Resource-efficient verification of quantum computing using Serfling's bound

Understand

Verifying quantum states is central to certifying the correct operation of various quantum information processing tasks.

• In particular, in measurement-based quantum computing, checking whether correct graph states are generated is essential for reliable quantum computing.
• Several verification protocols for graph states have been proposed, but none of these are particularly resource efficient: multiple copies are required to extract a single state that is guaranteed to be close to the ideal one.
• The best protocol currently known requires $O(n^{15})$ copies of the state, where $n$ is the size of the graph state.