[Paper Review] Clustering and enhanced classification using a hybrid quantum autoencoder

Maiyuren Srikumar, Charles D. Hill+1 more|arXiv (Cornell University)|Jul 26, 2021

Quantum Computing Algorithms and ArchitectureComputer Science57 references19 citations

TL;DR

This paper proposes a hybrid quantum autoencoder (HQA) that maps quantum states to a classical latent space via a variational quantum circuit and classical neural network, enabling clustering and semi-supervised classification of quantum states. The HQA achieves dimensionality reduction by training a parameterized quantum circuit to encode quantum state features into a classical representation, with numerical results showing effective clustering and classification using classical ML on the compressed data.

ABSTRACT

Quantum machine learning (QML) is a rapidly growing area of research at the intersection of classical machine learning and quantum information theory. One area of considerable interest is the use of QML to learn information contained within quantum states themselves. In this work, we propose a novel approach in which the extraction of information from quantum states is undertaken in a classical representational-space, obtained through the training of a hybrid quantum autoencoder (HQA). Hence, given a set of pure states, this variational QML algorithm learns to identify, and classically represent, their essential distinguishing characteristics, subsequently giving rise to a new paradigm for clustering and semi-supervised classification. The analysis and employment of the HQA model are presented in the context of amplitude encoded states - which in principle can be extended to arbitrary states for the analysis of structure in non-trivial quantum data sets.

Motivation & Objective

• To develop a method for learning and representing quantum state features in a classical latent space.
• To enable clustering and semi-supervised classification of quantum states using classical machine learning on compressed representations.
• To overcome the inaccessibility of quantum state information by transforming it into a classically accessible, low-dimensional vector space.
• To demonstrate that quantum data structure can be effectively learned and utilized via hybrid quantum-classical architectures on NISQ devices.

Proposed method

• Employs a hybrid quantum autoencoder (HQA) with a quantum neural network (QNN) encoder and a classical neural network (ANN) decoder.
• The QNN encoder maps input quantum states to a classical latent vector through measurement, enabling classical representation.
• The decoder reconstructs the input quantum state from the classical latent vector using a combination of ANN and QNN components.
• Uses a parameterized quantum circuit (PQC) with rotation and entangling layers (hardware-efficient ansatz) for variational optimization.
• Applies the parameter shift rule for gradient computation in the classical optimization loop to train the HQA.
• Employs the swap test to compute state fidelity as a loss function for training, enabling comparison between reconstructed and target quantum states.

Experimental results

Research questions

• RQ1 Can quantum state information be effectively compressed into a classical latent space using a hybrid quantum-classical architecture?
• RQ2 Can the classical representation learned by the HQA support meaningful clustering of quantum states?
• RQ3 Does the HQA enable improved classification performance on quantum data compared to direct quantum state analysis?
• RQ4 How does the HQA’s performance scale with the number of qubits and training iterations?
• RQ5 To what extent can the HQA capture the intrinsic manifold structure of quantum state data?

Key findings

• The HQA successfully learns a classical representation of quantum states that preserves essential distinguishing features for clustering and classification.
• Numerical simulations demonstrate effective clustering of amplitude-encoded quantum states using k-means on the classical latent vectors.
• The HQA achieves high-fidelity state reconstruction, with fidelity losses minimized through gradient-based optimization using the parameter shift rule.
• The training complexity scales as O((1 + PE)/ε²_ξ + (1 + PD)/ε²_fid), showing feasibility under NISQ constraints.
• The method enables semi-supervised classification by leveraging the classical latent space for downstream ML tasks.
• The approach provides a scalable framework for analyzing non-trivial quantum data sets by mapping them to a classically accessible, low-dimensional manifold.