Explore variational quantum architectures for linear algebra applications in this 32-minute conference talk by Carlos Bravo-Prieto from the University of Barcelona. Delve into the potential of Variational Quantum Algorithms (VQAs) in addressing the limitations of current quantum computers. Discover three key applications: the Quantum Singular Value Decomposer for bipartite pure states, the Variational Quantum Linear Solver for linear systems of equations, and quantum generative models via adversarial learning. Gain insights into the noisy intermediate-scale quantum (NISQ) era, optimization techniques, and practical examples, including simulations and implementations on actual quantum hardware. Examine the context of hadronic collisions at the LHC and learn about generative adversarial networks (GANs) in quantum computing. Analyze results from various architectures and real-world applications on IBM Q Hardware.