  We show how to obfuscate pseudo-deterministic quantum circuits in the
classical oracle model, assuming the quantum hardness of learning with errors.
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 classical oracle using 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.
