← 研踪 PaperTrailarXiv:2611.02370 · v1
State Synthesis with an NP oracle
首次提交 2026-11-02 09:34
版本更新 2026-11-02 09:34
雷达观测 2026-11-04 23:42
摘要
In this note, I describe a quantum algorithm that prepares an arbitrary state $|ψ\rangle$ to inverse exponential precision in polynomial time by making queries to an $\mathsf{NP}$ oracle, assuming one can directly query entries of the state vector corresponding to $|ψ\rangle$. The previous best upper bound on the complexity class required by an oracle for this task was $\mathsf{PP}$. I provide evidence that $\mathsf{NP}$ is the best possible upper bound by showing that any quantum algorithm using a $\mathsf{P}$ oracle, or even a $\mathsf{P/poly}$ oracle, requires exponentially many queries. I also discuss some implications of this result for the $\mathsf{QMA}$ search-to-decision problem and unitary synthesis.
作者备注：7 pages
观测到的版本
相邻记录可能跳过中间版本；首次发现 v2 及以上也会标为版本更新。
v1 · 2026-11-02 09:34 · 最新观测版本
State Synthesis with an NP oracle
In this note, I describe a quantum algorithm that prepares an arbitrary state $|ψ\rangle$ to inverse exponential precision in polynomial time by making queries to an $\mathsf{NP}$ oracle, assuming one can directly query entries of the state vector corresponding to $|ψ\rangle$. The previous best upper bound on the complexity class required by an oracle for this task was $\mathsf{PP}$. I provide evidence that $\mathsf{NP}$ is the best possible upper bound by showing that any quantum algorithm using a $\mathsf{P}$ oracle, or even a $\mathsf{P/poly}$ oracle, requires exponentially many queries. I also discuss some implications of this result for the $\mathsf{QMA}$ search-to-decision problem and unitary synthesis.
查看此版本解读 →查看此版本原文 ↗