Towards solving the BCS Hamiltonian gap in Near-Term Quantum Computers.

Currently, the use of quantum computers for simulation of physical systems is restricted by the presence of errors and (or) low qubit connectivity in the devices. In order to circumvent these restrictions we use a variational quantum algorithm called Variational Quantum Deflation to obtain the gap of a BCS Hamiltonian, which can lead to interesting implications for superconductivity research. We also compare two different kinds of 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 apply our method for an example with both 2 and 5 qubits. Furthermore, we show how to approximate the gap within one standard deviation, even with the presence of noise.