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：我们在若干基本假设下证明了量子优势，特别是仅基于单向函数（OWFs）的存在性。我们引入了低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是验证者与量子证明者之间的交互协议，包含两个阶段：在第一阶段，验证者具有概率多项式时间能力，并与证明者进行交互；在第二阶段，验证者转为低效计算模式，并依据第一阶段的交互记录作出判定。若证明者诚实，低效验证者以高概率接受；但任何经典恶意证明者被低效验证者接受的概率极低。我们的构造证明了以下结果：（1）若单向函数存在，则IV-PoQ存在；（2）若分布式抗碰撞哈希函数存在（当$\mathbf{SZK}$中存在平均困难问题时成立），则存在常数轮IV-PoQ。我们还基于最坏情况困难假设证明了量子优势：定义了辅助输入型IV-PoQ（AI-IV-PoQ），仅要求对任意恶意证明者存在无限多辅助输入使其无法作弊。我们以类似方法从辅助输入型承诺构造了AI-IV-PoQ，证明：（1）若辅助输入型单向函数存在（当$\mathbf{CZK}\not\subseteq\mathbf{BPP}$时成立），则AI-IV-PoQ存在；（2）若辅助输入型抗碰撞哈希函数存在（等价于$\mathbf{PWPP}\nsubseteq \mathbf{FBPP}$）或$\mathbf{SZK}\nsubseteq \mathbf{BPP}$，则存在常数轮AI-IV-PoQ。