  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.
