We show how to obfuscate pseudo-deterministic quantum circuits, assuming the quantum hardness of learning with errors (QLWE) and post-quantum virtual black-box (VBB) obfuscation for classical circuits. Given the classical description of a quantum circuit $Q$, our obfuscator outputs a quantum state $\ket{\widetilde{Q}}$ that can be used to evaluate $Q$ repeatedly on arbitrary inputs. Instantiating the VBB obfuscator for classical circuits with any candidate post-quantum indistinguishability obfuscator gives us the first candidate construction of indistinguishability obfuscation for all polynomial-size pseudo-deterministic quantum circuits. In particular, our scheme is the first candidate obfuscator for a class of circuits that is powerful enough to implement Shor's algorithm (SICOMP 1997). Our approach follows Bartusek and Malavolta (ITCS 2022), who obfuscate \emph{null} quantum circuits by obfuscating the verifier of an appropriate classical verification of quantum computation (CVQC) scheme. We go beyond null circuits by constructing a publicly-verifiable CVQC scheme for quantum \emph{partitioning} circuits, which can be used to verify the evaluation procedure of Mahadev's quantum fully-homomorphic encryption scheme (FOCS 2018). We achieve this by upgrading the one-time secure scheme of Bartusek (TCC 2021) to a fully reusable scheme, via a publicly-decodable \emph{Pauli functional commitment}, which we formally define and construct in this work. This commitment scheme, which satisfies a notion of binding against committers that can access the receiver's standard and Hadamard basis decoding functionalities, is constructed by building on techniques of Amos, Georgiou, Kiayias, and Zhandry (STOC 2020) introduced in the context of equivocal but collision-resistant hash functions.

翻译：我们展示了如何混淆伪确定性量子电路，假设存在带误差学习问题的量子硬度（QLWE）以及经典电路的后量子虚拟黑盒（VBB）混淆。给定量子电路$Q$的经典描述，我们的混淆器输出一个量子态$\ket{\widetilde{Q}}$，可用于在任意输入上重复评估$Q$。若将经典电路的VBB混淆器实例化为任意候选后量子不可区分性混淆器，我们便首次获得了对所有多项式规模伪确定性量子电路的不可区分性混淆候选构造。特别地，我们的方案是首个能够生成足以实现Shor算法（SICOMP 1997）的电路类别的混淆器。我们的方法遵循Bartusek和Malavolta（ITCS 2022）的思路，即通过混淆经典量子计算验证（CVQC）方案的验证器来混淆\emph{零}量子电路。通过为量子\emph{分割}电路构建可公开验证的CVQC方案，我们超越了零电路，该方案可用于验证Mahadev量子全同态加密方案（FOCS 2018）的评估过程。我们通过将Bartusek（TCC 2021）的一次性安全方案升级为可完全复用的方案来实现这一目标，该升级基于一种可公开解码的\emph{Pauli功能承诺}（本文正式定义并构造了该承诺）。该承诺方案满足对能访问接收方标准基和Hadamard基解码功能的承诺者的绑定性质，是通过借鉴Amos、Georgiou、Kiayias和Zhandry（STOC 2020）在可混淆但抗碰撞哈希函数背景下引入的技术而构造的。