The Variational Quantum Eigensolver (VQE) [1] is considered as one of the most promising algorithms for near-term applications on Noisy Intermediate-Scale Quantum (NISQ) devices. It is a hybrid algorithm which uses the variational Rayleigh-Ritz principle to find the ground state energy of a quantum mechanical system and is expected to be useful for a broad range of problems in various fields, ranging from condensed matter physics over quantum chemistry to optimization [2,3,4]. Although VQE has shown some resilience to noise from quantum hardware [2], noise is one of the main obstacles on the way to its application in practical use cases. Our work focuses on a systematic investigation of the effect of quantum noise on the performance of VQE on the example of the H2 molecule. 

Besides numerical comparisons of the suitability of different classical optimizers our studies include simulations of the results of VQE for increasing strength of various incoherent types of noise. We observe a systematic shift of the mean values of the resulting energies and find mathematical descriptions of the relationship between the found energy and the noise intensity. For better generalization our work comprises studies with four different ansatzes, including both chemically-inspired and hardware-efficient ansatzes, with varying complexity. The findings of the simulations are examined by comparisons with experiments on the superconducting processors of IBM Quantum.

[1]          A. Peruzzo, Nature Communications 5, 4213 (2014)
[2]          J. Tilly, Physics Reports 986, 1 (2022)
[3]          Y. Cao, Chemical Reviews 119, 10856 (2019)
[4]          N. Moll, Quantum Science and Technology 3, 030503 (2018)