量子变压器用物理特性实现精确逻辑推理，5-6个量子比特就搞定数学与语言规则。
Universal Quantum Transformer
- 用量子相位嵌入和SU(2)波干涉构建注意力机制，不依赖经典神经网络。
- 551至1650个参数下，精准学习模11算术、S4置换群和扫描语言三种规则。
- 在真实量子硬件上达97.5%准确率，突破经典模型的随机不稳定性。
经典连续空间神经网络难以精确捕捉数学或语言中的形式规则，常需大规模参数量来近似，仍存在收敛后的随机不稳定性，即所谓的grokking现象。本文提出通用量子变压器（UQT），一种原生量子计算架构，利用多量子比特系统的物理特性作为精确代数与组合推理的通用归纳偏置。该框架完全基于可调几何相位嵌入和SU(2)波干涉，无需模仿经典神经机制。我们证明，仅使用5或6个量子比特、551至1,650个可训练参数的相同量子注意力电路，即可精确学习三种截然不同的形式体系：循环模11算术（ℤ₁₁）、非阿贝尔代数（S₄置换群）及系统性语言组合性（SCAN语言）。相较之下，标准经典模型（如MLP和Transformer）在收敛时仍表现出随机不稳定性，而UQT实现了数学上精确的确定性泛化。我们定义这一更强范式为晶化（crystallization），超越已知的grokking现象。最后，我们在噪声中等规模量子（NISQ）硬件上部署UQT，于IBM量子计算机上实现97.5%准确率。结果表明，UQT提供了标准经典连续空间架构所不具备的结构性归纳偏置，适合精确形式推理任务。
原文摘要 · Abstract (English)
Classical continuous-space neural networks fundamentally struggle to lock into exact formal rules, whether mathematical, such as modular arithmetic and non-Abelian group algebra, or linguistic, such as systematic compositional generalization. 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 novel, quantum-native computing architecture that uses the physical properties of multi-qubit systems as a universal inductive bias for exact algebraic and compositional reasoning. Rather than translating classical neural mechanisms, our framework relies entirely on parameterized geometric phase embedding and $SU(2)$ wave-interference. We demonstrate that an identical quantum attention circuit, operating on a highly compact 5 or 6 qubit substrate with only 551 to 1,650 trainable parameters, exactly learns three highly distinct formal classes: cyclic modular arithmetic ($\mathbb{Z}_{11}$), non-Abelian algebra (the $S_4$ permutation group), and systematic linguistic compositionality (the SCAN language). While standard classical models, including multi-layer perceptrons (MLPs) and Transformers, exhibit stochastic instability at convergence, the UQT achieves mathematically exact, deterministic generalization. We define this stricter regime as crystallization: a step beyond the well-known phenomenon of grokking. Finally, we deploy the UQT on noisy intermediate-scale quantum (NISQ) hardware, achieving 97.5% accuracy on IBM Quantum computers. These results demonstrate that the UQT provides a structurally suited inductive bias for exact formal reasoning that standard classical continuous-space architectures do not natively provide.
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