Towards solving the BCS Hamiltonian gap in near-term quantum computers

Abstract

In this work, using a Noisy Intermediate-Scale Quantum (NISQ) framework, we obtain the gap of a Bardeen–Cooper–Schrieffer (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 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.

Keywords

• Variational Quantum Algorithms
• Quantum computing
• Quantum simulation
• NISQ