  Superposition, arguably the most fundamental property of quantum mechanics,
lies at the heart of quantum information science. However, how to create the
superposition of any two unknown pure states remains as a daunting challenge.
Recently, it is proved that such a quantum protocol does not exist if the two
input states are completely unknown, whereas a probabilistic protocol is still
available with some prior knowledge about the input states [M. Oszmaniec
\emph{et al.}, Phys. Rev. Lett. 116, 110403 (2016)]. The knowledge is that both
of the two input states have nonzero overlaps with some given referential
state. In this work, we experimentally realize the probabilistic protocol of
superposing two pure states in a three-qubit nuclear magnetic resonance system.
We demonstrate the feasibility of the protocol by preparing a families of input
states, and the average fidelity between the prepared state and expected
superposition state is over 99%. Moreover, we experimentally illustrate the
limitation of the protocol that it is likely to fail or yields very low
fidelity, if the nonzero overlaps are approaching zero. Our experimental
implementation can be extended to more complex situations and other quantum
systems.
