Quantum eigenpair solver with minimal sampling overhead

Abstract: The advantage that many quantum algorithms have over their classical counterparts may be lost when the results are extracted as classical data (output problem). One example are eigenpair solvers, which encode the eigenpairs in a quantum state. Extracting these states results in significant sampling overheads. We propose an amplitude-amplification-based post-filtering process that reduces the number of eigenpairs encoded in the final state to a feasible amount. Often for practical applications, computing a subset of all eigenpairs is sufficient, which drastically reduces the sampling overhead. We show, that our adapted eigenpair solver does not only compete with classical alternatives but outperforms them in terms of memory requirements, runtime, and versatility. This makes it an efficient end-to-end quantum algorithm with real-world application in science and engineering.