Single-copy stabilizer testing

Schedule

Abstract

We consider the problem of testing whether an unknown n-qubit quantum state |ψ⟩ is a stabilizer state, with only single-copy access. We give an algorithm solving this problem using O(n) copies, and conversely prove that Ω(n−−√) copies are required for any algorithm. The main observation behind our algorithm is that when repeatedly measuring in a randomly chosen stabilizer basis, stabilizer states are the most likely among the set of all pure states to exhibit linear dependencies in measurement outcomes. Our algorithm is designed to probe deviations from this extremal behavior. For the lower bound, we first reduce stabilizer testing to the task of distinguishing random stabilizer states from the maximally mixed state. We then argue that, without loss of generality, it is sufficient to consider measurement strategies that a) lie in the commutant of the tensor action of the Clifford group and b) satisfy a Positive Partial Transpose (PPT) condition. By leveraging these constraints, together with novel results on the partial transposes of the generators of the Clifford commutant, we derive the lower bound on the sample complexity.

Personal information

Marcel is a PhD student with Jens Eisert at the Dahlem Center for Complex Quantum Systems, Freie Universität Berlin. He is currently in his 5-th year and looking out for potential Post-Doc opportunities. He is broadly interested in all things related to Cliffords and the stabilizer formalism across quantum info. More concretely, he has personally worked on applications in the realm of quantum learning theory and quantum property testing.

Post Date

January 10, 2025

Centers

Quantum Computing Research Center

Topic

Quantum Computing