Solving the BCS Hamiltonian gap in Near-Term Quantum Computers

Currently, the use of quantum computers for simulation of physical systems is restricted because of errors induced by noise and low qubit connectivity in the devices. In order to surpass these restrictions we use a variational quantum algorithm called Variational Quantum Deflation to find the gap of a BCS Hamiltonian, which could lead to interesting implications for superconductivity. In this work we compare two optimizers, Constrained Optimization BY Linear Approximations (COBYLA) and Simultaneous Perturbation Stochastic Approximation (SPSA), and study the effect of decoherence caused by noise using simulations in real devices. We show how to approximate the gap, with high precision, even with the presence of noise.