Scaling and efficient classical simulation of the quantum Fourier transform

Kieran J. Woolfe, Charles D. Hill, Lloyd C. L. Hollenberg · 2017 · Quantum Information and Computation 17(1):1–14

| 编号 QQFT014 | 主题 量子傅里叶变换 | 链接 doi:10.26421/qic17.1-2-1 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。 We provide numerical evidence that the quantum Fourier transform can be efficiently represented in a matrix product operator with a size growing relatively slowly with the number of qubits. Additionally, we numerically show that the tensors in the operator converge to a common tensor as the number of qubits in the transform increases. Together these results imply that the application of the quantum Fourier transform to a matrix product state with n qubits of maximum Schmidt rank χ can be simulated in O(n (log(n))2 χ 2 ) time. We perform such simulations and quantify the error involved in representing the transform as a matrix product operator and simulating the quantum Fourier transform of periodic states.

可确认的信息

标题陈述的两件事是：给出 QFT 的标度行为，以及给出 QFT 的高效经典模拟。后者对本卷的意义在于：QFT 的输出（对 Haar 随机态、或在近似意义下）可以被经典采样，因此”QFT 本身”在若干场景里不是指数加速的来源。这一点在近似与截断 QFT与半经典 QFT两词条里都会用到。

本站词条在引用该文献时，会以 wikilink（sources/QQFT014）链接到本页；右侧「反向链接」面板自动列出所有引用它的词条。