ζ-QVAE: A Quantum Variational Autoencoder utilizing Regularized Mixed-state Latent Representations
arxiv(2024)
摘要
A major challenge in near-term quantum computing is its application to large
real-world datasets due to scarce quantum hardware resources. One approach to
enabling tractable quantum models for such datasets involves compressing the
original data to manageable dimensions while still representing essential
information for downstream analysis. In classical machine learning, variational
autoencoders (VAEs) facilitate efficient data compression, representation
learning for subsequent tasks, and novel data generation. However, no model has
been proposed that exactly captures all of these features for direct
application to quantum data on quantum computers. Some existing quantum models
for data compression lack regularization of latent representations, thus
preventing direct use for generation and control of generalization. Others are
hybrid models with only some internal quantum components, impeding direct
training on quantum data. To bridge this gap, we present a fully quantum
framework, ζ-QVAE, which encompasses all the capabilities of classical
VAEs and can be directly applied for both classical and quantum data
compression. Our model utilizes regularized mixed states to attain optimal
latent representations. It accommodates various divergences for reconstruction
and regularization. Furthermore, by accommodating mixed states at every stage,
it can utilize the full-data density matrix and allow for a "global" training
objective. Doing so, in turn, makes efficient optimization possible and has
potential implications for private and federated learning. In addition to
exploring the theoretical properties of ζ-QVAE, we demonstrate its
performance on representative genomics and synthetic data. Our results
consistently indicate that ζ-QVAE exhibits similar or better performance
compared to matched classical models.
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