  The use of Quantum Neural Networks (QNN) that are analogous to classical
neural networks, has greatly increased in the past decade owing to the growing
interest in the field of Quantum Machine Learning (QML). A QNN consists of
three major components: (i) data loading/encoding circuit, (ii) Parametric
Quantum Circuit (PQC), and (iii) measurement operations. Under ideal
circumstances the PQC of the QNN trains well, however that may not be the case
for training under quantum hardware due to presence of different kinds of
noise. Deeper QNNs with high depths tend to degrade more in terms of
performance compared to shallower networks. This work aims to reduce depth and
gate count of PQCs by replacing parametric gates with their approximate fixed
non-parametric representations. We propose a greedy algorithm to achieve this
such that the algorithm minimizes a distance metric based on unitary
transformation matrix of original parametric gate and new set of non-parametric
gates. From this greedy optimization followed by a few epochs of re-training,
we observe roughly 14% reduction in depth and 48% reduction in gate count at
the cost of 3.33% reduction in inferencing accuracy. Similar results are
observed for a different dataset as well with different PQC structure.
