  We propose an adaptive random quantum algorithm to obtain an optimized
eigensolver. Specifically, we introduce a general method to parametrize and
optimize the probability density function of a random number generator, which
is the core of stochastic algorithms. We follow a bioinspired evolutionary
mutation method to introduce changes in the involved matrices. Our optimization
is based on two figures of merit: learning speed and learning accuracy. This
method provides high fidelities for the searched eigenvectors and faster
convergence on the way to quantum advantage with current noisy
intermediate-scaled quantum computers.
