Comparative analysis of error mitigation techniques for variational quantum eigensolver implementations on IBM quantum system

Quantum computers are anticipated to transcend classical supercomputers for computationally intensive tasks by exploiting the principles of quantum mechanics. However, the capabilities of the current generation of quantum devices are limited due to noise or errors, and therefore implementation of error mitigation and/or correction techniques is pivotal to reliably process quantum algorithms. In this work, we have performed a comparative analysis of the error mitigation capability of the [[4,2,2]] quantum error-detecting code (QEC method), duplicate circuit technique, and the Bayesian read-out error mitigation (BREM) approach in the context of proof-of-concept implementations of variational quantum eigensolver (VQE) algorithm for determining the ground state energy of H$_2$ molecule. Based on experiments on IBM quantum device, our results show that the duplicate circuit approach performs superior to the QEC method in the presence of the hardware noise. A significant impact of cross-talk noise was observed when multiple mappings of the duplicate circuit and the QEC method were implemented simultaneously $-$ again the duplicate circuit approach overall performed better than the QEC method. To gain further insights into the performance of the studied error mitigation techniques, we also performed quantum simulations on IBM system with varying strengths of depolarising circuit noise and read-out errors which further supported the main finding of our work that the duplicate circuit offer superior performance towards mitigating of errors when compared to the QEC method. Our work reports a first assessment of the duplicate circuit approach for a quantum algorithm implementation and the documented evidence will pave the way for future scalable implementations of the duplicated circuit techniques for the error-mitigated practical applications of near-term quantum computers.