Program obfuscation aims to conceal a program's internal structure while preserving its functionality. A central open problem is whether an obfuscation scheme for arbitrary quantum circuits exists. Despite several efforts having been made toward this goal, prior works have succeeded only in obfuscating quantum circuits that implement either pseudo-deterministic functions or unitary transformations. Although unitary transformations already include a broad class of quantum computation, many important quantum tasks, such as state preparation and quantum error-correction, go beyond unitaries and fall within general completely positive trace-preserving maps. In this work, we construct the first quantum ideal obfuscation scheme for arbitrary quantum circuits that support quantum inputs and outputs in the classical oracle model assuming post-quantum one-way functions, thereby resolving an open problem posed in Bartusek et al. (STOC 2023), Bartusek, Brakerski, and Vaikuntanathan (STOC 2024), and Huang and Tang (FOCS 2025). At the core of our construction lies a novel primitive that we introduce, called the subspace-preserving strong pseudorandom unitary (spsPRU). An spsPRU is a family of efficient unitaries that fix every vector in a given linear subspace $S$, while acting as a Haar random unitary on the orthogonal complement $S^\perp$ under both forward and inverse oracle queries. Furthermore, by instantiating the classical oracle model with the ideal obfuscation scheme for classical circuits proposed by Jain et al. (CRYPTO 2023) and later enhanced by Bartusek et al. (arxiv:2510.05316), our obfuscation scheme can also be realized in the quantumly accessible pseudorandom oracle model.

翻译：程序混淆旨在隐藏程序的内部结构，同时保持其功能。一个核心的开放问题是：是否存在针对任意量子电路的混淆方案。尽管已有若干努力致力于此目标，但先前的工作仅成功混淆了实现伪确定性函数或酉变换的量子电路。虽然酉变换已经包含了广泛的量子计算类别，但许多重要的量子任务，如态制备和量子纠错，超越了酉变换的范畴，属于一般的完全正定保迹映射。在本工作中，我们基于后量子单向函数的假设，在经典预言机模型中首次构建了支持量子输入和输出的任意量子电路的量子理想混淆方案，从而解决了Bartusek等人（STOC 2023）、Bartusek、Brakerski和Vaikuntanathan（STOC 2024）以及Huang和Tang（FOCS 2025）中提出的一个开放问题。我们构建的核心在于引入了一种新颖的原语，称为子空间保持强伪随机酉（spsPRU）。spsPRU是一族高效的酉变换，它们固定给定线性子空间$S$中的每个向量，同时在正交补空间$S^\perp$上，在正向和反向预言机查询下，表现得像一个Haar随机酉。此外，通过使用Jain等人（CRYPTO 2023）提出并由Bartusek等人（arxiv:2510.05316）增强的经典电路理想混淆方案来实例化经典预言机模型，我们的混淆方案也可以在量子可访问的伪随机预言机模型中实现。