# Neural Quantum States

Hybrid quantum-classical Monte Carlo had been limited by the large classical cost of repeatedly processing quantum measurement data, with hardware demonstrations reaching only 16 qubits. Compressing those measurements into a differentiable machine-learning surrogate that supplies the wavefunction overlaps and derivatives Monte Carlo needs accelerates the end-to-end calculation by orders of magnitude on Google's Willow processor, bringing hydrogen chains and iron-sulfur clusters to chemical accuracy on up to 40 qubits, more than doubling the scale of earlier hardware demonstrations.

Hybrid quantum-classical Monte Carlo had been limited by the large classical cost of repeatedly processing quantum measurement data, with hardware demonstrations reaching only 16 qubits. Compressing those measurements into a differentiable machine-learning surrogate that supplies the wavefunction overlaps and derivatives Monte Carlo needs accelerates the end-to-end calculation by orders of magnitude on Google's Willow processor, bringing hydrogen chains and iron-sulfur clusters to chemical accuracy on up to 40 qubits, more than doubling the scale of earlier hardware demonstrations.

This work develops a theoretical framework for the generalization behavior of Transformer-based neural quantum states under in-context learning (ICL): it proves that there exists a Transformer architecture whose pointwise prediction error (MSE) decreases inversely with both the number of in-context examples and the Transformer depth, and that the depth required to achieve this guarantee scales only linearly with system size (the number of particles in continuous systems or qudits in discrete systems); the authors further extend the analysis to full quantum states formulated as rank-one density operators, deriving MSE-based generalization bounds under physical constraints over both continuous and discrete domains, and corroborate the predicted scaling with numerical simulations.

This work develops a theoretical framework for the generalization behavior of Transformer-based neural quantum states under in-context learning (ICL): it proves that there exists a Transformer architecture whose pointwise prediction error (MSE) decreases inversely with both the number of in-context examples and the Transformer depth, and that the depth required to achieve this guarantee scales only linearly with system size (the number of particles in continuous systems or qudits in discrete systems); the authors further extend the analysis to full quantum states formulated as rank-one density operators, deriving MSE-based generalization bounds under physical constraints over both continuous and discrete domains, and corroborate the predicted scaling with numerical simulations.