Testing honesty of quantum server

Alice, who does not have any sophisticated quantum technology, delegates her quantum computing to Bob, who has a fully-fledged quantum computer. Can she check whether the computation Bob performs for her is correct? She cannot recalculate the result by herself, since she does not have any quantum computer. A recent experiment with photonic qubits suggests she can. Here, I explain the basic idea of the result, and recent developments about secure cloud quantum computing.