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Quantum-Enhanced Conformal Methods for Multi-Output Uncertainty: A Holistic Exploration and Experimental Analysis

Emre Tasar

TL;DR

This paper validates coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data and confirms that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes.

Abstract

In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multioutput regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.

Quantum-Enhanced Conformal Methods for Multi-Output Uncertainty: A Holistic Exploration and Experimental Analysis

TL;DR

This paper validates coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data and confirms that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes.

Abstract

In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multioutput regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.
Paper Structure (49 sections, 6 equations, 1 figure)

This paper contains 49 sections, 6 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Materials and Methods
  3. Overview of the Pipeline
  4. Quantum Circuit Generation
  5. 2-Qubit Architecture.
  6. Random Gate Selection.
  7. Feature Extraction
  8. Measurement Vectors
  9. Single-Basis Setup ($4$D).
  10. Multi-Basis Setup ($12$D).
  11. Multi-Output Regression Model
  12. Distributional Conformal Inference
  13. Coverage and Set Size.
  14. Exchangeability in Quantum Data.
  15. Implementation Details and Code Structure
  16. ...and 34 more sections

Figures (1)

  • Figure 1: High-level flowchart depicting our method. A random or user-specified 2-qubit quantum circuit is run (possibly in multiple measurement bases), generating a probability vector (4D for single-basis, 12D for triple-basis). We combine gate-level features with these measured vectors to form $(\mathbf{X}, \mathbf{Y})$. A classical regressor is trained and later validated via distributional conformal sets, ensuring coverage near $(1-\alpha)$.