Noah Eckstein | Searcharxiv

arXiv2026

Quantum simulation of gauge theories on dynamical spacetimes via Floquet-induced matrix models

Quantum simulations of gauge theories are typically built on spatial lattices, an approach that has enabled major progress at the cost of requiring fixed background geometries and obscuring the treatment of curved and dynamical spacetimes. Large-$N$ matrix models offer an alternative, encoding spacetime geometry and gauge fields in the commutation structure of a set of Hermitian matrices, with the classical continuum emerging smoothly at large matrix dimensions. Here we introduce a Floquet framework that makes these models directly accessible to programmable quantum platforms. We show that Euclidean path integral weights of a Yang-Mills matrix models are reproduced, at leading order in the coupling, by the ensemble-averaged fidelities of Haar-random states evolved under periodic sequences of matrix operators. The observables for the simulated matrix model can then be accessed through established randomized benchmarking protocols in terms of the Loschmidt echo. The encoding requires exponentially fewer qubits than canonically quantized approaches. Numerically, we validate the fidelity-weight correspondence, demonstrate parallelized quantum circuits that sample the path-integral measure, and identify the deconfinement transition of an $SU(2)$ gauge field on both flat and expanding cosmological backgrounds. By avoiding a fixed spacetime lattice, the framework preserves continuous symmetries and unitarity on dynamical geometries, opening quantum simulation to field and spacetime dynamics beyond the reach of conventional lattice methods.

quant-ph↗

arXiv2026

Paradoxical noise preference in RNNs

In recurrent neural networks (RNNs) used to model biological neural networks, noise is typically introduced during training to emulate biological variability and regularize learning. The expectation is that removing the noise at test time should preserve or improve performance. Contrary to this intuition, we find that continuous-time RNNs (CTRNNs) often perform best at or near the training noise level. This noise preference typically arises when noise is injected inside the neural activation function; networks trained with noise injected outside the activation function perform best with zero noise. The phenomenon arises robustly in diverse tasks for large enough training noise; we also show the phenomenon arising in feedforward neural networks, not just in RNNs. Our analyses show that the phenomenon stems from noise-induced shifts of fixed points (stationary distributions) in the underlying stochastic dynamics of the RNNs. These fixed point shifts are noise-level dependent and bias the network outputs when the noise is removed, degrading performance. Analytical and numerical results show that the bias arises when neural states operate near activation-function nonlinearities, where noise is asymmetrically attenuated, and that performance optimization incentivizes operation near these nonlinearities; such performance incentives exist for networks with noise inside, but not outside, the activation function, explaining why only noise-in networks show the preference. Thus, networks can overfit to the training noise itself rather than just to the input-output data. The phenomenon is distinct from stochastic resonance, wherein nonzero noise enhances signal processing. Our findings reveal that training noise can become an integral part of the computation learned by neural networks, with implications for understanding neural population dynamics and for the design of robust artificial RNNs.

cs.NE↗