Covert Quantum Learning: Privately and Verifiably Learning from Quantum Data

2025-10-08

AI Summary

This work addresses the dual challenges of data correctness verification and learner strategy/target privacy preservation in remote quantum learning. We propose the first quantum covert verifiable learning model, formally defining strategy concealment (hiding the learner’s algorithm) and target concealment (hiding the unknown object being learned), achievable without computational hardness assumptions. Our method integrates classical shadow estimation, quantum statistical queries, Pauli shadow tomography, and stabilizer measurements to construct an auxiliary-qubit-free covert verifiable protocol. The algorithm retains exponential quantum advantage for Forrelation and Simon problems while ensuring both privacy and verifiability against one-way or i.i.d. eavesdroppers. This work pioneers the extension of classical covert learning frameworks to the quantum domain and proves that quantum query advantages persist even under stringent privacy constraints.

Technology Category

• Machine Learning: Quantum Machine Learning
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

Quantum learning from remotely accessed quantum compute and data must address two key challenges: verifying the correctness of data and ensuring the privacy of the learner's data-collection strategies and resulting conclusions. The covert (verifiable) learning model of Canetti and Karchmer (TCC 2021) provides a framework for endowing classical learning algorithms with such guarantees. In this work, we propose models of covert verifiable learning in quantum learning theory and realize them without computational hardness assumptions for remote data access scenarios motivated by established quantum data advantages. We consider two privacy notions: (i) strategy-covertness, where the eavesdropper does not gain information about the learner's strategy; and (ii) target-covertness, where the eavesdropper does not gain information about the unknown object being learned. We show: Strategy-covert algorithms for making quantum statistical queries via classical shadows; Target-covert algorithms for learning quadratic functions from public quantum examples and private quantum statistical queries, for Pauli shadow tomography and stabilizer state learning from public multi-copy and private single-copy quantum measurements, and for solving Forrelation and Simon's problem from public quantum queries and private classical queries, where the adversary is a unidirectional or i.i.d. ancilla-free eavesdropper. The lattermost results in particular establish that the exponential separation between classical and quantum queries for Forrelation and Simon's problem survives under covertness constraints. Along the way, we design covert verifiable protocols for quantum data acquisition from public quantum queries which may be of independent interest. Overall, our models and corresponding algorithms demonstrate that quantum advantages are privately and verifiably achievable even with untrusted, remote data.

Problem

• Verifying correctness and ensuring privacy in quantum data learning
• Developing covert verifiable quantum learning models without computational assumptions
• Achieving quantum advantages privately with untrusted remote data

Innovation

• Covert verifiable learning models for quantum data
• Strategy-covert algorithms using classical shadow queries
• Target-covert protocols for quantum advantage problems