Hierarchically discriminating Haar-randomness in quantum states from a black-box device

Understand

The concept of randomness in quantum computing has been central to constructing benchmarking tools, cryptographic protocols, as well as a proof of beyond-classical computation.

• Discerning whether quantum states (or unitaries) are randomly distributed is a computational task that requires an enormous amount of quantum computational resources.
• This work addresses such a challenge by introducing a hierarchical discrimination algorithm to efficiently test if a set of states $S$ generated from a black-box quantum device with an unknown distribution is (in)compatible with a random distribution.
• To this end, we reduce the complexity of the problem by selecting an observable with known spectrum to study the statistical properties of its expectation values with respect to the quantum states from an unknown (black-box) quantum device.