AI 中文总结
该研究针对并行量子算法解决量子复杂性理论的基本猜想，证明t次查询d轮量子算法可通过t^O(d²)次经典查询模拟，揭示量子加速需结构或深度，还对随机oracle下BPP与BQP问题有新启示。
AI 中文摘要
量子复杂性理论中最基本的猜想之一指出，每个t次查询的量子算法，在大多数输入上都可由poly(t)次查询的经典算法模拟。若该猜想成立，将为量子加速中结构的必要性提供广泛依据。我们针对并行量子算法解决了这一猜想，证明每个t次查询、d轮的量子算法，在大多数输入上可通过t^O(d²)次经典查询模拟。这表明，对于非结构化问题，超多项式加速需要超常数深度的量子电路，而指数加速则进一步需要多项式深度。相比之下，已知的大多数结构化问题加速都由高度并行的低深度算法实现。我们的技术还对随机oracle下BPP与BQP的状态这一同样长期存在的问题带来新启示。
英文摘要
One of the most basic conjectures in quantum complexity theory states that every $t$-query quantum algorithm can be simulated on most inputs by a $\mathrm{poly}(t)$-query classical algorithm. If true, this would provide broad justification for the need for structure in quantum speedups. We settle this conjecture for parallel quantum algorithms, showing that every $t$-query $d$-round quantum algorithm can be simulated on most inputs with $t^{O(d^2)}$ classical queries. This suggests that for unstructured problems, superpolynomial speedups would require quantum circuits of superconstant depth, and exponential speedups would further require polynomial depth. In contrast, most known speedups for structured problems are achieved by highly parallel, low-depth algorithms. Our techniques also carry new implications for the status of $\mathsf{BPP}$ vs. $\mathsf{BQP}$ relative to a random oracle, a similarly longstanding problem.
CommentsFOCS 2026
