发表机构
IBM Research（IBM研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出两种浅深度量子电路实现的采样问题，基于格假设对经典算法困难且可高效验证，编译了现有量子性证明，无需中间测量，证明浅量子电路可解决经典难任务。
AI 中文摘要
我们提出了一个采样问题，该问题可由浅量子电路求解，在格基假设下对多项式时间经典算法而言是困难的，且能被经典计算机高效验证。该量子采样器有两种实现方式：一种使用含单量子比特和两量子比特门的对数对数深度量子电路，即QNC⁰[log log]电路；另一种使用含无界扇入门的常数深度量子电路，即QAC⁰电路。我们的构造可视为将Arabadjieva等人（2025）提出的基于学习误差（LWE）的单轮量子性证明编译为极浅深度的版本。该编译的代价是依赖于非标准但有充分动机的假设：除Arabadjieva等人（2025）使用的格知识假设外，我们还需要LWE的自适应硬核比特性质的增强变体，对此我们提供了支持证据。与此前的浅深度量子性证明不同，此处的量子计算不需要中间电路测量或前馈，仅包含运行浅电路并从其输出分布中采样。这表明浅量子电路具有足够的结构来解决某些经典困难任务，且这些任务的解可被高效验证。
英文摘要
We give a sampling problem that is solvable by shallow quantum circuits, hard for polynomial-time classical algorithms under lattice-based assumptions, and efficiently verifiable by a classical computer. The quantum sampler admits two implementations: one uses log-logarithmic-depth quantum circuits with one- and two-qubit gates, i.e., $\mathsf{QNC}^0[\log\log]$ circuits, while the other uses constant-depth quantum circuits with unbounded fan-in gates, i.e., $\mathsf{QAC}^0$ circuits. Our construction can be seen as compiling the Learning with Errors (LWE)-based single-round proof of quantumness of Arabadjieva et al. (2025) to very low depth. The price paid for this compilation is the reliance on less standard, though well-motivated, assumptions: in addition to the lattice knowledge assumption used by Arabadjieva et al. (2025), we require a strengthened variant of the adaptive-hardcore-bit property of LWE, for which we provide supporting evidence. Unlike previous low-depth proofs of quantumness, the quantum computation here requires no mid-circuit measurements or feed-forward: it consists only of running a shallow circuit and sampling from its output distribution. This shows that shallow quantum circuits have sufficient structure to solve certain classically hard tasks whose solutions can be verified efficiently.
CommentsRevised admissibility conditions, corrected and clarified the supporting security analysis, and expanded the discussion of assumptions and related work. 48 pages, 1 table, 1 figure
