This work investigates Kolmogorov-Arnold network-based (KAN) wave-function Ans"atz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational efficiency and representational power against established methods. Our numerical experiments suggest some efficient training methods and we explore how the computational cost scales with desired precision, particle number, and system parameters. Roughly speaking, KANs seem to be 10 times cheaper computationally than other neural-network-based Ans"atz. We also introduce a novel approach for handling strong short-range potentials---a persistent challenge for many numerical techniques---which generalizes efficiently to higher-dimensional, physically relevant systems with short-ranged strong potentials common in atomic and nuclear physics.
Neural Quantum States (NQS) are a class of variational wave functions parametrized by neural networks (NNs) to study quantum many-body systems. In this work, we propose \texttt{SineKAN}, a NQS \textit{ansatz} based on Kolmogorov-Arnold Networks (KANs), to represent quantum mechanical wave functions as nested univariate functions. We show that \texttt{SineKAN} wavefunction with learnable sinusoidal activation functions can capture the ground state energies, fidelities and various correlation functions of the one dimensional Transverse-Field Ising model, Anisotropic Heisenberg model, and Antiferromagnetic
J1−J2 model with different chain lengths. In our study of the
J1−J2 model with
L=100 sites, we find that the \texttt{SineKAN} model outperforms several previously explored neural quantum state \textit{ansätze}, including Restricted Boltzmann Machines (RBMs), Long Short-Term Memory models (LSTMs), and Multi-layer Perceptrons (MLP) \textit{a.k.a.} Feed Forward Neural Networks, when compared to the results obtained from the Density Matrix Renormalization Group (DMRG) algorithm. We find that \texttt{SineKAN} models can be trained to high precisions and accuracies with minimal computational costs.
We investigate a variational Monte Carlo framework for trapped one-dimensional mixture of spin-
21 fermions using Kolmogorov-Arnold networks (KANs) to construct universal neural-network wavefunction ansätze. The method can, in principle, achieve arbitrary accuracy, limited only by the Monte Carlo sampling and was checked against exact results at sub-percent precision. For attractive interactions, it captures pairing effects, and in the impurity case it agrees with known results. We present a method of systematic transfer learning in the number of network parameters, allowing for efficient training for a target precision. We vastly increase the efficiency of the method by incorporating the short-distance behavior of the wavefunction into the ansätz without biasing the method.
The Kolmogorov-Arnold Network (KAN) places the trainable functions on the synapses rather than on the neurons. Existing quantum implementations either lack accuracy (Variational Quantum KAN, VQKAN) or rely on block encoding and Quantum Signal Processing, which demand many control gates and ancillae. We propose the Enhanced Variational Quantum Kolmogorov-Arnold Network (EVQKAN), a variational ansatz that emulates a
2Nq-dimensional KAN layer matrix by tiling controlled rotations through a sum-operator construction, using only
2Nq−1 trainable spline functions per layer. On the fitting of an elementary function, EVQKAN attains a significantly lower test error than Quantum Neural Networks (QNN), VQKAN and Adaptive VQKAN (Mann-Whitney
p<0.002, Cliff's
δ≤−0.86 over ten attempts; EVQKAN beats VQKAN on every attempt), though classical KAN is more accurate still. On a two-dimensional classification task the ordering reverses: under a leak-free protocol introduced here, EVQKAN classifies above chance (accuracy
0.620,
p=0.0005) but is significantly less accurate than a QNN carrying one fifth as many parameters (
Δaccuracy
−0.134,
p=0.0014;
ΔAUC
−0.252,
p=0.0002). We withdraw the classification results of an earlier version of this work: their encoding placed the target label into the circuit as a feature for EVQKAN but not for the methods it was compared against. The dominant error source is overfitting from an under-determined training set; enlarging that set closes the train-test gap by
58% (Spearman
p<10−3). We also report the circuit cost in full --- three layers emit
1017 operations, or
4110 two-qubit gates once the multi-controlled gates are decomposed --- so the construction is simulator-scale and fault-tolerant-era rather than NISQ-ready, with block encoding and qubitization the route to reducing it.
Abstract We implemented a quantum version of the Kolmogorov-Arnold Network (KAN) on a quantum circuit. It optimizes the weight of each synaptic connection to enhance the overall performance of the neurons. This approach offers a significant boost in efficiency over traditional neural networks, as it can be optimized more accurately and requires only a few neurons to solve complex problems. The KAN is a multi-layer network, similar to a traditional neural network, with each layer represented as a matrix containing parameters and feedback. This structure is linear and mirrors the form of Variational Quantum Algorithms. Thus, we propose the Variational Quantum Kolmogorov-Arnold Network (VQKAN) as a quantum version of the Kolmogorov-Arnold Network. We demonstrated the optimization of VQKAN for the fitting of the given function in some ways, such as by using ansatzes and comparisons.
The field of quantum chemistry has long been defined by the central computational challenge of the quantum many-body fermionic system problem, main the electronic Schrödinger equation. This exponential scaling makes it computationally intractable to solve, the exact governing electronic Schrödinger equation. Approximation methods have been developed, ranging from the widely used Density Functional Theory (DFT) to Coupled Cluster (CC) theory. While powerful, these conventional approaches often involve controlled truncations which caused a trade-off between accuracy, leaving many systems—particularly those with strong electron correlation—beyond the reach of ab initio simulation. Furthermore, the famous fermionic sign oscillation problem is particularly severe in stochastic methods like Quantum Monte Carlo (QMC). 1 Traditional Ansätze are also frequently engineered specifically for particular systems, which results in a fragmentation of results and fundamentally limits the transferability. Recent research demonstrates that with carefully designed architectures, ANNs can not only represent ground states of model systems with high precision but also tackle the sign problem, offering a promising path forward for strongly correlated electronic structure calculations.2,3 This review charts the paradigm shift driven by Neural Network Quantum States (NNQS), which leverage the representational power of deep learning to overcome these barriers. We detail the architectural evolution from Restricted Boltzmann Machines to autoregressive models like RNNs and Transformers, which enable exact, uncorrelated sampling and bypass critical bottlenecks.2,4,5Furthermore, we explore the geometric foundation of high-efficiency optimization via the neural networks, which decouples optimization cost from model complexity.6 The frontier of the field is marked by the integration of operator learning and hybrid quantum-classical frameworks, such as Reinforcement Learning for contracted quantum eigen-solvers and Quantum-Enhanced Neural Networks, which leverage quantum processors to enhance expressivity for hardware-efficient Ansätze.7,8 By framing the problem through the lens of computational resource allocation—specifically, trading exponential memory demands for polynomialcomplexity optimization and sampling—this review elucidates how recent advances at the intersection of artificial neural networks and quantum computing have evolved. The emergence of those methods not merely progress into a powerful simulation-tools, but also a hybrid computational interface.9 This convergence offers a versatile and systematically improvable framework for potentially addressing some of the most challenging problems in quantum physics and chemistry.
Abstract We implemented a quantum version of the Kolmogorov-Arnold Network (KAN) on a quantum circuit. It optimizes the weight of each synaptic connection to enhance the overall performance of the neurons. This approach offers a significant boost in efficiency over traditional neural networks, as it can be optimized more accurately and requires only a few neurons to solve complex problems. The KAN is a multi-layer network, similar to a traditional neural network, with each layer represented as a matrix containing parameters and feedback. This structure is linear and mirrors the form of Variational Quantum Algorithms. Thus, we propose the Variational Quantum Kolmogorov-Arnold Network (VQKAN) as a quantum version of the Kolmogorov-Arnold Network. We demonstrated the optimization of VQKAN for fitting the given function in various ways, such as by using ansatzes and comparisons.