Realization of quantum Fourier transform over Z_N

Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform （QFT） over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over Z_N can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over Z_N. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over Z_N.

Applications of quantum Fourier transform in photon-added coherent state

Quantum Fourier transform is realized by the Hadamard gate in a quantum computer, which can also be considered as a Hadamard transform. We introduce the Hadamard transformed photon-added coherent state （HTPACS）, which is obtained by letting the photon-added coherent state （PACS） across the quantum Hadamard gate, from this result. It is found that the HTPACS can be considered as a coordinate-momentum mutual exchanging followed by a squeezing transform of the PACS. In addition, the non-classical statistical properties of HTPACS, such as squeezing coefficient, Mandel parameter, etc., are also discussed.

Quantum Fourier Transform and Phase Estimation in Qudit System

量 Fourier 变换和量阶段评价是为许多量算法的关键部件，例如发现顺序， factoring，和等等。在这篇文章，量 Fourier 变换和阶段评价的一般过程为高维的大小写被调查。他们能在一台 qudit 量计算机在主程序跑被看作子程序，并且量电路被给。

Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

一(n， n ) 多党的量秘密分享的阀值计划古典或量消息基于分离的量 Fourier 变换被建议。在我们的建议计划，仅当所有参加者在音乐会工作，秘密消息，被使用前面的量 Fourier 变换编码并且由使用颠倒译码，以如此的一个方法被切开并且分享，它能在他们之中被重建。而且，我们也讨论这个协议怎么必须小心地为改正错误或一个不诚实的参加者被设计。安全分析证明我们的计划是安全的。另外，这个计划有它与量计算完全兼容的一个优点并且更容易在分布式的量认识到安全计算。

Realization of -bit semiclassical quantum Fourier transform on IBM's quantum cloud computer

To overcome the difficulty of realizing large-scale quantum Fourier transform(QFT) within existing technology, this paper implements a resource-saving method(named t-bit semiclassical QFT over Z_(2~n)), which could realize large-scale QFT using an arbitrary-scale quantum register. By developing a feasible method to realize the control quantum gate Rk, we experimentally realize the 2-bit semiclassical QFT over Z_(2~3) on IBM's quantum cloud computer, which shows the feasibility of the method. Then, we compare the actual performance of 2-bit semiclassical QFT with standard QFT in the experiments.The squared statistical overlap experimental data shows that the fidelity of 2-bit semiclassical QFT is higher than that of standard QFT, which is mainly due to fewer two-qubit gates in the semiclassical QFT. Furthermore, based on the proposed method, N = 15 is successfully factorized by implementing Shor's algorithm.

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embeddedin a microcavity,and then some of its applications are investigated,i.e.,Deutsch-Jozsa.algorithm and Shot's quantumfactoring.In particular,the detailed process of implementing one-qubit Deutsch Jozsa algorithm and the factorization ofN=15 are given.The microcavity mode is only virtually excited in the whole interaction,so the effective decoherent hasslight effect on the current scheme.These schemes would be an important step to fabricate a solid quantum computer.

Simple Scheme for Realizing the General Conditional Phase Shift Gate and a Simulation of Quantum Fourier Transform in Circuit QED

We propose a theoretical scheme for realizing the general conditional phase shift gate of charge qubitssituated in a high-Q superconducting transmission line resonator.The phase shifting angle can be tuned from 0 to 2n bysimply adjusting the qubit-resonator detuning and the interaction time.Based on this gate proposal,we give a detailedprocedure to implement the three-qubit quantum Fourier transform with circuit quantum electrodynamics (QED).Acareful analysis of the decoherence sources shows that the algorithm can be achieved with a high fidelity using currentcircuit QED techniques.

An Image Encryption Method Based on Quantum Fourier Transformation

The image security problem is an important area in information security, and image encryption plays a vital role in this day. To protect the image encryption from the attack of quantum algorithm appeared recently, an image encryption method based on quantum Fourier transformation is proposed here. First, the image encryption and Fourier transformation are discussed here, then a encryption function is proposed. Second, a quantum Fourier transformation is introduced to quantum encryption, and the full step of quantum encryption is given as well. Third, the security of the proposed quantum encryption if analyzed, and some propositions are also presented. Lastly, some conclusions are indicated and some possible directions are also listed.

Quantum entangled fractional Fourier transform based on the IWOP technique

In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

t-bit semiclassical quantum Fourier transform

Because of the difficulty of building a high-dimensional quantum register,this paper presents an implementation of the high-dimensional quantum Fourier transform(QFT)based on a low-dimensional quantum register.First,we define the t-bit semi- classical quantum Fourier transform.In terms of probability amplitude,we prove that the transform can realize quantum Fourier transformation,illustrate that the requirement for the two-qubit gate reduces obviously,and further design a quantum circuit of the transform.Combining the classical fixed-window method and the implementation of Shor's quantum factorization algorithm,we then redesign a circuit for Shor's algorithm,whose required computation resource is approximately equal to that of Parker's.The requirement for elementary quantum gates for Parker's algorithm is 3 O (logN),and the quantum register for our circuit re- quires t-1 more dimensions than Parker's.However,our circuit is t2 times as fast as Parker's,where t is the width of the window.

Convolution Theorem of Fractional Fourier Transformation Derived by Representation Transformation in Quantum Mechancis

Based on our previous paper (Commun.Theor.Phys.39 (2003) 417) we derive the convolution theoremof fractional Fourier transformation in the context of quantum mechanics,which seems a convenient and neat way.Generalization of this method to the complex fractional Fourier transformation case is also possible.

Quantum Discrete Fourier Transform in an Ion Trap System

<正> We propose two schemes for the implementation of quantum discrete Fourier transform in the ion trap sys-tem.In each scheme we design a tunable two-qubit phase gate as the main ingredient.The experimental implementationof the schemes would be an important step toward complex quantum computation in the ion trap system.

The Fourier slice transformation of the Wigner operator and the quantum tomogram of the density operator

Using the Weyl quantization scheme and based on the Fourier slice transformation （FST） of the Wigner operator, we construct a new expansion formula of the density operator p, with the expansion coefficient being the FST of p＇s classical Weyl correspondence, and the latter the Fourier transformation of p＇s quantum tomogram. The coordinate momentum intermediate representation is used as the Radon transformation of the Wigner operator.

Quantum-Classical Algorithm for an Instantaneous Spectral Analysis of Signals:A Complement to Fourier Theory

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schr&#246;dinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

三值量子基本门及其对量子Fourier变换的电路实现

理论上可以把量子基本门组合在一起来实现任何量子电路和构建可伸缩的量子计算机。但由于构建量子线路的量子基本门数量庞大,要正确控制这些量子门十分困难。因此,如何减少构建量子线路的基本门数量是一个非常重要和非常有意义的课题。提出采用三值量子态系统构建量子计算机,并给出了一组三值量子基本门的功能定义、算子矩阵和量子线路图。定义的基本门主要包括三值量子非门、三值控制非门、三值Hadamard门、三值量子交换门和三值控制CRk门等。通过把量子Fourier变换推广到三值量子态,成功运用部分三值量子基本门构建出能实现量子Fourier变换的量子线路。通过定量分析发现,三值量子Fourier变换的线路复杂度比二值情况降低了至少50%,表明三值量子基本门在降低量子计算线路复杂度方面具有巨大优势。

量子Fourier变换在实现Deutsch-Jozsa算法中的应用

提出利用量子Fourier变换解决Deutsch-Jozsa算法问题的观点.结合量子Fourier变换和DeutschJozsa算法的量子电路,找到一种利用量子Fourier变换解决Deutsch-Jozsa算法新的量子电路,并考察该量子电路中各个线路的量子状态,结合算法对该量子线路的状态进行研究.结果表明:利用量子Fourier变换解决Deutsch问题,能够有效地提高运算速度,节省运算时间.

多量子位量子Fourier变换的仿真实现研究

量子Fourier变换(QFT)是许多量子算法的关键子例行程序,核磁共振系统(NMR)是目前最有希望实现量子计算的物理系统之一。在介绍QFT,并对其进行进一步分析,得到了多量子位QFT的实现逻辑线路后,应用多量子算符代数理论,给出了基本量子逻辑门的核磁共振实现,分解了QFT各相应的逻辑操作,设计了相应的核磁共振脉冲序列。并通过量子计算仿真程序进行了实现多量子位QFT的实验验证,证明了所设计的NMR脉冲序列的合理性和实用性。

N个接收方的同时密集编码协议

针对当前同时密集编码中接收方数量受限问题,通过引入n比特量子傅里叶变换,提出了具有多个接收方的非受控和受控同时密集编码协议。在非受控多方同时密集编码协议中,发送方在待传粒子上执行编码以及加锁操作,接收方只有联合执行解锁操作,才能同时获得最终的编码信息;在受控多方同时密集编码协议中,只有全体接收者在控制者的允许下通过协作才能完成信息的传输。通过对内部和外部攻击进行了分析,证实了同时密集编码协议的安全性。此外,所提出的方案中只使用Bell基测量,在实验条件下容易实现。

量子Fourier变换的分解

量子Fourier变换(Quantum Fourier Transform)是量子计算中的一种重要算法.量子计算机可以使用基于Shor的量子Fourier变换和基于Grover的量子搜索算法来解决那些在经典计算机上需要过多资源才能求解的问题.将作用在n量子比特上的量子Fourier变换Fn分解为有限个简单酉算子的乘积,并给出了相应的图示说明,使得人们可以更好地理解与应用量子Fou-rier变换以及它的有效线路.

量子安全多方计算协议研究进展

量子安全多方计算是量子信息技术与隐私保护计算技术相结合形成的新兴交叉领域,作为量子密码学的一个重要分支,在安全性、计算效率等方面有着经典安全多方计算所不能及的优点。量子安全多方求和(Quantum Secure Multi-party Summation,QSMS)作为量子安全多方计算的一个最基本运算过程,近年来获得了广泛的关注。本文梳理了近期QSMS协议的研究进展,根据协议所依据的基本原理进行了分类,并介绍了一些代表性协议的基本原理和典型特点。