Ancilla-free certification of unitary quantum processes

TL;DR

This paper introduces an ancilla-free quantum certification algorithm for unitary processes that outperforms previous methods by requiring fewer uses of the unitary and no high-dimensional ancilla systems.

Contribution

It presents a new efficient algorithm for certifying unitary quantum processes without ancilla, reducing the number of uses from O(ε^{-2}) to O(ε^{-1}) and eliminating the need for high-dimensional ancilla.

Findings

Achieves O(ε^{-1}) query complexity for unitary certification

Eliminates the need for high-dimensional ancilla systems

Outperforms previous algorithms in efficiency

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.