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Near-term quantum computation holds potential across multiple applicationdomains. However, imperfect preparation and evolution of states due toalgorithmic and experimental shortcomings, characteristic in the near-termimplementation, would typically result in measurement outcomes deviating fromthe ideal setting. It is thus crucial for any near-term application to quantifyand bound these output errors. We address this need by deriving robustnessintervals which are guaranteed to contain the output in the ideal setting. Thefirst type of interval is based on formulating robustness bounds assemi-definite programs, and uses only the first moment and the fidelity to theideal state. Furthermore, we consider higher statistical moments of theobservable and generalize bounds for pure states based on the non-negativity ofGram matrices to mixed states, thus enabling their applicability in the NISQera where noisy scenarios are prevalent. Finally, we demonstrate our results inthe context of the variational quantum eigensolver (VQE) on noisy and noiselesssimulations.

Toward Reliability in the NISQ Era: Robust Interval Guarantee for Quantum Measurements on Approximate States