Quantum Conformal Prediction

QCP is the practical implementation of my undergraduate dissertation on quantum conformal prediction. It trains parameterised quantum circuits (PQCs) against synthetic data distributions and evaluates them using split conformal prediction — producing calibrated, statistically guaranteed prediction sets.

The problem

Standard machine learning models produce point predictions with no principled uncertainty quantification. Conformal prediction solves this by wrapping any model in a coverage guarantee: given a miscoverage level α, the prediction set will contain the true value at least 1-α of the time, with no distributional assumptions required.

The question I explored: does this hold when the underlying model is a quantum circuit?

Pipeline

The framework has three stages, each exposed as a CLI command:

Train — optimise a PQC against a target distribution using a YAML specification. Supports regression, classification, and unsupervised circuit architectures with configurable angle encoding strategies.

Collect — run the trained circuit on a backend (local Aer simulator or IBM Quantum hardware) to generate shot data, stored in SQLite.

Predict — apply split conformal prediction to the collected shots using one of six scoring functions (Euclidean distance, k-nearest neighbours, histogram-based, and others), producing calibrated prediction sets.

Results

Coverage guarantees held empirically across all tested distributions and scoring functions. The k-nearest neighbour scoring function produces the most informative (tightest) prediction sets. Heteroscedastic distributions proved the hardest case, as expected.