Self-attention variational wavefunctions for the 2D homogeneous electron gas up to N=169 yield energies below DMC and a converged collective-mode dispersion including a roton-like minimum.
Is attention all you need to solve the correlated electron problem?
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abstract
The attention mechanism has transformed artificial intelligence research by its ability to learn relations between objects. In this work, we explore how a many-body wavefunction ansatz constructed from a large-parameter self-attention neural network can be used to solve the interacting electron problem in solids. By a systematic neural-network variational Monte Carlo study on a moir\'e quantum material, we demonstrate that the self-attention ansatz provides an accurate and efficient solution without human bias. Moreover, our numerical study finds that the required number of variational parameters scales roughly as $N^2$ with the number of electrons, which opens a path towards efficient large-scale simulations.
years
2026 3representative citing papers
A compact neural statebank based on autoregressive Transformers simulates 34-qubit quantum circuits with ~0.01 infidelity using 0.3 million parameters, outperforming tested approximate simulators.
Zero-point energy corrections from quantum fluctuations destabilize the classical honeycomb bilayer Wigner crystal and stabilize the 30-degree quasicrystalline state over a broad parameter range.
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Accurate Self-Attention Wavefunctions at Large Scale
Self-attention variational wavefunctions for the 2D homogeneous electron gas up to N=169 yield energies below DMC and a converged collective-mode dispersion including a roton-like minimum.
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Simulating quantum circuits with a neural statebank
A compact neural statebank based on autoregressive Transformers simulates 34-qubit quantum circuits with ~0.01 infidelity using 0.3 million parameters, outperforming tested approximate simulators.
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Quantum Electron Quasicrystal
Zero-point energy corrections from quantum fluctuations destabilize the classical honeycomb bilayer Wigner crystal and stabilize the 30-degree quasicrystalline state over a broad parameter range.