The cost function is evaluated with an extended version of the Bell measurement circuit that can simultaneously measure multiple SB operators and therefore reduces the number of circuits required by the evaluation process. The proposed VQE scheme is applied to find band gap energies of metal-halide-perovskite supercells that have finite dimensions with closed boundaries and are described with an sp³ TB model. Experimental results confirm that the proposed scheme gives solutions that follow well the accurate ones but, more importantly, has computing efficiency that is obviously superior to the commutativity-based Pauli grouping methods. Extending the application scope of VQE to three-dimensional confined atomic structures, this work can serve as a practical guideline for handling TB simulations and, more generally, for calculations of sparse Hermitian matrices in the noise-intermediate-scale quantum devices.