As quantum computers are developing, they are beginning to become useful for practical applications, for example in the field of quantum metrology. In this work, a variational quantum algorithm is used to find an optimal probe state for measuring parameters in a noisy environment. This is achieved by optimizing a cost on a quantum computer, based on the Fisher information of the parameters to be estimated. These parameters are then estimated using maximum likelihood estimators. In a simulation, a probe state was found that performed better than the best possible state for noiseless measurements, although this could not be reproduced on an actual quantum computer.