Efficient distributed inner product estimation via Pauli sampling

Understand

Cross-platform verification is the task of comparing the output states produced by different physical platforms using solely local quantum operations and classical communication.

• While protocols have previously been suggested for this task, their exponential sample complexity renders them unpractical even for intermediate-scale quantum systems.
• In this work, we propose a novel protocol for this task based on Pauli sampling, a subroutine which generates Paulis distributed according to their weight in the expansion of a quantum state in the Pauli basis.
• We show that our protocols for both Pauli sampling and cross-platform verification are efficient for pure states with low magic and entanglement (i.e., of the order $O(\log n)$).