  Entanglement plays an important role in quantum communication, algorithms,
and error correction. Schmidt coefficients are correlated to the eigenvalues of
the reduced density matrix. These eigenvalues are used in Von Neumann entropy
to quantify the amount of the bipartite entanglement. In this paper, we map the
Schmidt basis and the associated coefficients to quantum circuits to generate
random quantum states. We also show that it is possible to adjust the
entanglement between subsystems by changing the quantum gates corresponding to
the Schmidt coefficients. In this manner, random quantum states with predefined
bipartite entanglement amounts can be generated using random Schmidt basis.
This provides a technique for generating equivalent quantum states for given
weighted graph states, which are very useful in the study of entanglement,
quantum computing, and quantum error correction.
