Fast-fowarding quantum dynamics with quantum Krylov subspace algorithms

In this talk, I will present a new method for fast-forwarding quantum dynamics simulations using quantum Krylov subspace algorithms. Our approach consists of a hybrid quantum classical algorithm that constructs a projected Schrodinger equation in a Krylov subspace, where the matrix elements are computed using the quantum computer and the Krylov-based fast-forwarding is performed on a classical computer. We show that this method is highly competitive to other quantum variational fast-forwarding techniques, requiring less resources overall for a wide variety of Hamiltonians relevant to nuclear physics, condensed matter physics, and quantum chemistry. We validate our approach through numerical experiments of various molecular systems, showing excellent recovery of ideal quantum dynamics beyond the coherence time of near-term quantum computers.