  Given their potential to demonstrate near-term quantum advantage, variational
quantum algorithms (VQAs) have been extensively studied. Although numerous
techniques have been developed for VQA parameter optimization, it remains a
significant challenge. A practical issue is that quantum noise is highly
unstable and thus it is likely to shift in real time. This presents a critical
problem as an optimized VQA ansatz may not perform effectively under a
different noise environment. For the first time, we explore how to optimize VQA
parameters to be robust against unknown shifted noise. We model the noise level
as a random variable with an unknown probability density function (PDF), and we
assume that the PDF may shift within an uncertainty set. This assumption guides
us to formulate a distributionally robust optimization problem, with the goal
of finding parameters that maintain effectiveness under shifted noise. We
utilize a distributionally robust Bayesian optimization solver for our proposed
formulation. This provides numerical evidence in both the Quantum Approximate
Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE)
with hardware-efficient ansatz, indicating that we can identify parameters that
perform more robustly under shifted noise. We regard this work as the first
step towards improving the reliability of VQAs influenced by shifted noise from
the parameter optimization perspective.
