Covert Quantum Learning: Privately and Verifiably Learning from Quantum Data
Abhishek Anand, Matthias C. Caro, Ari Karchmer, Saachi Mutreja
TL;DR
This work develops a framework for covert (verifiable) learning with quantum data, separating target-covertness (hiding the object learned) from strategy-covertness (hiding the learner’s approach) and showing that quantum advantages can be achieved privately and verifiably through remote data access. It introduces new models for covert learning—spanning covert quantum statistical queries, covert learning from public examples, and covert verifiable quantum data acquisition—along with construction of algorithms that operate without computational hardness assumptions. The paper leverages tools like classical shadows, phase-state certification, and two-copy quantum measurements to realize efficient, privacy-preserving, and verifiable learning tasks, including learning quadratic functions and stabilizer states, Pauli shadow tomography, and solving Forrelation and Simon’s problem covertly. These results demonstrate that quantum advantages can be harnessed in a privacy-preserving, verifiable manner when data is accessed remotely, with concrete protocols tailored to adversary constraints such as unidirectional or ancilla-free models. Overall, the framework broadens the scope of covert learning to quantum domains and provides a suite of techniques and templates for secure, verifiable quantum data processing with potential applications in quantum information science and beyond.
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.