  In this work, we aim at augmenting the decisions output by quantum models
with "error bars" that provide finite-sample coverage guarantees. Quantum
models implement implicit probabilistic predictors that produce multiple random
decisions for each input through measurement shots. Randomness arises not only
from the inherent stochasticity of quantum measurements, but also from quantum
gate noise and quantum measurement noise caused by noisy hardware. Furthermore,
quantum noise may be correlated across shots and it may present drifts in time.
This paper proposes to leverage such randomness to define prediction sets for
both classification and regression that provably capture the uncertainty of the
model. The approach builds on probabilistic conformal prediction (PCP), while
accounting for the unique features of quantum models. Among the key technical
innovations, we introduce a new general class of non-conformity scores that
address the presence of quantum noise, including possible drifts. Experimental
results, using both simulators and current quantum computers, confirm the
theoretical calibration guarantees of the proposed framework.
