Quantum Variational Autoencoder Based on Weak Measurements With Fuzzy Filtering of Input Data

Introduction. The development of quantum computing and artificial intelligence necessitates the development of hybrid quantum-classical algorithms for solving complex computational problems. The relevance of the research is due to the need for new approaches to making creative AI decisions in conditions of exhaustion of training samples. (QVA) based on weak measurements with fuzzy filtering of input data is a promising research direction. The article first proposes a quantum variational autoencoder (QVA) based on weak measurements, which expands the space of possible solutions due to quantum effects – qubit entanglement, superposition of states and information teleportation. A fundamentally important modification is the introduction of weak measurements, which provide information about the quantum system with minimal impact on its state. The purpose of the article is to improve AI through modeling of autoencoder algorithms using weak measurements and fuzzy logic. Results. For the first time, numerical simulation of KVA based on weak measurements with fuzzy filtering was performed on classical computers and cloud services. The quality of KVA reconstruction is comparable to classical autoencoders. The simulation was performed for a one-dimensional signal, since for the CIFAR-10 and MNIST training samples, the simulation requires more than 5 petabytes of RAM. The KVA runtime in Google Colab was approximately 40 seconds. Conclusions. The integration of the fuzzy filtering mechanism into the KVA structure expands the capabilities of processing distorted and incomplete data. Such a modification increases the model's resistance to thermal noise and input data artifacts, improving the quality of information compression. Fuzzy clustering allows the system to effectively operate with ambiguous situations under conditions of uncertainty. Computer simulations have shown that adapting the fuzzy membership function to the type of input data, increasing the number of latent variables, and selecting the learning rate of the neural network can improve the quality of the reconstruction of the input signal. Keywords: quantum computing, neural network, variational autoencoder, fuzzy logic, weak measurements.