quantum simulation engineers

Abstract: Neural operators that learn physical laws from data should generalize beyond their training distribution and expose the learned law in closed form. The Kolmogorov-Arnold neural operator achieves both for position-dependent dynamics by learning a dense pseudo-differential symbol over all positions and frequencies, at a cost that grows with the square of the resolution and with closed forms that must be read out by hand. This dense symbol is unnecessary: a finite-order variable-coefficient differential operator has a symbol whose separation rank is bounded by the number of its coefficient functions, independently of the resolution, and the symbols that this network learns on its own benchmarks have rank two. We introduce the Kolmogorov-Arnold flow (KAFlow), which learns the generator of a physical operator as a low-rank symbol built from univariate Kolmogorov-Arnold functions, fixes the gauge of these functions so that every term has a unique place, integrates the dynamics with exact exponential integrators, and distills its closed form automatically. On the synthetic benchmarks of the Kolmogorov-Arnold neural operator, KAFlow lowers the out-of-distribution loss by 3.4 to 11 times and recovers every coefficient to within 10^-4 without symbolic templates, reaching the precision floor of the data. On long-horizon quantum dynamics, it lowers the state infidelity by up to 6 orders of magnitude, and by 30 times when trained only on position and momentum measurements. KAFlow also learns a variable-order fractional operator 15 times more accurately than existing operator networks and discovers nonlocal, fractional and non-polynomial dispersion relations on which sparse regression fails.

Abstract: The stochastic variational method (SVM) is one of the most powerful methods to solve quantum few-body systems precisely in various fields, such as nuclear and atomic physics. To the best of our knowledge, no SVM code optimized for GPUs has been reported. We developed a parallel SVM code for few-body clusters of $^4$He atoms and optimized it for two GPU architectures, NVIDIA GH200 and AMD Instinct MI300A, with the entire code written by an AI coding agent. On the algorithmic side, we introduce the secular-equation method with the Gu--Eisenstat prescription for solving the generalized eigenvalue problem within the SVM framework. The main part of the code tuning is to batch the many small matrices so that the GPUs are used efficiently, together with an array layout in memory optimized for coalesced addressing. For the five-body system with 4800 SVM basis states, the tuned SVM code runs 16.2 (14.7) times faster on the NVIDIA GH200 (AMD MI300A) than the same tuned code on the Intel Xeon Max CPU system, and 168 (153) times faster than the first working CPU implementation. The achieved performance brings 6-body and larger cluster systems within reach.

Abstract: Quantum algorithms require embedding linear operators into unitaries using block encodings. The costs associated with these block encodings determine whether a quantum speedup is achieved. Efficient \emph{shift decomposition} encodings have been proposed for 2D homogeneous scalar operators. Here, we present exact block encodings for 2D homogeneous elasticity, 2D two-phase bilinear Poisson, and 2D two-phase elasticity periodic finite-element operators. For 2D homogeneous elasticity, the resulting linear combination of unitaries (LCU) has $L = 17$ terms for every Poisson ratio $ν$ and every mesh resolution, and the subnormalization is the closed form $α= E(33+ν)/\bigl[6(1-ν^{2})\bigr]$, exceeding $\|\mathbf{K}\|_{2}$ by the resolution-independent factor $(33+ν)/24$. To address two-phase periodic microstructures, we introduce two oracles with distinct roles: a node-to-element oracle, built from cyclic shifts, that carries a nodal index to each of the four incident element indices, and a microstructure-specific material oracle that marks phase membership with a sign. This yields 25 and 57 LCU terms for two-phase Poisson and elasticity, respectively; the latter reduces to 49 at $ν= 1/3$. The term counts are independent of mesh resolution, volume fraction, and phase contrast. The subnormalizations, provided in closed form, are independent of mesh resolution and volume fraction. In the scalar case, the tight bound $α= \|\mathbf{K}\|_\infty$ is achieved whenever a node lies entirely in the stiffer phase. In the elasticity case, that bound is not attained, since the shear coupling contributes entries of both signs to a row. An open-source implementation is available at https://github.com/UW-ERSL/PyBlockEncode