Real-Time Dynamics for Computing Hamiltonian Properties

One of the most promising expected applications of near-term quantum computers lies in the study of static and dynamical properties of quantum many-body systems. Many quantum computing algorithms have been proposed with this goal in mind, with a focus on Hamiltonian eigenvalue extraction, a problem central to chemistry, physics, and materials science. However, the majority of established quantum algorithms require a prohibitively large number of resources for near-term hardware. Here we discuss a number of quantum algorithms relying on real-time evolution for energy eigenvalue determination such as quantum Krylov methods and the recently introduced observable-Dynamic Mode Decomposition. Real-time evolution is native to quantum hardware, making these algorithms particularly suited for the near term. We provide strong theoretical and numerical evidence that these methods can converge rapidly even in the presence of noise and demonstrate their efficacies numerically on a range of chemically relevant Hamiltonians.