Effectiveness of error-mitigation techniques for VQE under realistic noise sources

It is estimated that NISQ technology will become a reality in the near future, and with its arrival, some light will be shed over the standing conjecture that the threshold of useful quantum supremacy lies somewhere between 50 and 100 qubits. This intermediate scale is however insufficient to attain fault-tolerance. Hybrid quantum-classical algorithms, like the Variational Quantum Eigensolver (VQE) and error-mitigation techniques might become a necessity to produce meaningful calculations. We perform full density-matrix simulations of the VQE algorithm to estimate the electronic ground state energies of small molecules and study the effectiveness of various error mitigation techniques to reduce the deleterious impact of different realistic noise sources. We focus on noise sources relevant to trapped-ion and spin qubits. We determine the resources needed to perform proof-of-concept VQE-based quantum chemical calculations on near-term quantum computers.