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 (textttQBET), a framework for evaluating quantum, classical, and hybrid transformer architectures. In this toolbox, we introduce lean metrics for Simplicity Bias (textttSB) and Expressivity (textttEXP), for comparing across various models, and extend the analysis of textttSB to generative and multiclass-classification tasks. We show that textttQBET 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 textttSB metric and comparing their relative performance.