Kolmogorov Arnold Networks is a novel multilayer neuromorphic network that can exhibit higher accuracy than a neural network. It can learn and predict more accurately than neural networks with a smaller number of parameters, and many research groups worldwide have adopted it. As a result, many types of applications have been proposed. This network can be used as a generator solely or with a Generative Adversarial Network; however, KAN has a slower speed of learning than neural networks for the number of parameters. Hence,it has not been researched as a generator. Therefore, we propose a novel Generative Adversarial Network called Generative Adversarial Variational Quantum KAN that uses Variational Quantum KAN as a generator. This method enables efficient learning with significantly fewer parameters by leveraging the computational advantages of quantum circuits and their output distributions. We performed the training and generation task on MNIST and CIFAR10, and revealed that our method can achieve higher accuracy than neural networks and Quantum Generative Adversarial Network with less data.
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 various ways, such as by using ansatzes and comparisons.
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 fitting the given function in various ways, such as by using ansatzes and comparisons.
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.
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.
Generative adversarial network (GAN) is one of the widely-adopted machine-learning frameworks for a wide range of applications such as generating high-quality images, video, and audio contents. However, training a GAN could become computationally expensive for large neural networks. In this work, we propose a hybrid quantum-classical architecture for improving GAN (denoted as QC-GAN). The performance was examed numerically by benchmarking with a classical GAN using MindSpore Quantum on the task of hand-written image generation. The generator of the QC-GAN consists of a quantum variational circuit together with a one-layer neural network, and the discriminator consists of a traditional neural network. Leveraging the entangling and expressive power of quantum circuits, our hybrid architecture achieved better performance (Frechet Inception Distance) than the classical GAN, with much fewer training parameters and number of iterations for convergence. We have also demonstrated the superiority of QC-GAN over an alternative quantum GAN, namely pathGAN, which could hardly generate 16$\times$16 or larger images. This work demonstrates the value of combining ideas from quantum computing with machine learning for both areas of Quantum-for-AI and AI-for-Quantum.