4,101 research outputs found
Hamiltonian Simulation Using Linear Combinations of Unitary Operations
We present a new approach to simulating Hamiltonian dynamics based on
implementing linear combinations of unitary operations rather than products of
unitary operations. The resulting algorithm has superior performance to
existing simulation algorithms based on product formulas and, most notably,
scales better with the simulation error than any known Hamiltonian simulation
technique. Our main tool is a general method to nearly deterministically
implement linear combinations of nearby unitary operations, which we show is
optimal among a large class of methods.Comment: 18 pages, 3 figure
Inexact Arnoldi residual estimates and decay properties for functions of non-Hermitian matrices
We derive a priori residual-type bounds for the Arnoldi approximation of a
matrix function and a strategy for setting the iteration accuracies in the
inexact Arnoldi approximation of matrix functions. Such results are based on
the decay behavior of the entries of functions of banded matrices.
Specifically, we will use a priori decay bounds for the entries of functions of
banded non-Hermitian matrices by using Faber polynomial series. Numerical
experiments illustrate the quality of the results
- …