Search

There is a strong interest in quantum search algorithms, particularly in problems with multiple adjacent solutions. In the hypercube, part of the energy of the quantum system is retained in states adjacent to the target states, decreasing the chances of the target states being observed. This paper applies the Multiself-loop Lackadaisical Quantum Walk with Partial Phase Inversion to search for multiple adjacent marked vertices on the hypercube. Aspects like the type of marked vertices are considered in addition to using multiple self-loops and weight compositions. Two scenarios are analyzed. Firstly, the relative position of non-adjacent marked vertices together with adjacent marked vertices. Secondly, only adjacent marked vertices are analyzed. Here, we show experimentally that, with partial phase inversion, a quantum walk can amplify the probability amplitudes of the target states, reaching success probabilities of values close to $1$. We also show that the relative position of non-adjacent marked vertices does not significantly influence the search results. Our results demonstrate that the partial phase inversion of target states is a promising alternative to search adjacent solutions with quantum walks, which is a key capacity for real search applications., Comment: 10 pages, 3 figures, 6 tables. arXiv admin note: text overlap with arXiv:2305.01121

The lackadaisical quantum walk, a quantum analog of the lazy random walk, is obtained by adding a weighted self-loop transition to each state. Impacts of the self-loop weight $l$ on the final success probability in finding a solution make it a key parameter for the search process. The number of self-loops can also be critical for search tasks. This article proposes the quantum search algorithm Multi-self-loop Lackadaisical Quantum Walk with Partial Phase Inversion, which can be defined as a lackadaisical quantum walk with multiple self-loops, where the target state phase is partially inverted. In the proposed algorithm, each vertex has $m$ self-loops, with weights $l' = l/m$, where $l$ is a real parameter. The phase inversion is based on Grover's algorithm and acts partially, modifying the phase of a given quantity $s < m$ of self-loops. We also propose two new weight values based on two ideal weights $l$ used in the literature. On a hypercube structure, we analyzed the situation where $s=1$ and $1 \leqslant m \leqslant 30$. We investigated the effects of partial phase inversion in the search for $1$ to $12$ marked vertices. As a result, this proposal improved the maximum success probabilities to values close to $1$ in $O (\sqrt{(n+m)\cdot N})$, where $n$ is the hypercube degree. This article contributes with a new perspective on the use of quantum interferences in constructing new quantum search algorithms., Comment: 17 pages, 21 figures, 4 tables

The need for computational resources grows as computational algorithms gain popularity in different sectors of the scientific community. This search has stimulated the development of several cloud platforms that abstract the complexity of computational infrastructure. Unfortunately, the cost of accessing these resources could leave out various studies that could be carried by a simpler infrastructure. In this article, we present a platform for distributing computer simulations on resources available on a network using containers that abstracts the complexity needed to configure these execution environments and allows any user can benefit from this infrastructure. Simulations could be developed in any programming language (like Python, Java, C, R) and with specific execution needs within reach of the scientific community in a general way. We will present results obtained in running simulations that required more than 1000 runs with different initial parameters and various other experiments that benefited from using the platform., Comment: 17 pages, 8 figures

By using both ray and wave optics, we show that a simple device which consists on a film of hyperbolic metamaterial on the surface of a catenoid can be used to trap light. From the study of the trajectories, we observe a tendency for the light rays to wrap, and eventually be trapped, around the neck of the device. The wave equation appears to have an effective attractive potential, and their solutions confirm the bound states suggested by the trajectories. The relevant equations are solved numerically using neural networks., Comment: 5 pages, 4 figures

This work proposes a computational procedure that uses a quantum walk in a complete graph to train classical artificial neural networks. The idea is to apply the quantum walk to search the weight set values. However, it is necessary to simulate a quantum machine to execute the quantum walk. In this way, to minimize the computational cost, the methodology employed to train the neural network will adjust the synaptic weights of the output layer, not altering the weights of the hidden layer, inspired in the method of Extreme Learning Machine. The quantum walk algorithm as a search algorithm is quadratically faster than its classic analog. The quantum walk variance is $O(t)$ while the variance of its classic analog is $O(\sqrt{t})$, where $t$ is the time or iteration. In addition to computational gain, another advantage of the proposed procedure is to be possible to know \textit{a priori} the number of iterations required to obtain the solutions, unlike the classical training algorithms based on gradient descendent., Comment: 10 Pages, 4 Figures

This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic weights of a classical artificial neural network. Each vertex of this complete graph represents a possible synaptic weight set in the $w$-dimensional search space, where $w$ is the number of weights of the neural network. To know the number of iterations required \textit{a priori} to obtain the solutions is one of the main advantages of the procedure. Another advantage is that the proposed method does not stagnate in local minimums. Thus, it is possible to use the quantum walk search procedure as an alternative to the backpropagation algorithm. The proposed method was employed for a $XOR$ problem to prove the proposed concept. To solve this problem, the proposed method trained a classical artificial neural network with nine weights. However, the procedure can find solutions for any number of dimensions. The results achieved demonstrate the viability of the proposal, contributing to machine learning and quantum computing researches., Comment: 19 pages, 7 figures

Adding self-loops at each vertex of a graph improves the performance of quantum walks algorithms over loopless algorithms. Many works approach quantum walks to search for a single marked vertex. In this article, we experimentally address several problems related to quantum walk in the hypercube with self-loops to search for multiple marked vertices. We first investigate the quantum walk in the loopless hypercube. We saw that neighbor vertices are also amplified and that approximately $1/2$ of the system energy is concentrated in them. We show that the optimal value of $l$ for a single marked vertex is not optimal for multiple marked vertices. We define a new value of $l = (n/N)\cdot k$ to search multiple marked vertices. Next, we use this new value of $l$ found to analyze the search for multiple marked vertices non-adjacent and show that the probability of success is close to $1$. We also use the new value of $l$ found to analyze the search for several marked vertices that are adjacent and show that the probability of success is directly proportional to the density of marked vertices in the neighborhood. We also show that, in the case where neighbors are marked, if there is at least one non-adjacent marked vertex, the probability of success increases to close to $1$. The results found show that the self-loop value for the quantum walk in the hypercube to search for several marked vertices is $l = (n / N) \cdot k $., Comment: 12 pages, 20 figures

Quantum computing promises to improve the information processing power to levels unreachable by classical computation. Quantum walks are heading the development of quantum algorithms for searching information on graphs more efficiently than their classical counterparts. A quantum-walk-based algorithm standing out in the literature is the lackadaisical quantum walk. The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully. Firstly, we show that only one of the two stopping conditions found in the literature is suitable for simulations. We also demonstrate that the final success probability depends on both the space density of solutions and the relative distance between solutions. Furthermore, this work generalizes the lackadaisical quantum walk to search for multiple solutions on grids of arbitrary dimensions. In addition, we propose an optimal adjustment of the self-loop weight $l$ for such $d$-dimensional grids. It turns out other fits of $l$ found in the literature are particular cases. Finally, we observe a two-to-one relation between the steps of the lackadaisical quantum walk and Grover's algorithm, which requires modifications in the stopping condition. In conclusion, this work deals with practical issues one should consider when applying the lackadaisical quantum walk, besides expanding the technique to a broader range of search problems., Comment: Accepted manuscript. 23 pages, 7 figures

The activation function plays a fundamental role in the artificial neural network learning process. However, there is no obvious choice or procedure to determine the best activation function, which depends on the problem. This study proposes a new artificial neuron, named global-local neuron, with a trainable activation function composed of two components, a global and a local. The global component term used here is relative to a mathematical function to describe a general feature present in all problem domain. The local component is a function that can represent a localized behavior, like a transient or a perturbation. This new neuron can define the importance of each activation function component in the learning phase. Depending on the problem, it results in a purely global, or purely local, or a mixed global and local activation function after the training phase. Here, the trigonometric sine function was employed for the global component and the hyperbolic tangent for the local component. The proposed neuron was tested for problems where the target was a purely global function, or purely local function, or a composition of two global and local functions. Two classes of test problems were investigated, regression problems and differential equations solving. The experimental tests demonstrated the Global-Local Neuron network's superior performance, compared with simple neural networks with sine or hyperbolic tangent activation function, and with a hybrid network that combines these two simple neural networks.

Laser Interferometer Gravitational-Wave Observatory (LIGO) was the first laboratory to measure the gravitational waves. It was needed an exceptional experimental design to measure distance changes much less than a radius of a proton. In the same way, the data analyses to confirm and extract information is a tremendously hard task. Here, it is shown a computational procedure base on artificial neural networks to detect a gravitation wave event and extract the knowledge of its ring-down time from the LIGO data. With this proposal, it is possible to make a probabilistic thermometer for gravitational wave detection and obtain physical information about the astronomical body system that created the phenomenon. Here, the ring-down time is determined with a direct data measure, without the need to use numerical relativity techniques and high computational power.

It is crucial for the wine industry to have methods like electronic nose systems (E-Noses) for real-time monitoring thresholds of acetic acid in wines, preventing its spoilage or determining its quality. In this paper, we prove that the portable and compact self-developed E-Nose, based on thin film semiconductor (SnO2) sensors and trained with an approach that uses deep Multilayer Perceptron (MLP) neural network, can perform early detection of wine spoilage thresholds in routine tasks of wine quality control. To obtain rapid and online detection, we propose a method of rising-window focused on raw data processing to find an early portion of the sensor signals with the best recognition performance. Our approach was compared with the conventional approach employed in E-Noses for gas recognition that involves feature extraction and selection techniques for preprocessing data, succeeded by a Support Vector Machine (SVM) classifier. The results evidence that is possible to classify three wine spoilage levels in 2.7 seconds after the gas injection point, implying in a methodology 63 times faster than the results obtained with the conventional approach in our experimental setup.