  We consider quantum circuits composed of single-qubit operations and global
entangling gates generated by Ising-type Hamiltonians. It is shown that such
circuits can implement a large class of unitary operators commonly used in
quantum algorithms at a very low cost -- using a constant or effectively
constant number of global entangling gates. Specifically, we report
constant-cost implementations of Clifford operations with and without ancillae,
constant-cost implementation of the multiply controlled gates with linearly
many ancillae, and an $O(\log^*(n))$ cost implementation of the $n$-controlled
single-target gates using logarithmically many ancillae. This shows a
significant asymptotic advantage of circuits enabled by the global entangling
gates.
