Ancilla-free certification of unitary quantum processes

• URL: http://arxiv.org/abs/2211.15647v1
• Date: Mon, 28 Nov 2022 18:53:11 GMT
• Title: Ancilla-free certification of unitary quantum processes
• Authors: Wei Xie
• Abstract summary: We study efficient quantum certification algorithms for unitary quantum process using no ancilla. We give an algorithm that distinguishes the two cases with $O(varepsilon-1)$ uses of the unitary, using fewer or no ancilla, outperforming previous relevant results.
• Score: 2.3889084213601346
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study efficient quantum certification algorithms for unitary quantum process using no ancilla. Previous study showed that one can distinguish whether an unknown unitary $U$ is equal to or $\varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with $O(\varepsilon^{-2})$ uses of the unitary, in which the Choi state is used and thus a high dimensional ancilla system is always needed. We give an algorithm that distinguishes the two cases with $O(\varepsilon^{-1})$ uses of the unitary, using fewer or no ancilla, outperforming previous relevant results.

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