中文摘要：

量子傅里叶变换是量子计算中一种重要的量子逻辑门.任意量子位的傅里叶变换可以分解为一系列普适的单比特量子逻辑门和两比特量子逻辑门,这种分解方式使得傅里叶变换的实验实现简单直观,但所用的实验时间显然不是最短的.本文利用优化控制和数值计算方法对Ising耦合体系中多量子位傅里叶变换的实验时间进行优化,优化后的实现方法明显短于传统方法.优化方法的核磁共振实验实现验证了其有效性.

英文摘要：

Quantum Fourier transform （QFT） is a quantum analogue of the classical discrete Fourier transform. It is a fundamental quantum gate in quantum algorithms which has an exponential advantage over the classical computation and has been excessively studied. Normally, an n-qubit quantum Fourier transform could be resolved into the tensor product of n single-qubit operations, and each operation could be implemented by a Hadamard gate and a controlled phase gate. Then the complexity of an n-qubit QFT is of order O（n^2）. To reduce the complexity of quantum operations, optimal control （OC） method has recently been used successfully to find the minimum time for implementing a quantum operation. Up to now, two types of quantum optimal control methods have been presented, i.e. analytical and numerical methods. The analytical approach is to change the problem of efficient synthesis of unitary transformations into the geometrical one of finding the shortest paths. Numerical optimal control procedures are based on the gradient methods （GRAPE, Gradient Ascent Pulse Engineering） and Krotov methods. Notable application mainly focus on nuclear magnetic resonance fields, including imaging, liquid-state NMR, solid-state NMR, and NMR quantum computation. One obvious advantage of optimal control NMR quantum computation is that the OC unitary evolution transformation pulse sequences are normally shorter than the conventional corresponding ones. Here we use the optimal control method to find the minimum duration for implementing QFT quantum gate. A linear spin chain with nearest-neighbor Ising interaction is used to find the optimization. And the optimized pulse sequence is experimentally demonstrated on an NMR quantum information processor. By using optimal control method with numerical calculation, a three-qubit QFT in an indirect-linear-coupling chain system is optimized. The duration of the OC QFT is obviously shorter than that of conventional approaches. The OC pulse sequence has been experimentally implemented on a