Error-Resistant Quantum Matrix Element Estimation

A wide variety of quantum algorithms, ranging from quantum-kernel-based machine learning to eigensolvers for quantum chemistry, rely on evaluation of matrix elements with quantum computers. These matrix elements are often classically intractable to evaluate precisely. The eigenspectra of the resulting matrices, whether partially or completely estimated with a quantum computer, are often the subject of interest for further classical processing. However, quantum matrix element evaluation methods suffer from environmental noise and device error, which can corrupt fundamental properties of the evaluated matrix. Each error channel—such as depolarizing noise, coherent error, relaxation, and stochastic perturbation—adversely contributes to deviation from the noise-free ideal. In this talk, we will show how realistic device error propagates through quantum matrix element estimation algorithms and discuss its effect on estimated matrix eigenspectra. We will then present an error mitigation technique to make the estimation process more robust and provide estimates on resource requirements and error tolerance. We will demonstrate our error mitigation technique for a real-world quantum chemistry application with noisy simulations.