  The success of the current generation of Noisy Intermediate-Scale Quantum
(NISQ) hardware shows that quantum hardware may be able to tackle complex
problems even without error correction. One outstanding issue is that of
coherent errors arising from the increased complexity of these devices. These
errors can accumulate through a circuit, making their impact on algorithms hard
to predict and mitigate. Iterative algorithms like Quantum Imaginary Time
Evolution are susceptible to these errors. This article presents the
combination of both noise tailoring using Randomized Compiling and error
mitigation with a purification. We also show that Cycle Benchmarking gives an
estimate of the reliability of the purification. We apply this method to the
Quantum Imaginary Time Evolution of a Transverse Field Ising Model and report
an energy estimation and a ground state infidelity both below 1\%. Our
methodology is general and can be used for other algorithms and platforms. We
show how combining noise tailoring and error mitigation will push forward the
performance of NISQ devices.
