We explore the computational implications of a superposition of spacetimes, a phenomenon hypothesized in quantum gravity theories. This was initiated by Shmueli (2024) where the author introduced the complexity class $\mathbf{BQP^{OI}}$ consisting of promise problems decidable by quantum polynomial time algorithms with access to an oracle for computing order interference. In this work, it was shown that the Graph Isomorphism problem and the Gap Closest Vector Problem (with approximation factor $\mathcal{O}(n^{3/2})$) are in $\mathbf{BQP^{OI}}$. We extend this result by showing that the entire complexity class $\mathbf{SZK}$ (Statistical Zero Knowledge) is contained within $\mathbf{BQP^{OI}}$. This immediately implies that the security of numerous lattice based cryptography schemes will be compromised in a computational model based on superposition of spacetimes, since these often rely on the hardness of the Learning with Errors problem, which is in $\mathbf{SZK}$.

翻译：我们探讨了时空叠加态的计算含义，这一现象由量子引力理论所假设。该研究始于Shmueli (2024) 的工作，其中作者提出了复杂度类 $\mathbf{BQP^{OI}}$，该类由可通过量子多项式时间算法判定的承诺问题构成，且该算法能够访问用于计算序干涉的预言机。该研究证明了图同构问题与间隙最近向量问题（近似因子为 $\mathcal{O}(n^{3/2})$）属于 $\mathbf{BQP^{OI}}$。我们扩展了这一结果，证明了整个复杂度类 $\mathbf{SZK}$（统计零知识）包含于 $\mathbf{BQP^{OI}}$ 之中。这直接意味着，在基于时空叠加态的计算模型中，众多基于格的密码学方案的安全性将受到威胁，因为这些方案通常依赖于误差学习问题的困难性，而该问题属于 $\mathbf{SZK}$。