AI 中文总结
该研究将Wolpert的普遍自预测不可能性转化为有限资源可实现的量子控制实验室障碍，定义哥德尔安全架构，其结果成为自主量子技术可靠运行的工程约束。
AI 中文摘要
可编程量子控制系统越来越依赖预测模块进行认证、实时反馈和自主决策。这一发展提出了一个基本问题：自分析量子平台能否普遍预测自身的实验结果？Wolpert将普遍自预测的不可能性形式化。本文将该限制转化为可在有限资源下实现的明确实验室障碍。我们考虑可编程量子控制场景，其中预测器可作为子程序嵌入其分析的实验中。我们的对角构造使用Kleene递归定理，将任何确定性有界时间预测器转换为编码自身规格的可逆协议。所得协议在该规格上调用预测器，并确定性产生与预测矛盾的经典指针记录。对于高效预测器，该编译具有多项式开销，可作为容错量子电路和最小马赫-曾德尔干涉仪实现，这些实现将可计算理论自指与可编程量子硬件关联起来。我们还引入并正式定义了哥德尔安全架构，这些架构阻断了协议描述对同一运行中可影响指针的执行器的禁止因果路径。我们分析了它们对实时量子纠错的影响，包括由此产生的表达能力权衡。随着量子控制环路计算表达能力的增长，自指的极限不再仅仅是数学抽象，而成为自主量子技术可靠运行的明确工程约束。
英文摘要
Programmable quantum control systems increasingly rely on predictive modules for certification, real-time feedback, and autonomous decision-making. This development raises a fundamental question: can self-analyzing quantum platforms universally predict their own experimental outcomes? Wolpert formalized a general impossibility of universal self-prediction. Here we translate that limitation into an explicit laboratory obstruction that can be realized with finite resources. We consider settings with programmable quantum control in which predictors can be embedded as subroutines within the experiments they analyze. Our diagonal construction uses Kleene's recursion theorem to transform any deterministic bounded-time predictor into a reversible protocol encoding its own specification. The resulting protocol invokes the predictor on that specification and deterministically produces a classical pointer record that contradicts the forecast. For efficient predictors, the compilation has polynomial overhead and admits concrete physical realizations as a fault-tolerant quantum circuit and as a minimal Mach-Zehnder interferometer. These realizations connect computability-theoretic self-reference to programmable quantum hardware. We also introduce and formally define Gödel-safe architectures. These architectures block the forbidden causal path from the protocol description to an actuator that can affect the pointer during the same run. We analyze their implications for real-time quantum error correction, including the resulting expressiveness trade-offs. As quantum control loops grow in computational expressiveness, the limits of self-reference cease to be mere mathematical abstractions and become explicit engineering constraints for the reliable operation of autonomous quantum technologies.
Comments22 pages, 2 figures, supplementary material
Journal refQuantum Sci. Technol. 11 045001 (2026)
