Model selection in hybrid quantum neural networks with applications to quantum transformer architectures

Quantum machine learning models generally lack principled design guidelines, often requiring full resource-intensive training across numerous choices of encodings, quantum circuit designs and initialization strategies to find effective configuration. To address this challenge, we develope the Quantum Bias-Expressivity Toolbox ($\texttt{QBET}$), a framework for evaluating quantum, classical, and hybrid transformer architectures. In this toolbox, we introduce lean metrics for Simplicity Bias ($\texttt{SB}$) and Expressivity ($\texttt{EXP}$), for comparing across various models, and extend the analysis of $\texttt{SB}$ to generative and multiclass-classification tasks. We show that $\texttt{QBET}$ enables efficient pre-screening of promising model variants obviating the need to execute complete training pipelines. In evaluations on transformer-based classification and generative tasks we employ a total of $18$ qubits for embeddings ($6$ qubits each for query, key, and value). We identify scenarios in which quantum self-attention variants surpass their classical counterparts by ranking the respective models according to the $\texttt{SB}$ metric and comparing their relative performance.

Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation

In this work, we introduce the Quantum Generative Adversarial Autoencoder (QGAA), a quantum model for generation of quantum data. The QGAA consists of two components: (a) Quantum Autoencoder (QAE) to compress quantum states, and (b) Quantum Generative Adversarial Network (QGAN) to learn the latent space of the trained QAE. This approach imparts the QAE with generative capabilities. The utility of QGAA is demonstrated in two representative scenarios: (a) generation of pure entangled states, and (b) generation of parameterized molecular ground states for H$_2$ and LiH. The average errors in the energies estimated by the trained QGAA are 0.02 Ha for H$_2$ and 0.06 Ha for LiH in simulations upto 6 qubits. These results illustrate the potential of QGAA for quantum state generation, quantum chemistry, and near-term quantum machine learning applications.