论文标题
多部分高维量子状态工程通过离散时间量子步行
Multipartite High-dimensional Quantum State Engineering via Discrete Time Quantum Walk
论文作者
论文摘要
量子状态工程，即任意量子状态的产生和控制，由于其在量子信息和计算中的广泛应用，引起了越来越多的关注。但是，理论上没有一般方法，现有方案也很大程度上取决于所选的实验平台。在本手稿中，我们为$ c $ c $ d $ d $维系统的任意量子状态的工程任务提供了两个方案，它们都是基于离散的时间量子步行，并具有$ 2^c $二维的时间和位置依赖性的依赖性股。第一个过程是$ d $ - 步骤的量子步行，其中所有$ d $硬币都是非认同的，而第二个过程是$ o（d）$ - 步骤量子步行，其中仅$ o（\ log d）$硬币是非认同的。给出了准备通用状态的具体示例，以证明我们提出的第一个方案。我们还展示了如何使用这些方案来降低长距离量子通信的成本，而系统中所涉及的粒子彼此遥远。此外，可以应用第一个方案来为量子状态准备问题提供另一种方法，这是量子信息处理的基本任务之一。我们借助我们的量子状态工程方案来设计用于量子状态制备的电路，该方案均匀地均与电路的大小和深度相匹配。
Quantum state engineering, namely the generation and control of arbitrary quantum states, is drawing more and more attention due to its wide applications in quantum information and computation. However, there is no general method in theory, and the existing schemes also depend heavily on the selected experimental platform. In this manuscript, we give two schemes for the engineering task of arbitrary quantum state in $c$-partite $d$-dimensional system, both of which are based on discrete-time quantum walk with a $2^c$-dimensional time- and position-dependent coin. The first procedure is a $d$-step quantum walk where all the $d$ coins are non-identity, while the second procedure is an $O(d)$-step quantum walk where only $O(\log d)$ coins are non-identity. A concrete example of preparing generalized Bell states is given to demonstrate the first scheme we proposed. We also show how these schemes can be used to reduce the cost of long-distance quantum communication when the particles involved in the system are far away from each other. Furthermore, the first scheme can be applied to give an alternative approach to the quantum state preparation problem which is one of the fundamental tasks of quantum information processing. We design circuits for quantum state preparation with the help of our quantum state engineering scheme that match the best current result in both size and depth of the circuit asymptotically.
