Interactive proofs for verifying (quantum) learning and testing

TL;DR

This paper investigates how resource-constrained quantum learners and testers can leverage interaction with untrusted provers, demonstrating limitations of classical interaction and showcasing advantages of quantum communication in delegated learning and testing.

Contribution

It proves that classical interaction does not help resource-limited learners, but quantum communication enables significant advantages through delegation in learning and testing.

Findings

Classical interaction does not improve resource-limited learners.

Quantum communication enables resource-constrained quantum verifiers to gain advantages.

Delegation to untrusted provers can be beneficial with quantum communication.

Abstract

We consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular, we ask the following question: Could a resource-constrained learner/tester use interaction with a resource-unconstrained but untrusted party to solve a learning or testing problem more efficiently than they could without such an interaction? In this work, we answer this question both abstractly and for concrete problems, in two complementary ways: For a wide variety of scenarios, we prove that a resource-constrained learner cannot gain any advantage through classical interaction with an untrusted prover. As a special case, we show that for the vast majority of testing and learning problems in which quantum memory is a meaningful resource, a memory-constrained quantum algorithm cannot overcome its limitations via classical communication with a memory-unconstrained quantum prover. In contrast, when quantum communication is allowed, we construct a variety of interactive proof protocols, for specific learning and testing problems, which allow memory-constrained quantum verifiers to gain significant advantages through delegation to untrusted provers. These results highlight both the limitations and potential of delegating learning and testing problems to resource-rich but untrusted third parties.