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

TL;DR

This paper demonstrates a method to compute the BCS Hamiltonian gap using NISQ quantum computers, analyzing hardware constraints, optimizer performance, and noise effects for small qubit systems.

Contribution

It introduces a variational quantum deflation approach tailored for NISQ devices to estimate the BCS gap, including hardware considerations and noise robustness analysis.

Findings

Successfully estimated the BCS gap for 2 and 5 qubits.

Compared optimizer performance, finding SPSA more noise-resilient.

Achieved gap approximation within one standard deviation despite noise.

Abstract

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.