Obfuscation of Arbitrary Quantum Circuits

2026-01-13

AI Summary

This work addresses a long-standing open problem in quantum cryptography: achieving ideal obfuscation for arbitrary quantum circuits that support quantum input and output, including non-unitary operations such as state preparation and quantum error correction. Building upon post-quantum one-way functions in the classical oracle model, the paper introduces a novel primitive—subspace-preserving strong pseudorandom unitaries (spsPRUs)—and integrates it with recent advances in classical circuit obfuscation to construct the first ideal obfuscation scheme for general completely positive trace-preserving (CPTP) maps. This breakthrough overcomes prior limitations restricted to unitary transformations or quasi-deterministic functions, resolving several key open questions posed at STOC 2023, STOC 2024, and FOCS 2025.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• quantum obfuscation
• arbitrary quantum circuits
• completely positive trace-preserving maps
• quantum computation
• program obfuscation

Innovation

• quantum obfuscation
• arbitrary quantum circuits
• spsPRU
• post-quantum one-way functions
• completely positive trace-preserving maps