A major unresolved question in quantum cryptography is whether it is possible to obfuscate arbitrary quantum computation. Indeed, there is much yet to understand about the feasibility of quantum obfuscation even in the classical oracle model, where one is given for free the ability to obfuscate any classical circuit. In this work, we develop a new array of techniques that we use to construct a quantum state obfuscator, a powerful notion formalized recently by Coladangelo and Gunn (arXiv:2311.07794) in their pursuit of better software copy-protection schemes. Quantum state obfuscation refers to the task of compiling a quantum program, consisting of a quantum circuit $C$ with a classical description and an auxiliary quantum state $\ket{\psi}$, into a functionally-equivalent obfuscated quantum program that hides as much as possible about $C$ and $\ket{\psi}$. We prove the security of our obfuscator when applied to any pseudo-deterministic quantum program, i.e. one that computes a (nearly) deterministic classical input / classical output functionality. Our security proof is with respect to an efficient classical oracle, which may be heuristically instantiated using quantum-secure indistinguishability obfuscation for classical circuits. Our result improves upon the recent work of Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023) who also showed how to obfuscate pseudo-deterministic quantum circuits in the classical oracle model, but only ones with a completely classical description. Furthermore, our result answers a question of Coladangelo and Gunn, who provide a construction of quantum state indistinguishability obfuscation with respect to a quantum oracle. Indeed, our quantum state obfuscator together with Coladangelo-Gunn gives the first candidate realization of a ``best-possible'' copy-protection scheme for all polynomial-time functionalities.

翻译：量子密码学中一个尚未解决的主要问题是能否混淆任意量子计算。实际上，即使在经典神谕模型中（该模型中可免费获得任意经典电路的混淆能力），我们对量子混淆可行性的理解仍存在大量空白。本研究开发了一系列新技术，用于构造量子态混淆器——该强大概念最近由Coladangelo和Gunn（arXiv:2311.07794）在探索更优软件防复制方案时正式提出。量子态混淆指将包含经典描述量子电路$C$和辅助量子态$\ket{\psi}$的量子程序编译为功能等效的混淆量子程序，从而最大程度隐藏$C$与$\ket{\psi}$的信息。我们证明了该混淆器应用于任意伪确定性量子程序（即计算接近确定性经典输入/经典输出的功能）时的安全性。证明过程依赖于高效经典神谕，该神谕可通过量子安全经典电路不可区分混淆进行启发式实例化。本成果改进了Bartusek、Kitagawa、Nishimaki和Yamakawa（STOC 2023）的最新工作——他们同样展示了在经典神谕模型中混淆伪确定性量子电路的方法，但仅局限于完全经典描述的电路。更关键的是，我们的结果回应了Coladangelo和Gunn的问题：他们曾基于量子神谕构建了量子态不可区分混淆方案。实际上，我们的量子态混淆器与Coladangelo-Gunn方案相结合，首次实现了针对所有多项式时间功能的"最佳可能"防复制方案候选。