HamLib is an extensive dataset of qubit Hamiltonians spanning a large range of problem sizes and instances that is designed for testing quantum algorithms, software and hardware.
In this paper, we introduce the multi-observable dynamic mode decomposition (MODMD) approach combining ODMD with classical shadows for efficient low-lying energy computations on near-term and early fault-tolerant quantum computers.
In this paper, we introduce k-NoCliD, a method to reduce the number of measurements for estimating expectation values that relaxes the constraint of commutativity.
We propose two methods for implementing operator resolvents on a quantum computer based on Hamiltonian simulation: a first method based on discretization of integral representations of the resolvent through Gauss quadrature rule and a second method that leverages a continuous variable ancilla qubit. We use these results to study the implementation of rational functions on a quantum computer and illustrate their potential for estimating low-lying energies.