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Jonathan H. A. de Carvalho

Publications and source records attributed to Jonathan H. A. de Carvalho.

9 recordsLinked to original sources
arXiv2026

Quantum-classical hybrid models based on error correction for time series forecasting

Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.

quant-ph↗
arXiv2024

Multi-self-loop Lackadaisical Quantum Walk with Partial Phase Inversion

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. On a hypercube structure, we analyzed the situation where $1 \leqslant m \leqslant 30$. We also propose two new weight values based on two ideal weights $l$ used in the literature. 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.

quant-ph↗
arXiv2024

Search for Multiple Adjacent Marked Vertices on the Hypercube by a Quantum Walk with Partial Phase Inversion

In this paper, we analyze the application of the Multi-self-loop Lackadaisical Quantum Walk on the hypercube that uses partial phase inversion to search for multiple adjacent marked vertices. We evaluate the influence of the relative position of non-adjacent marked vertices. The use of self-loops and the composition of their weights are an essential part of the construction process of new quantum search algorithms based on lackadaisical quantum walks, however, other aspects have been considered, such as, for example, the type of marked vertices. Part of the energy of a quantum system is retained in states adjacent to the target state. This behavior causes the probability amplitudes of these states to be amplified to values equivalent to those of the target state, reducing their chances of being observed. Here we show experimentally that with the use of partial phase inversion, it is possible to amplify their probability amplitudes to values close to 1 even in scenarios with adjacent marked vertices. We also show that the relative position of the non-adjacent marked vertices did not significantly influence the results. The lackadaisical quantum walk generalization to only a single self-loop and the ideal composition of a weight value was sufficient to obtain advances to quantum search algorithms based on quantum walks. However, the results show that many other aspects need to be taken into account for the construction of new quantum algorithms. It was possible to add gains in the maximum probabilities of success compared to other results found in the literature. In one of the most significant cases, the probability of success increased from $p \approx 0.38$ to $p > 0.99$. Therefore, the use of partial phase inversion brings new contributions to the development of new quantum search algorithms based on quantum walks and the use of multiple self-loops.

quant-ph↗
arXiv2023

Parametrized constant-depth quantum neuron

Quantum computing has been revolutionizing the development of algorithms. However, only noisy intermediate-scale quantum devices are available currently, which imposes several restrictions on the circuit implementation of quantum algorithms. In this paper, we propose a framework that builds quantum neurons based on kernel machines, where the quantum neurons differ from each other by their feature space mappings. Besides contemplating previous schemes, our generalized framework can instantiate quantum neurons with other feature mappings. We present here a neuron that applies a tensor-product feature mapping to an exponentially larger space. The proposed neuron is implemented by a circuit of constant depth with a linear number of elementary single-qubit gates. The existing neuron applies a phase-based feature mapping with an exponentially expensive circuit implementation, even using multi-qubit gates. Additionally, the proposed neuron has parameters that can change its activation function shape. Here, we show the activation function shape of each quantum neuron. It turns out that parametrization allows the proposed neuron to optimally fit underlying patterns that the existing neuron cannot fit, as demonstrated in the toy problems addressed here. The feasibility of those quantum neuron solutions is also contemplated in the demonstration through executions on a quantum simulator. Finally, we compare those kernel-based quantum neurons in the problem of handwritten digit recognition, where the performances of quantum neurons that implement classical activation functions are also contrasted here. The repeated evidence of the parametrization potential achieved in real-life problems allows concluding that this work provides a quantum neuron with improved discriminative abilities. As a consequence, the generalized framework of quantum neurons can contribute toward practical quantum advantage.

quant-ph↗
arXiv2023

PESC -- Parallel Experiment for Sequential Code

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.

cs.DC↗
arXiv2023

On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids

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.

quant-ph↗
arXiv2021

Lackadaisical quantum walk in the hypercube to search for multiple marked vertices

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 $.

quant-ph↗
arXiv2021

Quantum Walk to Train a Classical Artificial Neural Network

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.

quant-ph↗
arXiv2021

Classical Artificial Neural Network Training Using Quantum Walks as a Search Procedure

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.

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