Empirical forward interest rates drive the debt markets. Libor and Euribor futures data is used to calibrate and test models of interest rates based on the formulation of quantum finance. In particular, all the model parameters, including interest rate volatilities, are obtained from market data. The random noise driving the forward interest rates is taken to be a Euclidean two dimension quantum field. We analyze two models, namely the bond forward interest rates, which is a linear theory and the Libor Market Model, which is a nonlinear theory. Both the models are analyzed using Libor and Euribor data, with various approximations to match the linear and nonlinear models. The results are quite good, with the linear model having an accuracy of about 99% and the nonlinear model being slightly less accurate. We extend our analysis by directly using the Zero Coupon Yield Curve (ZCYC) data for Libor and for bonds; but due to some technical difficulties we could not derive the models parameters directly from the ZCYC data.