Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Li, Christine, Parham, Natalie
Institution: Columbia University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220667598