  In this work, using a NISQ framework, we obtain the gap of a BCS Hamiltonian.
This could lead to interesting implications for superconductivity research. For
such task, we choose to use the Variational Quantum Deflation and analyze the
hardware restrictions that are needed to find the energy spectra on current
quantum hardware. We also compare two different kinds of classical optimizers,
Constrained Optimization BY Linear Approximations (COBYLA) and Simultaneous
Perturbation Stochastic Approximation (SPSA), and study the effect of
decoherence caused by the presence of noise when using simulations in real
devices. We implement this method for a system with both 2 and 5 qubits.
Furthermore, we show how to approximate the gap within one standard deviation,
even with the presence of noise.
