Guoming Wang, Ruizhe Zhang
Previously, there was no known way to use a near-term quantum computer to reliably compute many useful properties of quantum materials or molecules. Existing methods were either not reliable (e.g. using the VQE heuristic) or not possible with a near-term quantum computer (e.g. combining the techniques of ground state preparation plus operator expectation estimation, which require a fault-tolerant quantum computer). This paper proposes a reliable, near-term method for computing useful properties beyond just the ground state energy of a Hamiltonian. Major applications of this work include the design of materials and molecules and solving linear systems of equations. This ground state property estimation (GSPE) method is a hybrid quantum-classical algorithm. The quantum portion of the algorithm employs a simple, low-depth quantum circuit and the classical portion contains a novel post-processing procedure to extract the information of the ground state property from quantum sample data. By off-loading a significant portion of the compute to the classical post-processing, the method is feasible for implementation on early fault-tolerant quantum computers. Furthermore, with its provable performance guarantees, the method reveals a path for using these devices to create industry value.