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，假设学习带误差的量子困难性（QLWE）和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$\ket{\widetilde{Q}}$，该量子态可用于在任意输入上重复计算$Q$。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混淆器，即可得到所有多项式大小伪确定性量子电路的第一个候选不可区分混淆方案。特别地，我们的方案是首个能够实现Shor算法（SICOMP 1997）的电路类别的候选混淆器。我们的方法遵循Bartusek和Malavolta（ITCS 2022）的思路，他们通过混淆量子计算经典验证（CVQC）方案的验证器来混淆\emph{零量子}电路。我们超越了零电路，为量子\emph{分割}电路构建了公开可验证的CVQC方案，该方案可用于验证Mahadev的量子全同态加密方案（FOCS 2018）的计算过程。我们通过将Bartusek（TCC 2021）的一次性安全方案升级为完全可重用方案来实现这一目标，具体利用了在本文中正式定义并构造的公开可解码\emph{Pauli函数承诺}。该承诺方案满足对能够访问接收者的标准和Hadamard基解码功能的承诺者的绑定性质，其构造基于Amos、Georgiou、Kiayias和Zhandry（STOC 2020）在歧义但抗碰撞哈希函数背景下引入的技术。