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In this paper, continuous-time quantum walk on hypercube is discussed in view of Cartesian product structure. We find that the n -fold Cartesian power of the complete graph K 2 is the n -dimensional hypercube, which give us new ideas for the study of quantum walk on hypercube. Combining the product structure, the spectral distribution of the graph and the quantum decomposition of the adjacency matrix, the probability amplitudes of the continuous-time quantum walker's position at time t are given, and it is discussed that the probability distribution for the continuous-time case is uniform when t = (π ∕ 4) n. The application of this product structure greatly improves the study of quantum walk on complex graphs, which has far-reaching influence and great significance. [ABSTRACT FROM AUTHOR]

In this paper, continuous-time quantum walk is discussed based on the view of quantum probability, i.e. the quantum decomposition of the adjacency matrix A of graph. Regard adjacency matrix A as Hamiltonian which is a real symmetric matrix with elements 0 or 1, so we regard  e − i t A  as an unbiased evolution operator, which is related to the calculation of probability amplitude. Combining the quantum decomposition and spectral distribution  μ  of adjacency matrix A, we calculate the probability amplitude reaching each stratum in continuous-time quantum walk on complete bipartite graphs, finite two-dimensional lattices, binary tree, N -ary tree and N -fold star power G ⋆ N . Of course, this method is also suitable for studying some other graphs, such as growing graphs, hypercube graphs and so on, in addition, the applicability of this method is also explained. [ABSTRACT FROM AUTHOR]

The problem of diffraction of E-polarized light at normal falling on a grating of infinitely thin metallic strips is solved. Light is represented as a flux of particles – photons. The problem of determining the psifunction of a photon scattered by the grating is led down to the Riemann-Hilbert boundary problem. A strict solution is obtained in the form of a convergent infinite system of linear algebraic equations. The system equations are valid for any relation between wavelength and period of the structure and any relation between slit width and strip width. As follows from a comparison of the de Broglie representation of the psi-function and its decomposition into Fourier series, the possible values of the photon momentum component perpendicular to its initial direction of motion are determined by even values of the "quantum" of momentum, whose magnitude is determined by the grating period. Photons passed through or reflected by the grating get discrete values of momentum when interacting with the grating and deviate at discrete angles. Numerical calculations show that the diffraction maxima are located in front of the slit and have some internal structure that depends on the ratio between the grating period and the photon wavelength. As the ratio of the grating period to the photon wavelength increases, the diffraction peak splits. When the ratio becomes less than unity, the diffraction pattern disappears, we have a uniform illumination. Therefore, the value of the specified ratio, equal to one, is the threshold. [ABSTRACT FROM AUTHOR]

We discuss the problem of filtering out abnormal states from a larger number of quantum states. For this type of problem with N items to be searched, both the traditional search by enumeration and classical Grover search algorithm have the complexity about O (N). In this letter a novel quantum search scheme with exponential speed up is proposed for abnormal states. First, a new comprehensive quantum operator is well-designed to extract the superposition state containing all abnormal states with unknown number L (≪ N) with complexity O (1) in probability 1 via well-designed parallel phase comparison. Then, every abnormal state is achieved respectively from L abnormal states via O (4 L 2) times' measurement. Finally, a numerical example is given to show the efficiency of the proposed scheme. [ABSTRACT FROM AUTHOR]

A probability amplitude-encoded multichannel representation for quantum audio signals (or simply PMQA) is proposed in this study. As an entangled state, PMQA requires only one qubit to epitomise the bipolar decimal amplitude values of a quantum audio signal, which leads to considerable conservation of qubit resources relative to similar models. Furthermore, the representation provides an embodiment of a signal that can be manipulated via quantum circuits for signal and channel level operations to merge, add, invert, delay, swap, etc. different audio contents. Compared to available quantum audio representations, the proposed PMQA provides lower complexity, and its operations provide essential building blocks for applications in future quantum audio processing. [ABSTRACT FROM AUTHOR]

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The probability amplitudes for quantum entanglement, also known as Bell sates, are utilized to arrive explicitly at the identity matrix I and the σ x , σ y , and σ z Pauli matrices, via a straight-forward 2 × 2 matrix representation that utilizes the vector direct product. It is also indicated that this approach is completely equivalent to the utilization of the Kronecker product ⊗ to multiply the relevant ket vectors. Furthermore, it is shown that the polarization rotation matrix R, operating on the various versions of the probability amplitude for quantum entanglement, yields four identities elegantly interconnecting these probability amplitudes. [ABSTRACT FROM AUTHOR]

This paper focuses on modeling a disorder ensemble of quantum dots (QDs) as a special kind of Random Geometric Graphs (RGG) with weighted links. We compute any link weight as the overlap integral (or electron probability amplitude) between the QDs (=nodes) involved. This naturally leads to a weighted adjacency matrix, a Laplacian matrix, and a time evolution operator that have meaning in Quantum Mechanics. The model prohibits the existence of long-range links (shortcuts) between distant nodes because the electron cannot tunnel between two QDs that are too far away in the array. The spatial network generated by the proposed model captures inner properties of the QD system, which cannot be deduced from the simple interactions of their isolated components. It predicts the system quantum state, its time evolution, and the emergence of quantum transport when the network becomes connected.

We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.

Grover's search algorithm is one of the most significant quantum algorithms, which can obtain quadratic speedup of the extensive search problems. Since Grover's search algorithm cannot be implemented on a real quantum computer at present, its quantum simulation is regarded as an effective method to study the search performance. When simulating the Grover's algorithm, the storage space required is exponential, which makes it difficult to simulate the high-qubit Grover's algorithm. To this end, we deeply study the storage problem of probability amplitude, which is the core of the Grover simulation algorithm. We propose a novel memory-efficient method via amplitudes compression, and validate the effectiveness of the method by theoretical analysis and simulation experimentation. The results demonstrate that our compressed simulation search algorithm can help to save nearly 87.5% of the storage space than the uncompressed one. Thus under the same hardware conditions, our method can dramatically reduce the required computing nodes, and at the same time, it can simulate at least 3 qubits more than the uncompressed one. Particularly, our memory-efficient simulation method can also be used to simulate other quantum algorithms to effectively reduce the storage costs required in simulation. [ABSTRACT FROM AUTHOR]

In the modern manufacture industry, the lot-sizing planning is one of the key elements that can maximize the economic benefit of companies, but what it focuses on is to determine the best production schedule, as driven by the demands of given batch products, in order to minimize the sum of various costs such as manufacture, inventory and adjustment or maximize the profits. In recent years, the swarm intelligence algorithms such as the genetic algorithm and the particle swarm optimization provide a new way for solving complex Lotsizing problems, but they are prone to local optimum. In order to fill this gap and obtain a global optimum, this paper integrates the quantum algorithm into the classical evolutionary genetic algorithm. First, the unique probability amplitude and qubit in quantum theory are accessed to encode the decision variables for output as expected; then, in the iterative process, the quantum spin angle is dynamically adjusted to control the gene mutation rate, and maintain the genetic information that the optimal individuals involve, for fear of trapping in local optimum. The case study of the Lot-sizing problem shows that, in relation to the abovementioned algorithms, the quantum evolutionary algorithm features higher resolution accuracy and convergence rate, and can effectively solve the complex multi-constraint Lot-sizing problem and improve the company's Productivity. [ABSTRACT FROM AUTHOR]