TY - JOUR
T1 - Product Formulas for Exponentials of Commutators
JF - Journal of Mathematical Physics
Y1 - 2013
A1 - Andrew M. Childs
A1 - Nathan Wiebe
AB - We provide a recursive method for constructing product formula approximations to exponentials of commutators, giving the first approximations that are accurate to arbitrarily high order. Using these formulas, we show how to approximate unitary exponentials of (possibly nested) commutators using exponentials of the elementary operators, and we upper bound the number of elementary exponentials needed to implement the desired operation within a given error tolerance. By presenting an algorithm for quantum search using evolution according to a commutator, we show that the scaling of the number of exponentials in our product formulas with the evolution time is nearly optimal. Finally, we discuss applications of our product formulas to quantum control and to implementing anticommutators, providing new methods for simulating many-body interaction Hamiltonians.
VL - 54
U4 - 062202
UR - http://arxiv.org/abs/1211.4945v2
CP - 6
J1 - J. Math. Phys.
U5 - 10.1063/1.4811386
ER -