  In this paper, we develop a Lie group theoretic approach for parametric
representation of unitary matrices. This leads to develop a quantum neural
network framework for quantum circuit approximation of multi-qubit unitary
gates. Layers of the neural networks are defined by product of exponential of
certain elements of the Standard Recursive Block Basis, which we introduce as
an alternative to Pauli string basis for matrix algebra of complex matrices of
order $2^n$. The recursive construction of the neural networks implies that the
quantum circuit approximation is scalable i.e. quantum circuit for an
$(n+1)$-qubit unitary can be constructed from the circuit of $n$-qubit system
by adding a few CNOT gates and single-qubit gates.
