Dimensionality reduction with variational encoders based on subsystem purification

TL;DR

This paper introduces a quantum variational autoencoder that reduces the dimensionality of high-dimensional quantum states, preserving essential features for machine learning tasks, demonstrated on the Bars and Stripes dataset with high accuracy.

Contribution

It proposes a novel quantum autoencoder architecture based on subsystem purification and tensor product output, enabling effective dimensionality reduction in quantum states.

Findings

Achieved 95% classification accuracy on Bars and Stripes dataset.

Demonstrated effective state compression while retaining features for supervised learning.

Validated the method's potential for efficient encoding in high-dimensional quantum spaces.

Abstract

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.