Variational Quantum Transformer Architecture for Synthetic Language Generation

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by $\textsf{QNC}^0$ circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model ($\textsf{DLM}$) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern $\textsf{DLM}$s rely on. 2. Functional separation. We exhibit a function computable in $\land \circ \textsf{QNC}^0[\log\log n]$ (i.e., a family of O$(\log\log n)$-depth $\textsf{QNC}^0$ circuits, where $n$ is the input length, followed by a single classical $\mathsf{AND}$ gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width $n^{Ω(1)}$. Together, our work initiates the study of quantum advantage in the era of large language models.

Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96% of the $R^2$ of attention-based VQCs while using 40-50% fewer parameters, and consistently outperform equal-capacity MLPs (mean $R^2{=}0.829$ vs.\ MLP$_{720}$'s $0.753$ on Boston Housing, 3-seed average); \textbf{(ii)}FC-VQC's Type4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}expressibility saturates at circuit depth${\approx}\,3$, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.

Classical continuous-space neural networks fundamentally struggle to lock into exact mathematical symmetries, such as modular arithmetic and non-commutative algebra. To approximate these discrete logical rules, they often rely on massive parameter scaling, resulting in stochastic instability even after delayed generalization phenomena known as grokking. Here, we introduce the Universal Quantum Transformer (UQT), a fundamentally novel, quantum-native computing architecture that uses the physical properties of multi-qubit systems as a universal inductive bias for exact mathematical and algebraic reasoning. Rather than translating classical neural mechanisms, our framework relies entirely on parameterized geometric phase embedding and $SU(2)$ wave-interference. We demonstrate that the quantum attention circuit, operating on a highly compact 5-qubit substrate, perfectly learns two highly distinct formal classes: cyclic modular arithmetic ($\mathbb{Z}_{11}$) and non-Abelian algebra (the $S_4$ permutation group). While classical attention-based networks exhibit stochastic instability at convergence, the UQT achieves mathematically exact, deterministic generalization. We refer to this phenomenon as crystallization: a step beyond the well-known phenomenon of grokking. Crucially, this framework yields massive computational and memory advantages by theoretically bypassing the quadratic bottleneck of classical self-attention, and by logarithmically compressing the required representation dimension to eliminate the massive over-parameterization inherent to classical networks. Finally, we deploy this architecture on noisy intermediate-scale quantum (NISQ) hardware, proving its viability on current IBM Quantum computers. These results establish parameterized quantum topology as a universally superior physical substrate for exact artificial intelligence.