Obfuscation of Arbitrary Quantum Circuits
Miryam Mi-Ying Huang, Er-Cheng Tang
TL;DR
The paper tackles the fundamental problem of obfuscating arbitrary quantum circuits, extending beyond unitary maps to general CPTP maps. It introduces a novel primitive, the subspace-preserving strong pseudorandom unitary (spsPRU), which fixes a chosen subspace $S$ and behaves like a Haar-random unitary on $S^ot$, enabling reusability and ancilla verification for non-unitary computations. By embedding a general quantum map into a unitary circuit $Q'$ and applying an ideal unitary obfuscation, the authors achieve quantum ideal obfuscation and, consequently, quantum indistinguishability obfuscation (QiO) in the classical oracle model under post-quantum one-way functions. They also develop an efficient construction of spsPRU using post-quantum PRPs and restricted $2$-designs, along with a path-recording oracle to simulate Haar sampling on $S^ot$. The results close a major gap in quantum obfuscation, offering a pathway to practical quantum functional encryption and related security applications, while leaving open questions about plain-model QiO and broader implications of spsPRU primitives.
Abstract
Program obfuscation aims to conceal a program's internal structure while preserving its functionality. A central open problem is whether an obfuscation scheme for arbitrary quantum circuits exists. Despite several efforts having been made toward this goal, prior works have succeeded only in obfuscating quantum circuits that implement either pseudo-deterministic functions or unitary transformations. Although unitary transformations already include a broad class of quantum computation, many important quantum tasks, such as state preparation and quantum error-correction, go beyond unitaries and fall within general completely positive trace-preserving maps. In this work, we construct the first quantum ideal obfuscation scheme for arbitrary quantum circuits that support quantum inputs and outputs in the classical oracle model assuming post-quantum one-way functions, thereby resolving an open problem posed in Bartusek et al. (STOC 2023), Bartusek, Brakerski, and Vaikuntanathan (STOC 2024), and Huang and Tang (FOCS 2025). At the core of our construction lies a novel primitive that we introduce, called the subspace-preserving strong pseudorandom unitary (spsPRU). An spsPRU is a family of efficient unitaries that fix every vector in a given linear subspace $S$, while acting as a Haar random unitary on the orthogonal complement $S^\perp$ under both forward and inverse oracle queries. Furthermore, by instantiating the classical oracle model with the ideal obfuscation scheme for classical circuits proposed by Jain et al. (CRYPTO 2023) and later enhanced by Bartusek et al. (arxiv:2510.05316), our obfuscation scheme can also be realized in the quantumly accessible pseudorandom oracle model.