论文标题
用全球大门构建量子电路
Constructing quantum circuits with global gates
论文作者
论文摘要
有各种门集可用于描述量子计算。关于量子计算的文献中特别受欢迎的门，由任意的单量门门和2 Quibit CNOT门组成。但是，CNOT门并不总是可以在给定的物理量子计算机上实现的天然多量相互作用，需要将这些CNOT门转换为本机门集的汇编步骤。一个特别有趣的案例，需要进行汇编，用于离子陷阱量子计算机，自然的纠缠操作可以在2量Quarbit上起作用，甚至可以一次在所有量子位上起作用。这要求采用完全不同的方法来构建高效电路。在本文中，我们研究了将使用2 Qubit门转换为使用全球门的电路的给定电路的问题。我们的三个主要贡献如下。首先，我们找到了一种有效的算法，用于将由Clifford门和任意相位门组成的任意电路转换为一个由单量门门组成的电路，以及与原始电路中存在的非cliff阶段数量成正比的许多全局相互作用。其次，我们找到了一种一般策略，可以将所有量子位定为仅针对量子组的一个量子位的全局门。与未针对的量子位数量相比，这种方法与（Maslov＆Nam，N。J.Phys。2018）中的指数缩放相反，与未针对的量子位的数量线性缩放。第三，我们将合成任意N Qubit Clifford电路所需的全球大门数量提高了（Maslov＆Nam，N。J.Phys。2018）至6n-8。
There are various gate sets that can be used to describe a quantum computation. A particularly popular gate set in the literature on quantum computing consists of arbitrary single-qubit gates and 2-qubit CNOT gates. A CNOT gate is however not always the natural multi-qubit interaction that can be implemented on a given physical quantum computer, necessitating a compilation step that transforms these CNOT gates to the native gate set. A particularly interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than 2 qubits and can even act globally on all qubits at once. This calls for an entirely different approach to constructing efficient circuits. In this paper we study the problem of converting a given circuit that uses 2-qubit gates to one that uses global gates. Our three main contributions are as follows. First, we find an efficient algorithm for transforming an arbitrary circuit consisting of Clifford gates and arbitrary phase gates into a circuit consisting of single-qubit gates and a number of global interactions proportional to the number of non-Clifford phases present in the original circuit. Second, we find a general strategy to transform a global gate that targets all qubits into one that targets only a subset of the qubits. This approach scales linearly with the number of qubits that are not targeted, in contrast to the exponential scaling reported in (Maslov & Nam, N. J. Phys. 2018). Third, we improve on the number of global gates required to synthesise an arbitrary n-qubit Clifford circuit from the 12n-18 reported in (Maslov & Nam, N. J. Phys. 2018) to 6n-8.
