  In this work, we solve differential equations using quantum Chebyshev feature
maps. We propose a tensor product over a summation of Pauli-Z operators as a
change in the measurement observables resulting in improved accuracy and
reduced computation time for initial value problems processed by floating
boundary handling. This idea has been tested on solving the complex dynamics of
a Riccati equation as well as on a system of differential equations.
Furthermore, a second-order differential equation is investigated in which we
propose adding entangling layers to improve accuracy without increasing the
variational parameters. Additionally, a modified self-adaptivity approach of
physics-informed neural networks is incorporated to balance the multi-objective
loss function. Finally, a new quantum circuit structure is proposed to
approximate multivariable functions, tested on solving a 2D Poisson's equation.
