In the paper, we consider quantum circuits for the Quantum Fourier Transform (QFT) algorithm. The QFT algorithm is a very popular technique used in many quantum algorithms. We present a generic method for constructing quantum circuits for this algorithm implementing on quantum devices with restrictions. Many quantum devices (for example, based on superconductors) have restrictions on applying two-qubit gates. These restrictions are presented by a qubit connectivity graph. Typically, researchers consider only the linear nearest neighbor (LNN) architecture of the qubit connection, but current devices have more complex graphs. We present a method for arbitrary connected graphs that minimizes the number of CNOT gates in the circuit for implementing on such architecture. We compare quantum circuits built by our algorithm with existing quantum circuits optimized for specific graphs that are Linear-nearest-neighbor (LNN) architecture, ``sun'' (a cycle with tails, presented by the 16-qubit IBMQ device) and ``two joint suns'' (two joint cycles with tails, presented by the 27-qubit IBMQ device). Our generic method gives similar results with existing optimized circuits for ``sun'' and ``two joint suns'' architectures, and a circuit with slightly more CNOT gates for the LNN architecture. At the same time, our method allows us to construct a circuit for arbitrary connected graphs.

翻译：本文研究了用于量子傅里叶变换（QFT）算法的量子电路。QFT算法是一种广泛应用于多种量子算法的核心技术。我们提出了一种通用方法，用于在具有限制条件的量子设备上构建实现该算法的量子电路。许多量子设备（例如基于超导体的设备）在应用双量子比特门时存在限制，这些限制由量子比特连通图表示。通常，研究者仅考虑线性最近邻（LNN）量子比特连接架构，但当前设备具有更复杂的连通图。我们提出了一种适用于任意连通图的方法，旨在最小化在此类架构上实现电路所需的CNOT门数量。我们将通过本算法构建的量子电路与针对特定图优化的现有量子电路进行了比较，这些特定图包括线性最近邻（LNN）架构、“日冕”图（一种带尾环的循环结构，由16量子比特IBMQ设备呈现）以及“双联日冕”图（两个带尾环的联合循环结构，由27量子比特IBMQ设备呈现）。对于“日冕”和“双联日冕”架构，我们的通用方法所得结果与现有优化电路相近；对于LNN架构，所得电路包含的CNOT门数量略多。同时，我们的方法能够为任意连通图构建量子电路。