用于验证（量子）学习与测试的交互式证明
Interactive proofs for verifying (quantum) learning and testing
- Department of Computer Science, University of Warwick, UK（沃里克大学计算机科学系）
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, Berlin, Germany（柏林自由大学复杂量子系统中心）
- Helmholtz-Zentrum Berlin für Materialien und Energie, Berlin, Germany（柏林材料与能源研究中心）
- IBM Quantum, Almaden Research Center, San Jose, CA, USA（IBM量子，阿姆登研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究探讨资源受限的学习者能否通过与不可信但资源丰富的证明者交互提升测试与学习效率，证明经典交互无优势，但量子通信可带来显著优势。
AI中文摘要：
我们考虑了在资源约束（如有限内存或弱数据访问）存在的情况下，从数据中进行测试和学习的问题，这些约束限制了测试或学习的效率和可行性。特别是，我们提出以下问题：一个资源受限的学习者/测试者能否通过与一个资源不受限但不可信的方进行交互，从而比在没有这种交互的情况下更高效地解决学习或测试问题？在这项工作中，我们从抽象层面和具体问题层面，以两种互补的方式回答了这个问题：对于多种场景，我们证明了资源受限的学习者无法通过与不可信证明者的经典交互获得任何优势。作为一个特例，我们表明，对于绝大多数量子内存是有意义资源的测试和学习问题，内存受限的量子算法无法通过与内存不受限的量子证明者进行经典通信来克服其局限性。相反，当允许量子通信时，我们为特定的学习和测试问题构建了多种交互式证明协议，这些协议允许内存受限的量子验证者通过委托给不可信的证明者而获得显著优势。这些结果突显了将学习和测试问题委托给资源丰富但不可信的第三方的局限性和潜力。
英文摘要：
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.
