  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.
