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

2026-06-30

AI Summary

This work addresses the formidable challenges in simulating two-dimensional frustrated quantum systems—stemming from the sign problem and the exponential growth of Hilbert space—by introducing a holographic quantum Transformer architecture. This model leverages a generative global self-attention mechanism to efficiently capture nonlocal entanglement and employs interpretable attention maps to recover the underlying physical interaction structure. The study innovatively proposes a “holographic transfer” zero-shot extrapolation protocol, integrating neural-symbolic methods, continuous positional encoding interpolation, and attention head re-initialization to enable direct scaling from small to large lattices without retraining. Applied to the strongly frustrated 8×8 J1-J2 Heisenberg model, the approach achieves a ground-state energy of E/N = −0.5001(1) and successfully generalizes zero-shot to a 10×10 lattice with E/N = −0.49782(3), matching the performance of state-of-the-art variational methods.

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.

Problem

• frustrated quantum systems
• sign problem
• Hilbert space complexity
• quantum simulation
• J1-J2 Heisenberg model

Innovation

• Holographic Quantum Transformer
• generative attention
• zero-shot size extrapolation
• frustrated quantum systems
• neuro-symbolic architecture