  The exact number of CNOT and single qubit gates needed to implement a Quantum
Algorithm in a given architecture is one of the central problems of Quantum
Computation. In this work we study the importance of concise realizations of
Partially defined Unitary Transformations for better circuit construction using
the case study of Dicke State Preparation. The Dicke States $(\left|D^n_k
\right>)$ are an important class of entangled states with uses in many branches
of Quantum Information. In this regard we provide the most efficient
Deterministic Dicke State Preparation Circuit in terms of CNOT and single qubit
gate counts in comparison to existing literature. We further observe that our
improvements also reduce architectural constraints of the circuits. We
implement the circuit for preparing $\left| D^4_2 \right>$ on the "ibmqx2"
machine of the IBM QX service and observe that the error induced due to noise
in the system is lesser in comparison to the existing circuit descriptions. We
conclude by describing the CNOT map of the generic $\left| D^n_k \right>$
preparation circuit and analyze different ways of distributing the CNOT gates
in the circuit and its affect on the induced error.
