论文标题
量子傅立叶添加，简化为Toffoli添加
Quantum Fourier Addition, Simplified to Toffoli Addition
论文作者
论文摘要
量子添加电路被认为是两种类型的：1）仅使用经典的可逆门（CNOT和TOFFOLI）的Toffolli-Adder电路，以及2）基于量子傅立叶变换的QFT-ADDER电路。我们将QFT-ADDITION电路的第一个系统翻译介绍为基于Toffoli的加法器。该结果表明，QFT添加的基本上具有相同的承重成本（例如T计数）与最具成本效益的Toffoli-Adder：而不是使用QFT电路的大门分解，而是更有效地合并门。为了实现这一目标，我们为多控制门制定了新的电路身份，并以算法的方式应用了身份。使用的技术可用于自动化量子电路优化启发式。
Quantum addition circuits are considered being of two types: 1) Toffolli-adder circuits which use only classical reversible gates (CNOT and Toffoli), and 2) QFT-adder circuits based on the quantum Fourier transformation. We present the first systematic translation of the QFT-addition circuit into a Toffoli-based adder. This result shows that QFT-addition has fundamentally the same fault-tolerance cost (e.g. T-count) as the most cost-efficient Toffoli-adder: instead of using approximate decompositions of the gates from the QFT circuit, it is more efficient to merge gates. In order to achieve this, we formulated novel circuit identities for multi-controlled gates and apply the identities algorithmically. The employed techniques can be used to automate quantum circuit optimisation heuristics.
