Machine Learning Framework for Efficient Prediction of Quantum Wasserstein Distance

TL;DR

This paper introduces a machine learning framework that accurately and efficiently predicts quantum Wasserstein distances, facilitating real-time quantum error correction and analysis in multiqubit systems.

Contribution

It presents a novel ML-based approach that significantly reduces computational complexity for quantum Wasserstein distance estimation, validated on three-qubit systems.

Findings

Random Forest model achieves near-perfect accuracy ($R^2=0.9999$)

Framework successfully verifies key quantum information theory bounds

Enables scalable, real-time quantum error analysis

Abstract

The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains computationally challenging for multiqubit systems due to exponential scaling. We present a machine learning framework that efficiently predicts the quantum W-distance by extracting physically meaningful features from quantum state pairs, including Pauli measurements, statistical moments, quantum fidelity, and entanglement measures. Our approach employs both classical neural networks and traditional machine learning models. On three-qubit systems, the best-performing Random Forest model achieves near-perfect accuracy ($R^2 = 0.9999$) with mean absolute errors on the order of $10^{-5}$. We further validate the framework's practical utility by successfully verifying two fundamental theoretical propositions in quantum information theory: the bound on measurement probability differences between unitary operations and the $W_1$ gate error rate bound. The results establish machine learning as a viable and scalable alternative to traditional numerical methods for W-distance computation, with particular promise for real-time quantum circuit assessment and error correction protocol design in NISQ devices.