Probabilistic exact universal quantum circuits for transforming unitary operations
Probabilistic exact universal quantum circuits for transforming unitary operations
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DOI：
10.1103/physreva.100.062339
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发表时间：
2019-09
影响因子：
2.9
通讯作者：
Marco T'ulio Quintino;Qingxiuxiong Dong;A. Shimbo;A. Soeda;M. Murao
中科院分区：
文献类型：
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作者：
Marco T'ulio Quintino;Qingxiuxiong Dong;A. Shimbo;A. Soeda;M. Murao
本文解决了设计通用量子电路的问题，以概率预示的方式将$d$维的$k$使用转换为$d$维的$k$输入操作到$d$维的$k$输出操作。考虑了三类协议：并行电路，其中输入操作可以同时进行；自适应电路，其中允许顺序使用输入操作；通用协议，其中输入操作的使用可以在没有明确因果顺序的情况下执行。对于这三类，我们开发了一种系统的半定规划方法，该方法寻找一个以最大成功概率获得期望变换的电路。然后，我们详细分析了三种特定的转换；酉转置，酉复共轭，酉反转。对于幺正转置和幺正逆，我们证明了对于任意固定维数d，自适应电路在使用方面比并行电路有指数级的提高。对于酉复共轭和酉反演，证明了如果使用次数严格小于d-1，则成功的概率必然为零。我们还讨论了不确定因果顺序协议相对于因果顺序协议的优势，并引入了延迟输入态量子电路的概念。
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are considered, parallel circuits, where the input-operations can be simultaneously, adaptive circuits, where sequential uses of the input-operations are allowed, and general protocols, where the use of the input-operations may be performed without a definite causal order. For these three classes, we develop a systematic semidefinite programming approach that finds a circuit which obtains the desired transformation with the maximal success probability. We then analyse in detail three particular transformations; unitary transposition, unitary complex conjugation, and unitary inversion. For unitary transposition and unitary inverse, we prove that for any fixed dimension $d$, adaptive circuits have an exponential improvement in terms of uses $k$ when compared to parallel ones. For unitary complex conjugation and unitary inversion we prove that if the number of uses $k$ is strictly smaller than $d-1$, the probability of success is necessarily zero. We also discuss the advantage of indefinite causal order protocols over causal ones and introduce the concept of delayed input-state quantum circuits.