The contrast between classical and quantum search procedures can be likened to

This article 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 requireda priorito 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.This article 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 requireda priorito 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.

arXiv:2108.12448IEEE Transactions on ComputersFeb 9, 202114 citations

Quantum Searching & Classical Analogues

Lov K. Grover

APSMar 1, 20020 citations

Applications of Harmonic Analysis in Quantum Computing.

Bohan Zhang

The quantum Fourier transformation has been demonstrated to be a useful tool in dealing with quantummechanical problems. This paper discusses how quantum Fourier transformation is applied in finding the period of functions within Shor’s algorithm, allowing the algorithm to be much more efficient in factorizing large integers than classic algorithms. This paper also discusses how Grover’s algorithm uses the concept of harmonic process, where amplitude amplification is likened to harmonic oscillation for improving the efficiency of searching unsorted data base. The paper further explores the application of harmonic analysis in quantum error correction, particularly in stabilizer codes. The paper also introduces wavelet analysis as an alternative approach for detecting and correcting localized quantum errors. Finally, the paper extends the discussion into the potential future directions of harmonic analysis in quantum computing, such as extending Fourier transformation to non-abelian groups and using spherical harmonics in quantum algorithms which may optimize current quantum algorithms and solve currently unsolved quantum questions.The quantum Fourier transformation has been demonstrated to be a useful tool in dealing with quantummechanical problems. This paper discusses how quantum Fourier transformation is applied in finding the period of functions within Shor’s algorithm, allowing the algorithm to be much more efficient in factorizing large integers than classic algorithms. This paper also discusses how Grover’s algorithm uses the concept of harmonic process, where amplitude amplification is likened to harmonic oscillation for improving the efficiency of searching unsorted data base. The paper further explores the application of harmonic analysis in quantum error correction, particularly in stabilizer codes. The paper also introduces wavelet analysis as an alternative approach for detecting and correcting localized quantum errors. Finally, the paper extends the discussion into the potential future directions of harmonic analysis in quantum computing, such as extending Fourier transformation to non-abelian groups and using spherical harmonics in quantum algorithms which may optimize current quantum algorithms and solve currently unsolved quantum questions.

Science and Technology of Engineering Chemistry and Environmental ProtectionNov 12, 20240 citations

Simulation-Based Comparison of Classical Linear Search and Grover’s Quantum Algorithm

Tsvetelina Stefanova, Tsvetozar Stefanov Georgiev

Lecture notes in networks and systemsJan 1, 20260 citations

A review on quantum search algorithms

Pulak Ranjan Giri, V. E. Korepin

arXiv:1602.02730Quantum Information ProcessingNov 13, 201782 citations

Applications of Harmonic Analysis in Quantum Computing

Bohan Zhang

The quantum Fourier transformation has been demonstrated to be a useful tool in dealing with quantum-mechanical problems. This paper discusses how quantum Fourier transformation is applied in finding the period of functions within Shor’s algorithm, allowing the algorithm to be much more efficient in factorizing large integers than classic algorithms. This paper also discusses how Grover’s algorithm uses the concept of harmonic process, where amplitude amplification is likened to harmonic oscillation for improving the efficiency of searching unsorted data base. The paper further explores the application of harmonic analysis in quantum error correction, particularly in stabilizer codes. The paper also introduces wavelet analysis as an alternative approach for detecting and correcting localized quantum errors. Finally, the paper extends the discussion into the potential future directions of harmonic analysis in quantum computing, such as extending Fourier transformation to non-abelian groups and using spherical harmonics in quantum algorithms which may optimize current quantum algorithms and solve currently unsolved quantum questions.The quantum Fourier transformation has been demonstrated to be a useful tool in dealing with quantum-mechanical problems. This paper discusses how quantum Fourier transformation is applied in finding the period of functions within Shor’s algorithm, allowing the algorithm to be much more efficient in factorizing large integers than classic algorithms. This paper also discusses how Grover’s algorithm uses the concept of harmonic process, where amplitude amplification is likened to harmonic oscillation for improving the efficiency of searching unsorted data base. The paper further explores the application of harmonic analysis in quantum error correction, particularly in stabilizer codes. The paper also introduces wavelet analysis as an alternative approach for detecting and correcting localized quantum errors. Finally, the paper extends the discussion into the potential future directions of harmonic analysis in quantum computing, such as extending Fourier transformation to non-abelian groups and using spherical harmonics in quantum algorithms which may optimize current quantum algorithms and solve currently unsolved quantum questions.

Science and Technology of Engineering Chemistry and Environmental ProtectionJun 26, 20250 citations

w

-dimensional search space, where

w

is the number of weights of the neural network. To know the number of iterations requireda priorito 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.