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arXiv:2603.11189

DysonNet: Constant-Time Local Updates for Neural Quantum States

Lucas Winter, Andreas Nunnenkamp

quant-phcond-mat.dis-nnSubmitted Mar 11, 2026• Announced Mar 13, 2026• 0 citations
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Abstract

Neural quantum states (NQS) provide a flexible variational framework for many-body wavefunctions, but suffer from high computational cost and limited interpretability. We introduce DysonNet, a broad class of NQS that couples strictly local nonlinearities through global linear layers. This structure is analogous to a truncated Dyson series which gives an intuitive interpretation of local wavefunction updates as scattering from static impurities. By resumming the scattering series, single-spin-flip updates can be computed in $\mathcal{O}(1)$ time, independent of system size, using an algorithm we call ABACUS. Implementing DysonNet with the state-space model S4, we obtain up to $230\times$ speedups over Vision-Transformers for computing the local estimator. This corresponds to an asymptotic $\mathcal{O}(N^2)$ improvement in training-time scaling, reaching $\mathcal{O}(N \log^2 N)$ total training complexity in area-law phases. Benchmarks on the 1D long-range Ising model and frustrated $J_1$-$J_2$ chains show that DysonNet matches state-of-the-art NQS accuracy while removing the dominant local-update overhead. More broadly, our results suggest a route to scalable NQS architectures where physical interpretability directly enables computational efficiency.

Comments
26 pages, 7 figures

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We introduce a new approach, based on neural quantum states (NQSs), to rapidly compute nuclear observables when couplings in nuclear Hamiltonians are varied. A single interaction-dependent NQS, trained across a range of couplings in the Hamiltonian, provides high-fidelity wavefunctions for that continuous range of interaction parameters. With access to the wavefunction for each set of couplings, any static observables can be computed efficiently without retraining the NQS. We apply this framework to two-body nuclear scattering and the deuteron ground state with local interactions derived from chiral effective field theory up to third order.
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