Dilated RNNs Induce Long-Range Correlations in Quantum States

The paper "Geometry-Induced Long-Range Correlations in Recurrent Neural Network Quantum States" proposes a simple architectural fix, dilated RNN, that gives autoregressive recurrent wave functions an explicit long-range inductive bias while preserving favorable forward-pass scaling. The authors prove analytically that dilation modifies the geometry of correlations and can induce power-law correlation decay in a linearized, perturbative limit, and they validate the claim numerically on two benchmark quantum states.

The work replaces dense short-range recurrence with dilated connections so recurrent units access distant lattice sites through structured skips (dilated connections). This keeps the model autoregressive and sample-efficient, unlike global self-attention. Key technical claims and results include:

• •Analytic derivation showing dilation changes the underlying correlation geometry and supports power-law scaling in a simplified linear regime.
• •Numerical experiments on the critical 1D transverse-field Ising model where dilated RNN reproduces the expected power-law connected two-point correlations, in contrast to exponential decay from conventional RNN ansatze.
• •Successful approximation of the one-dimensional Cluster state, demonstrating ability to capture long-range conditional correlations known to defeat standard RNN wave functions.

Neural Quantum States (NQS) built from RNN wave functions are attractive because they allow exact sampling without Markov-chain autocorrelation. However, standard RNNs are biased toward finite-length correlations, motivating expensive fixes such as transformer-style self-attention with heavy computational and memory cost. The paper positions dilation as a low-cost geometric inductive bias that addresses long-range dependency failure modes in NQS, trading minimal architectural complexity for substantial representational gain. This bridges ideas from dilated convolutional networks and sequence modeling into quantum many-body state representation.

Validate these results on larger system sizes, higher-dimensional lattices, and within variational optimization loops. Also compare wall-clock training and sampling cost to transformer-based NQS and gauge robustness to noise during optimization.