Title: Universal Quantum Transformer

Abstract:

Classical continuous-space neural networks face inherent difficulties in adhering to precise mathematical symmetries, including modular arithmetic and non-commutative algebra. To approximate these discrete logical rules, they typically depend on extensive parameter scaling, which leads to stochastic instability even when delayed generalization—often referred to as "grokking"—occurs. In this work, we present the Universal Quantum Transformer (UQT), a new quantum-native computing architecture that leverages the physical properties of multi-qubit systems as a universal inductive bias for exact mathematical and algebraic reasoning.

Unlike approaches that adapt classical neural mechanisms, our framework is built entirely on parameterized geometric phase embedding and $SU(2)$ wave-interference. We show that a quantum attention circuit, running on a compact 5-qubit substrate, successfully learns two distinct formal classes: cyclic modular arithmetic ($\mathbb{Z}_{11}$) and non-Abelian algebra (the $S_4$ permutation group). While classical attention-based models display stochastic instability upon convergence, the UQT achieves mathematically exact, deterministic generalization. We label this outcome "crystallization," representing a significant advancement over the established concept of grokking.

Furthermore, this framework offers substantial computational and memory benefits by theoretically circumventing the quadratic bottleneck associated with classical self-attention. It also logarithmically compresses the necessary representation dimension, thereby removing the excessive over-parameterization common in classical networks. To validate its practical application, we deployed this architecture on noisy intermediate-scale quantum (NISQ) hardware, demonstrating its functionality on current IBM Quantum computers. These findings position parameterized quantum topology as a universally superior physical substrate for achieving exact artificial intelligence.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC