Fast-forwarding quantum evolution

We investigate the problem of fast-forwarding quantum evolution, whereby dynamics certain systems can be simulated with gate complexity that is sublinear in evolution time. provide a definition considers model computation, Hamiltonians induce and properties initial states. Our accounts for any asymptotic improvement general case we use it to demonstrate several systems. In particular, show some local spin whose taken into block diagonal form using an efficient circuit, such as those are permutation-invariant, exponentially fast-forwarded. also classes positive semidefinite systems, known frustration-free, polynomially fast-forwarded, provided state supported on subspace sufficiently low energies. Last, all quadratic fermionic number-conserving bosonic fast-forwarded where gates exponentials specific or operators, respectively. results extend physical were previously while not necessarily requiring methods diagonalize efficiently. further develop connection between precise energy measurements polynomial improvements.