Aaronson-Ambainis 猜想获证明，ArXiv 发布详细解读
Proof of the Aaronson-Ambainis Conjecture: An Exposition
这条值得看两个点：一是 Aaronson-Ambainis 猜想本身被证明了，量子算法在多数输入上能被经典模拟；二是证明者用的是 PSI 的研究系统加非公开 Anthropic 模型，AI 参与数学研究的又一实例。做量子计算或复杂度理论的人应该读解读部分，四个步骤的讲法很清楚。
一篇 ArXiv 论文（编号 2611.11626）对 Aaronson-Ambainis 猜想的近期证明做了完整解读。该猜想指出：任何次数为 d 的多项式 p: {0,1}^n → [0,1] 都存在影响力至少为 poly(Var(p)/d) 的变量。这一结论意味着量子查询算法在大多数输入上可以被经典算法高效模拟，并给出了随机预言机世界与真实世界中 BPP 与 BQP 问题的近似等价关系。
论文将证明组织为四个主要步骤，并把每一步与布尔函数分析和概率组合学的已有文献联系起来。为突出核心思路，作者没有优化参数，表述得到的指数弱于原始证明。
作者说明部分披露了一个背景细节：证明由 David Turturean 借助 Physical Superintelligence（PSI）开发的研究系统和一个非公开的 Anthropic 模型完成，随后共享给论文作者撰写解读；Anthropic 的公开模型也参与了这一过程，但作者未从 Anthropic 或 PSI 获得报酬。
Proof of the Aaronson-Ambainis Conjecture: An Exposition
We give an exposition of a recent proof of the Aaronson-Ambainis conjecture, which states that every degree-$d$ polynomial $p : \{0,1\}^n \to [0,1]$ has a variable of influence at least $\mathrm{poly}(\mathrm{Var}(p)/d)$. This implies that quantum query algorithms for decision problems can be efficiently simulated classically on most inputs. It also yields a near-equivalence between the status of the $\mathsf{BPP}$ vs. $\mathsf{BQP}$ problem in the random oracle and unrelativized worlds. We organize the proof around four main steps and discuss how each connects to the literature on the analysis of boolean functions and probabilistic combinatorics. To bring out the key ideas, we do not optimize parameters, and our presentation yields weaker exponents than the original. $\textbf{Authors' note.}$ The proof was discovered by David Turturean using a research system developed at Physical Superintelligence (PSI), in combination with a non-public Anthropic model. The proof was then shared with the authors, who worked to understand it and prepare this exposition. Anthropic's public models were used in this process. The authors did not receive financial compensation from Anthropic or PSI. This article is not intended for publication at a conference or in a journal.
This report is categorized under AITOP's "Papers" desk, focusing on US frontier AI labs and Silicon Valley technology leaders. Within our cross-regional analytical framework, it directly maps to AI developer toolchains, coding agents, and engineering workflows and US-China foundation model benchmarks and commercialization comparison. Key entities and technical topics under continuous tracking include Aaronson-Ambainis猜想, BQP, 量子计算, Anthropic.
Primary source verification: published directly by arXiv: Anthropic with first-party authority.
