Quantum Conformal Prediction for Reliable Uncertainty Quantification in Quantum Machine Learning

In this work, we aim at augmenting the decisions output by quantum models with "error bars" that provide finitesample 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. Quantum machine learning (QML) is currently viewed as a promising paradigm for the optimization of algorithms that can leverage existing noisy intermediate scale quantum (NISQ) computers [1]-[3]. The authors are with the King's Communications, Learning & Information Processing (KCLIP) lab within the Centre for Intelligent Information Processing Systems (CIIPS), Department of Engineering, King's College London, London WC2R 2LS, U.K. (e-mail: sangwoo.park@kcl.ac.uk; osvaldo.simeone@kcl.ac.uk). This work was supported by the European Research Council (ERC) under the European Union's Horizon 2020 Research and Innovation Programme (grant agreement No. 725732), by the European Union's Horizon Europe project CENTRIC (101096379), by an Open Fellowship of the EPSRC (EP/W024101/1), by the EPSRC project (EP/X011852/1), and by Project REASON, a UK Government funded project under the Future Open Networks Research Challenge (FONRC) sponsored by the Department of Science Innovation and Technology (DSIT). This paper addresses the problem of using M samples drawn from quantum model to produce error bars at coverage probability 1 α for the target variable given a test input. The ground-truth (unknown) minimal 1 α conditional support for a regression problem is shown as the gray area.