论文标题
近似量子傅里叶变换的T计数优化
T-count optimization of approximate quantum Fourier transform
论文作者
论文摘要
量子傅立叶变换（QFT）是一种无处不在的量子操作，用于众多量子计算应用中。构建QFT电路的主要障碍是需要许多基本门。在基本门中，T门占据了容忍度实施的成本。当前，构造近似于误差O（\ Varepsilon）的N Qut QFT电路所需的最小的T计数为〜8nlog_2（n/\ varepsilon）。此外，近似QFT电路中T门的深度（t-depth）为〜2nlog_2（n/\ varepsilon）。使用Toffoli大门和量子添加器构建了该近似QFT电路。在这项研究中，我们提出了一个近似于误差O（\ Varepsilon）的新的N QUT电路。我们的近似QFT电路显示了〜4nlog_2（n/\ varepsilon）和〜nlog_2（n/\ varepsilon）的T计数。 Toffoli大门占先前研究报告的大约QFT回路中T计数的一半，这在我们的施工中是不必要的。在我们近似QFT电路中占主导地位的t-depth的领先顺序项的量子添加器平行排列以减少T深度。
The quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the elementary gates, T gates dominate the cost of fault-tolerant implementation. Currently, the smallest-known T-count required to construct an n-qubit QFT circuit approximated to error O(\varepsilon) is ~8nlog_2(n/\varepsilon). Moreover, the depth of T gates (T-depth) in the approximate QFT circuit is ~2nlog_2(n/\varepsilon). This approximate QFT circuit was constructed using Toffoli gates and quantum adders. In this study, we present a new n-qubit QFT circuit approximated to error O(\varepsilon). Our approximate QFT circuit shows a T-count of ~4nlog_2(n/\varepsilon) and a T-depth of ~nlog_2(n/\varepsilon). Toffoli gates, which account for half of the T-count in the approximate QFT circuit reported in the previous study, are unnecessary in our construction. Quantum adders, which dominate the leading order term of T-depth in our approximate QFT circuit, are arranged in parallel to reduce T-depth.
