发表机构
Columbia University（哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为量子态制备下界建立了Razborov-Rudich自然证明障碍的量子类比，证明在标准密码学假设下，自然性质无法证明超多项式下界，并指出现有技术均属此类。
AI 中文摘要
我们识别出一个障碍，有助于解释为何证明更强的量子态制备下界一直如此困难。具体而言，我们为态制备下界建立了Razborov-Rudich自然证明障碍的量子类比。我们将量子态的一个性质称为“自然的”，如果它对足够大比例的Haar随机态成立，并且在给定态的所有振幅时可以被高效检验。在标准密码学假设下，我们证明没有任何自然性质能够证明超多项式态制备下界，即使针对Magic Hierarchy的固定层级也是如此。我们表明，若干现有的态制备下界技术在我们的意义下是自然的，包括基于近似度、不是局部哈密顿量的唯一基态以及互信息的方法。
英文摘要
We identify a barrier that helps explain why proving stronger quantum state-preparation lower bounds has been so difficult. In particular, we establish a quantum analogue of the Razborov-Rudich natural proofs barrier for state-preparation lower bounds. We call a property of quantum states \emph{natural} if it holds for a sufficiently large fraction of Haar-random states and can be efficiently tested when given all of the state's amplitudes. Under a standard cryptographic assumption, we show that no natural property can prove superpolynomial state-preparation lower bounds even against a fixed level of the Magic Hierarchy. We show that several existing state-preparation lower-bound techniques are natural in our sense, including arguments based on approximate degree, not being a unique ground state of a local Hamiltonian, and mutual information.
