In this paper, we present the development of a quantum computing method for calculating the value at risk ($VaR$) for a portfolio of assets managed by a finance institution. We extend the conventional Monte Carlo algorithm to calculate the $VaR$ of an arbitrary number of assets by employing random variable algebra and Taylor series approximation. The resulting algorithm is suitable to be executed in real quantum computers. However, the noise affecting current quantum computers renders them almost useless for the task. We present a methodology to mitigate the noise impact by using neural networks to compensate for the noise effects. The system combines the output from a real quantum computer with the neural network processing. The feedback is used to fine tune the quantum circuits. The results show that this approach is useful for estimating the $VaR$ in finance institutions, particularly when dealing with a large number of assets. We demonstrate the validity of the proposed method with up to 139 assets. The accuracy of the method is also proven. We achieved an error of less than $1\%$ in the empirical measurements with respect to the parametric model.