  We suggest and investigate a scheme for non-deterministic noiseless linear
amplification of coherent states using successive photon addition, $(\hat
a^{\dagger})^2$, where $\hat a^\dagger$ is the photon creation operator. We
compare it with a previous proposal using the photon addition-then-subtraction,
$\hat a \hat a^\dagger$, where $\hat a$ is the photon annihilation operator,
that works as an appropriate amplifier only for weak light fields. We show that
when the amplitude of a coherent state is $|\alpha| \gtrsim 0.91$, the $(\hat
a^{\dagger})^2$ operation serves as a more efficient amplifier compared to the
$\hat a \hat a^\dagger$ operation in terms of equivalent input noise. Using
$\hat a \hat a^\dagger$ and $(\hat a^{\dagger})^2$ as basic building blocks, we
compare combinatorial amplifications of coherent states using $(\hat a \hat
a^\dagger)^2$, $\hat a^{\dagger 4}$, $\hat a \hat a^\dagger\hat a^{\dagger 2}$,
and $\hat a^{\dagger 2}\hat a \hat a^\dagger$, and show that $(\hat a \hat
a^\dagger)^2$, $\hat a^{\dagger 2}\hat a \hat a^\dagger$, and $\hat a^{\dagger
4}$ exhibit strongest noiseless properties for $|\alpha| \lesssim 0.51$, $0.51
\lesssim |\alpha| \lesssim 1.05 $, and $|\alpha|\gtrsim 1.05 $, respectively.
We further show that the $(\hat a^{\dagger})^2$ operation can be used for
amplifying superpositions of the coherent states. In contrast to previous
studies, our work provides efficient schemes to implement a noiseless amplifier
for light fields with medium and large amplitudes.
