Speaker
Ryan LaRose
Description
Quantum Krylov methods are strong candidates for computing ground states on NISQ and MegaQuop computers. While typically implemented with powers of the time evolution unitary $e^{-iH t}$ for a given Hamiltonian $H$, convergence can be markedly faster with powers of the Hamiltonian $H$ itself as in classical methods. We discuss these convergence rates and present several ways to implement Hamiltonian powers on quantum computers, including qubitization and randomized methods, for use in quantum Krylov. We compare the approaches by providing resource estimates for common applications on current and future quantum computers.