Current quantum computers typically have a few tens of qubits and are prone to errors due to imperfect gate implementations or undesired coupling with the environment.
Among many of the proposed near-term applications to try to surpass these inconveniences, the field of Variational Quantum Algorithms (VQAs) is held as one of the most promising approaches. Thus, it seems natural to explore the use of VQAs for different applications, and more specifically, for linear algebra.
In this talk, we focus on a few applications that make use of variational approaches: (1) the Quantum Singular Value Decomposer, which produces the singular value
decomposition of bipartite pure states, (2) the Variational Quantum Linear Solver, for solving linear systems of equations, and (3) Quantum generative models via adversarial
learning, to learn underlying distribution functions.