Holographic Quantum Transformer: A Generalist Neuro-Symbolic Architecture for Solving Frustrated Systems via Generative Attention

Abstract

Simulating two-dimensional frustrated quantum matter is a grand challenge due to the sign problem and exponential Hilbert space complexity. In this work, we introduce the Holographic Quantum Transformer (HQT), a physics-inspired generative architecture that leverages global self-attention to resolve non-local entanglement patterns. We validate HQT on the square lattice $J_1-J_2$ Heisenberg model. On the heavily frustrated $8 \times 8$ lattice at the quantum critical point ($J_2=0.5$), HQT reaches a ground-state energy per site ($E/N$) of $\mathbf{-0.5001(1)}$, consistent with the expected finite-size scaling trend. Beyond numerical accuracy, HQT exhibits intrinsic physical awareness, autonomously recovering the underlying $J_2$ interaction geometry through interpretable attention maps. Our central contribution is ``Holographic Transfer", a zero-shot size-extrapolation protocol with rapid alignment: a model trained on $8 \times 8$ systems is directly projected onto larger $10 \times 10$ lattices via continuous positional-embedding interpolation and head re-initialization, achieving high-fidelity initialization and rapid convergence. This zero-shot protocol yields an energy of $E/N = \mathbf{-0.49782(3)}$, statistically consistent with the variational state of the art while requiring no from-scratch training on the target lattice. Our results establish generative attention as a scalable paradigm for transferable quantum simulation.