Two fundamental problems exist in the use of quantum computation to process an image or signal. The first one is how to represent giant data, such as image data, using quantum state without losing information. The second one is how to load a colossal volume of data into the quantum registers of a quantum CPU from classical electronic memory. Researches on these two questions are rarely reported. Here an entangled state is used to represent an image (or vector) for which two entangled registers are used to store a vector component and its classical address. Using the representation, n
 1 + n
 2 + 8 qubits are used to store the whole information of the gray image that has a $2^{n_1 } \times 2^{n_2 } $
 size at a superposition of states, a feat is not possible with a classic computer. The way of designing a unitary operation to load data, such as a vector (or image), into the quantum registers of a quantum CPU from electronic memory is defined herein as a quantum loading scheme (QLS). In this paper, the QLS with time complexity O(log2
 N) is presented where N denotes the number of vector components, a solution that would break through the efficiency bottleneck of loading data. QLS would enable a quantum CPU to be compatible with electronic memory and make possible quantum image compression and quantum signal processing that has classical input and output.

A theoretical framework for quantum image representation and data loading scheme

Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field It is found that the phenomenon of entanglement sudden death ( ESD) as well as sudden birth ( ESB) appear during the evolution process for particular initial states The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence of decoherence

https://iopscience.iop.org/article/10.1088/0256-307X/25/9/006/pdf

Sudden death, birth and stable entanglement in a two-qubit heisenberg XY spin chain

The impurities of exchange couplings, external magnetic fields and Dzyaloshinskii–Moriya (DM) interaction considered as Gaussian distribution, and the entanglement in one-dimensional random XY spin systems is investigated by the method of solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics at central locations of ferromagnetic and antiferromagnetic chains have been studied by varying the three impurities and the strength of DM interaction. (i) For the ferromagnetic spin chain, the weak DM interaction can improve the amount of entanglement to a large value, and the impurities have the opposite effect on the entanglement below and above critical DM interaction. (ii) For the antiferromagnetic spin chain, DM interaction can enhance the entanglement to a steady value. Our results imply that DM interaction strength, the impurity and exchange couplings (or magnetic field) play competing roles in enhancing quantum entanglement.

Entanglement in One-Dimensional Random XY Spin Chain with Dzyaloshinskii Moriya Interaction

We consider the dynamics of quantum correlations of two coupled spin qubits with Dzyaloshinsky-Moriya (DM) interaction influenced by a local external magnetic field along the z-direction and coupled to bath spin-
 $\frac{1}{2}$
 particles as independent non-Markovian environment. For this model, we calculate the entanglement measure of concurrence, quantum discord and quantum dissonance and find effects of DM interaction, bath-system coupling constant and temperature on the dynamics of quantum correlation. At last, we obtain the teleportation for this model by using fidelity and observe changes of DM interaction, bath-system coupling constant, temperature and magnetic field on fidelity.

Dynamics of Quantum Dissonance of Two Qubit XXZ Model with Dzyloshinsky-Moriya Interaction Coupled to Non-Markovian Environment

Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ |01 +sin θ|10 at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B, anisotropic parameter Δ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.

Decoherence Effect in An Anisotropic Two-Qubit Heisenberg XYZ Model with Inhomogeneous Magnetic Field

The discrete Fourier transform (DFT) is the base of modern signal processing 1-dimensional fast Fourier transform (ID FFT) and 2D FFT have time complexity O (N log N) and O (N2 log N) respectively Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm DFT has two properties One property is that DFT is energy conservation transform The other property is that many DFT coefficients are close to zero The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy One-dimensional quantum DFT (ID QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper The quantum algorithm for convolution estimation is also presented in this paper Compared with FFT, ID and 2D QDFT have time complexity O(√N) and O (N) respectively QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

We investigate the dynamics of genuine three-qubit entanglement in the Ising model of three spins. A scheme is presented for generating the genuine three-qubit entanglement by the nearest-neighbour couplings. The effect of magnetic fields on the dynamics of genuine three-qubit entanglement is also discussed.

Pang Chao-Yang

Papers

A quantum search algorithm of two entangled registers to realize quantum discrete Fourier transform of signal processing

Dynamics of Genuine Three-Qubit Entanglement in Ising Spin Systems