Construct quantum indistinguishability obfuscation from standard assumptions

Construct general-purpose quantum indistinguishability obfuscation from standard cryptographic or computational assumptions, thereby supplying a concrete instantiation of the primitive used for the paper’s verification and quantum-advantage protocols.

Background

The paper’s main protocols assume quantum indistinguishability obfuscation (qiO), implemented by a classical polynomial-time obfuscator that outputs a classical description of a quantum circuit. The authors emphasize that general-purpose qiO is an exceptionally strong primitive and that their results shift the main constructive burden onto establishing it.

The paper develops a conditional local-mixing framework for ancilla-free unitary circuits and shows how qiO for such circuits can imply qiO for tidy computations. However, this framework is presented as a route for studying candidate constructions rather than as a concrete instantiation. A successful construction from standard assumptions would make the proposed protocols less dependent on an uninstantiated primitive.