We demonstrate quantum advantage with several basic assumptions, specifically based on only the existence of OWFs. We introduce inefficient-verifier proofs of quantumness (IV-PoQ), and construct it from classical bit commitments. IV-PoQ is an interactive protocol between a verifier and a quantum prover consisting of two phases. In the first phase, the verifier is probabilistic polynomial-time, and it interacts with the prover. In the second phase, the verifier becomes inefficient, and makes its decision based on the transcript of the first phase. If the prover is honest, the inefficient verifier accepts with high probability, but any classical malicious prover only has a small probability of being accepted by the inefficient verifier. Our construction demonstrates the following results: (1)If one-way functions exist, then IV-PoQ exist. (2)If distributional collision-resistant hash functions exist (which exist if hard-on-average problems in $\mathbf{SZK}$ exist), then constant-round IV-PoQ exist. We also demonstrate quantum advantage based on worst-case-hard assumptions. We define auxiliary-input IV-PoQ (AI-IV-PoQ) that only require that for any malicious prover, there exist infinitely many auxiliary inputs under which the prover cannot cheat. We construct AI-IV-PoQ from an auxiliary-input version of commitments in a similar way, showing that (1)If auxiliary-input one-way functions exist (which exist if $\mathbf{CZK}\not\subseteq\mathbf{BPP}$), then AI-IV-PoQ exist. (2)If auxiliary-input collision-resistant hash functions exist (which is equivalent to $\mathbf{PWPP}\nsubseteq \mathbf{FBPP}$) or $\mathbf{SZK}\nsubseteq \mathbf{BPP}$, then constant-round AI-IV-PoQ exist.

翻译：我们基于几个基本假设，特别是仅依赖于OWFs（单向函数）的存在，展示了量子优势。我们引入了非高效验证者的量子性证明（IV-PoQ），并基于经典比特承诺构造了该协议。IV-PoQ是一个由验证者和量子证明者之间的交互协议，包含两个阶段。在第一阶段，验证者是概率多项式时间的，并与证明者进行交互。在第二阶段，验证者变为非高效的，并根据第一阶段的交互记录做出决定。如果证明者是诚实的，非高效验证者将以高概率接受；但任何经典恶意证明者被非高效验证者接受的概率都很小。我们的构造展示了以下结果：(1)如果单向函数存在，则IV-PoQ存在。(2)如果分布抗碰撞哈希函数存在（若$\mathbf{SZK}$中存在平均情形困难问题，则此类函数存在），则恒定轮数的IV-PoQ存在。我们还基于最坏情形困难假设展示了量子优势。我们定义了辅助输入IV-PoQ（AI-IV-PoQ），该协议仅要求：对于任何恶意证明者，存在无穷多个辅助输入，使得该证明者无法在此输入下作弊。我们以类似方式从辅助输入版本的承诺构造了AI-IV-PoQ，证明了：(1)如果辅助输入单向函数存在（若$\mathbf{CZK}\not\subseteq\mathbf{BPP}$，则此类函数存在），则AI-IV-PoQ存在。(2)如果辅助输入抗碰撞哈希函数存在（等价于$\mathbf{PWPP}\nsubseteq \mathbf{FBPP}$）或$\mathbf{SZK}\nsubseteq \mathbf{BPP}$，则恒定轮数的AI-IV-PoQ存在。