Paper 2026/043

Classical Obfuscation of Quantum Circuits via Publicly-Verifiable QFHE

Abstract

A classical obfuscator for quantum circuits is a classical program that, given the classical description of a quantum circuit $Q$, outputs the classical description of a functionally equivalent quantum circuit $\widetilde{Q}$ that hides as much as possible about $Q$. Previously, the only known feasibility result for classical obfuscation of quantum circuits (Bartusek and Malavolta, ITCS 2022) was limited to "null" security, which is only meaningful for circuits that always reject. On the other hand, if the obfuscator is allowed to compile the quantum circuit $Q$ into a quantum state $\ket{\widetilde{Q}}$, there exist feasibility results for obfuscating much more expressive classes of circuits: All pseudo-deterministic quantum circuits (Bartusek, Kitagawa, Nishimaki and Yamakawa, STOC 2023, Bartusek, Brakerski and Vaikuntanathan, STOC 2024), and even all unitaries (Huang and Tang, FOCS 2025). We show that (relative to a classical oracle) there exists a classical obfuscator for all pseudo-deterministic quantum circuits. As our main technical step, we give the first construction of a compact quantum fully-homomorphic encryption (QFHE) scheme that supports public verification of (pseudo-deterministic) quantum evaluation, relative to a classical oracle. To construct our QFHE scheme, we improve on an approach introduced by Bartusek, Kitagawa, Nishimaki and Yamakawa (STOC 2023), which previously required ciphertexts that are both quantum and non-compact due to a heavy use of quantum coset states and their publicly-verifiable properties. As part of our core technical contribution, we introduce new techniques for analyzing coset states that can be generated "on the fly", by proving new cryptographic properties of the one-shot signature scheme of Shmueli and Zhandry (CRYPTO 2025). Our techniques allow us to produce QFHE ciphertexts that are purely classical, compact, and publicly-verifiable. This additionally yields the first classical verification of quantum computation protocol for BQP that simultaneously satisfies blindness and public-verifiability.

Note: Preprint.