We initiate the study of quantum Interactive Oracle Proofs (qIOPs), a generalization of both quantum Probabilistically Checkable Proofs and quantum Interactive Proofs, as well as a quantum analogue of classical Interactive Oracle Proofs. In the model of quantum Interactive Oracle Proofs, we allow multiple rounds of quantum interaction between the quantum prover and the quantum verifier, but the verifier has limited access to quantum resources. This includes both queries to the prover's messages and the complexity of the quantum circuits applied by the verifier. The question of whether QMA admits a quantum interactive oracle proof system is a relaxation of the quantum PCP Conjecture. We show the following two main constructions of qIOPs, both of which are unconditional: - We construct a qIOP for QMA in which the verifier shares polynomially many EPR pairs with the prover at the start of the protocol and reads only a constant number of qubits from the prover's messages. - We provide a stronger construction of qIOP for QMA in which the verifier not only reads a constant number of qubits but also operates on a constant number of qubits overall, including those in their private registers. However, in this stronger setting, the communication complexity becomes exponential. This leaves open the question of whether strong qIOPs for QMA, with polynomial communication complexity, exist. As a key component of our construction, we introduce a novel single prover many-qubits test, which may be of independent interest.

翻译：我们首次系统研究了量子交互式预言证明（qIOPs）——这一模型同时推广了量子概率可检验证明与量子交互式证明，也是经典交互式预言证明的量子对应。在量子交互式预言证明模型中，我们允许量子证明者与量子验证者之间进行多轮量子交互，但验证者对量子资源的访问能力受到严格限制。这既包括对证明者消息的查询次数限制，也包含验证者所用量子电路的复杂度约束。关于QMA是否允许量子交互式预言证明系统存在的问题，是量子PCP猜想的松弛化表述。我们提出了以下两个无条件成立的qIOP主要构造方案：- 我们构建了适用于QMA的qIOP方案，其中验证者在协议初始阶段与证明者共享多项式数量的EPR纠缠对，且仅从证明者的消息中读取常数个量子比特。- 我们进一步给出了适用于QMA的更强qIOP构造，其中验证者不仅读取常数个量子比特，其整体操作（包括私有寄存器中的量子比特）也仅涉及常数个量子比特。然而在此强化设定下，通信复杂度将呈指数级增长。这为“是否存在具有多项式通信复杂度的强qIOP for QMA”这一开放问题留下了研究空间。作为构造的核心组件，我们提出了一种新颖的单证明者多量子比特测试方案，该方案可能具有独立的研究价值。