Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

Linear Transformation Theory of Quantum Field Operators and Its Applications

We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.

Unidirectional acoustic metamaterials based on nonadiabatic holonomic quantum transformations

Nonadiabatic holonomic quantum transformations(NHQTs)have attracted wide attention and have been applied in many aspects of quantum computation,whereas related research is usually limited to the field of quantum physics.Here we bring NHQTs into constructing a unidirectional acoustic metamaterial(UDAM)for shaping classical beams.The UDAM is made up of an array of three-waveguide couplers,where the propagation of acoustic waves mimics the evolution of NHQTs.The excellent agreement among analytical predictions,numerical simulations,and experimental measurements confirms the great applicability of NHQTs in acoustic metamaterial engineering.The present work extends research on NHQTs from quantum physics to the field of classical waves for designing metamaterials with simple structures and may pave a new way to design UDAMs that would be of potential applications in acoustic isolation,communication,and stealth.

Quantum Fourier Transform and Phase Estimation in Qudit System

The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.

Multiparty Quantum Secret Sharing Using Quantum Fourier Transform

A （n, n）-threshold scheme of multiparty quantum secret sharing of classical or quantum message is proposed based on the discrete quantum Fourier transform. In our proposed scheme, the secret message, which is encoded by using the forward quantum Fourier transform and decoded by using the reverse, is split and shared in such a way that it can be reconstructed among them only if all the participants work in concert. Fhrthermore, we also discuss how this protocol must be carefully designed for correcting errors and checking eavesdropping or a dishonest participant. Security analysis shows that our scheme is secure. Also, this scheme has an advantage that it is completely compatible with quantum computation and easier to realize in the distributed quantum secure computation.

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.

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.

Quantum Mechanical Hilbert Transformation for Normally Ordering Coulomb Potential-Type Operators

We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.

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 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.

Dynamic quantum secret sharing protocol based on two-particle transform of Bell states

To solve the problems of updating sub-secrets or secrets as well as adding or deleting agents in the quantum secret sharing protocol, we propose a two-particle transform of Bell states, and consequently present a novel dynamic quantum secret sharing protocol. The new protocol can not only resist some typical attacks, but also be more efficient than the existing protocols. Furthermore, we take advantage of the protocol to establish the dynamic secret sharing of a quantum state protocol for two-particle maximum entangled states.

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.

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 embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch 3ozsa. algorithm and Shor＇s quantum factoring. In particular, the detailed process of implementing one^qubit Deutsch Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight 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 qubits situated in a high-Q superconducting transmission line resonator. The phase shifting angle can be tuned from 0 to 27r by simply adjusting the qubit-resonator detuning and the interaction time. Based on this gate proposal, we give a detailed procedure to implement the three-qubit quantum Fourier transform with circuit quantum eleetrodynamics （QED）. A careful analysis of the decoherence sources shows that the algorithm can be achieved with a high fidelity using current circuit QED techniques.

Quantum Discrete Fourier Transform in an Ion Trap System

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

On Quantum Mechanical Hankel Transform and Its Applications

Based on our preceding works of how to relate the mathematical Hankel transform to quantum mechanical representation transform and how to express the Bessel equation by an operator identity in some appropriate representations we propose the concept of quantum mechanical Hankel transform with regard to quantum state vectors. Then we discuss its new applications.

TWO DIMENSIONAL MELLIN TRANSFORM IN QUANTUM CALCULUS

In this article, we introduce the two dimensional Mellin transform M4（f）（s,t）, give some properties, establish the Paley-Wiener theorem and Plancherel formula, present the Hausdorff-Young inequality, and find several applications for the two dimensional Mellin transform.

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.

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.

Hawking effect and quantum nonthermal radiation of an arbitrarily accelerating charged black hole using a new tortoise coordinate transformation

Using a new tortoise coordinate transformation, this paper investigates the Hawking effect from an arbitrarily accelerating charged black hole by the improved Damour-Ruffini method. After the tortoise coordinate transformation, the Klein-Gordon equation can be written as the standard form at the event horizon. Then extending the outgoing wave from outside to inside of the horizon analytically, the surface gravity and Hawking temperature can be obtained automatically. It is found that the Hawking temperatures of different points on the surface are different. The quantum nonthermal radiation characteristics of a black hole near the event horizon is also discussed by studying the Hamilton-Jacobi equation in curved spacetime and the maximum overlap of the positive and negative energy levels near the event horizon is given. There is a dimensional problem in the standard tortoise coordinate and the present results may be more reasonable.