Random State Approach to Quantum Computation of Electronic-Structure Properties

Classical computation of electronic properties in large-scale materials remains challenging. Quantum computation has the potential to offer advantages in memory footprint and computational scaling. However, general and viable quantum algorithms for simulating large-scale materials are still limited. We propose and implement random-state quantum algorithms to calculate electronic-structure properties of real materials. Using a random state circuit on a small number of qubits, we employ real-time evolution with first-order Trotter decomposition and Hadamard test to obtain electronic density of states, and we develop a modified quantum phase estimation algorithm to calculate real-space local density of states via direct quantum measurements. Furthermore, we validate these algorithms by numerically computing the density of states and spatial distributions of electronic states in graphene, twisted bilayer graphene quasicrystals, and fractal lattices, covering system sizes from hundreds to thousands of atoms. Our results manifest that the random-state quantum algorithms provide a general and qubit-effcient route to scalable simulations of electronic properties in large-scale periodic and aperiodic materials.