  Efficient methods for encoding and compression are likely to pave way towards
the problem of efficient trainability on higher dimensional Hilbert spaces
overcoming issues of barren plateaus. Here we propose an alternative approach
to variational autoencoders to reduce the dimensionality of states represented
in higher dimensional Hilbert spaces. To this end we build a variational based
autoencoder circuit that takes as input a dataset and optimizes the parameters
of Parameterized Quantum Circuit (PQC) ansatz to produce an output state that
can be represented as tensor product of 2 subsystems by minimizing Tr(\rho^2).
The output of this circuit is passed through a series of controlled swap gates
and measurements to output a state with half the number of qubits while
retaining the features of the starting state, in the same spirit as any
dimension reduction technique used in classical algorithms. The output obtained
is used for supervised learning to guarantee the working of the encoding
procedure thus developed. We make use of Bars and Stripes dataset (BAS) for an
8x8 grid to create efficient encoding states and report a classification
accuracy of 95% on the same. Thus the demonstrated example shows a proof for
the working of the method in reducing states represented in large Hilbert
spaces while maintaining the features required for any further machine learning
algorithm that follow.
