This note complements the upcoming paper "One-Way Ticket to Las Vegas and the Quantum Adversary" by Belovs and Yolcu, to be presented at QIP 2023. I develop the ideas behind the adversary bound - universal algorithm duality therein in a different form, using the same perspective as Barnum-Saks-Szegedy in which query algorithms are defined as sequences of feasible reduced density matrices rather than sequences of unitaries. This form may be faster to understand for a general quantum information audience: It avoids defining the "unidirectional relative $\gamma_{2}$-bound" and relating it to query algorithms explicitly. This proof is also more general because the lower bound (and universal query algorithm) apply to a class of optimal control problems rather than just query problems. That is in addition to the advantages to be discussed in Belovs-Yolcu, namely the more elementary algorithm and correctness proof that avoids phase estimation and spectral analysis, allows for limited treatment of noise, and removes another $\Theta(\log(1/\epsilon))$ factor from the runtime compared to the previous discrete-time algorithm.
翻译:本说明补充Belovs和Yolcu将在QIP 2023上介绍的即将出版的论文“前往拉斯维加斯和量子对流的单行票”,Belovs和Yolcu将在QIP 2023上介绍。我以不同的形式,用与Barnum-Saks-Szegedy相同的观点,在对质算法的定义中,查询算法被界定为可行的降低密度矩阵序列而不是单行序列。对于一般量子信息受众来说,这种形式可能更快理解:它避免定义“单向相对$\gamma%2}受量子对流”并明确将其与查询算法联系起来。这个证据也比较笼统,因为较低约束(和通用查询算法)适用于最佳控制问题的类别,而不仅仅是查询问题。此外,在Belovs-Yolcu中讨论的优点是避免阶段估计和光谱分析的更基本的算法和正确性证据,允许有限度地处理噪音,并将另外的美元/Theta(log=epslon-listal-altime)因素从运行到以前的离流时。