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 two-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. An especially interesting case where compilation is necessary is for ion trap quantum computers, where the natural entangling operation can act on more than two 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 two-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 and Nam 2018 New J. Phys. 20 033018). 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 and Nam 2018 New J. Phys. 20 033018) to 6n − 8.

有多种门集可用于描述量子计算。量子计算文献中一个特别流行的门集由任意单量子位门和双量子位 CNOT 门组成。然而，CNOT 门并不总是可以在给定的物理量子计算机上实现的自然多量子位交互，需要一个编译步骤将这些 CNOT 门转换为原生门集。需要编译的一个特别有趣的例子是离子阱量子计算机，其中自然纠缠操作可以作用于两个以上的量子位，甚至可以同时作用于所有量子位。这需要一种完全不同的方法来构建高效的电路。在本文中，我们研究了将使用两个量子位门的给定电路转换为使用全局门的电路的问题。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，可以将由 Clifford 门和任意相位门组成的任意电路转换为由单量子位门和与原始电路中存在的非 Clifford 相位数量成正比的多个全局相互作用组成的电路。其次，我们找到了一种通用策略，将针对所有量子位的全局门转换为仅针对量子位子集的全局门。与（Maslov 和 Nam 2018 我们找到了一种有效的算法，可以将由 Clifford 门和任意相位门组成的任意电路转换为由单量子位门和许多与原始电路中存在的非 Clifford 相位数量成正比的全局交互组成的电路。其次，我们找到了一种通用策略，将针对所有量子位的全局门转换为仅针对量子位子集的全局门。与（Maslov 和 Nam 2018 我们找到了一种有效的算法，可以将由 Clifford 门和任意相位门组成的任意电路转换为由单量子位门和许多与原始电路中存在的非 Clifford 相位数量成正比的全局交互组成的电路。其次，我们找到了一种通用策略，将针对所有量子位的全局门转换为仅针对量子位子集的全局门。与（Maslov 和 Nam 2018新的 J. Phys. 20 033018）。第三，我们将合成任意n- qubit Clifford 电路所需的全局门数从(Maslov and Nam 2018 New J. Phys. 20 033018) 中报告的 12 n - 18提高到 6 n - 8。