Neural network (NN) implementation using the general scheme of many-valued (MV) quantum computing (QC) is presented in this paper. The proposed method uses the many-valued orthonormal computational basis states to implement such computations. Physical implementation of NNQC is performed by controlling the potential to yield specific wavefunction as a result of solving Shrodinger's equation that governs the dynamics of QC.
Neural network (NN) implementation using the general scheme of many-valued (MV) quantum computing (QC) is presented in this paper. The proposed method uses the many-valued orthonormal computational basis states to implement such computations. Physical implementation of NNQC is performed by controlling the potential to yield specific wavefunction as a result of solving Shrodinger's equation that governs the dynamics of QC.
Abstract Artificial neural networks have been proposed as potential algorithms that could benefit from being implemented and run on quantum computers. In particular, they hold promise to greatly enhance Artificial Intelligence tasks, such as image elaboration or pattern recognition. The elementary building block of a neural network is an artificial neuron, i.e. a computational unit performing simple mathematical operations on a set of data in the form of an input vector. Here we show how the design for the implementation of a previously introduced quantum artificial neuron [npj Quant. Inf. 5, 26], which fully exploits the use of superposition states to encode binary valued input data, can be further generalized to accept continuous- instead of discrete-valued input vectors, without increasing the number of qubits. This further step is crucial to allow for a direct application of gradient descent based learning procedures, which would not be compatible with binary-valued data encoding.
The goal of the artificial neural network is to create powerful artificial problem solving systems. The field of quantum computation applies ideas from quantum mechanics to the study of computation and has made interesting progress. Quantum Neural Network (QNN) is one of the new paradigms built upon the combination of classical neural computation and quantum computation. It is argued that the study of QNN may explain the brain functionality in a better way and create new systems for information processing including solving some classically intractable problems. In this paper we have given an introductory representation of quantum artificial neural network to show how it can be modelled on the basis of double-slit experiment. Also an attempt is made to show the quantum mechanical representation of a classical neuron to implement Hadamard transformation.
Artificial neural networks (ANNs) and quantum computing (QC) have both received rapidly increasing interest in recent years for several reasons. Their roles in the mechanics community remain a subject of ongoing debate and research. ANNs have successfully been employed on problems previously considered unsolvable ( Silver et al. 2016 ), as well as on practical and illustrative problems especially in the image recognition domain ( Szegedy et al. 2013 , among others). The most straightforward way to interpret the behavior of ANNs is focusing on their ability to approximate any continuous function to arbitrary precision ( Kreinovich 1991 ). The adjustment to a given function happens automatically except for hyperparameters, such as the number of hidden layers or the learning rate, which remain constant during training. This makes them a perfect tool for reducing computational cost in otherwise time-consuming simulations. Quantum computing on the other hand has received some publicity in 2018 mainly because of a paper published by Google Quantum A.I. Lab scientists defining quantum supremacy ( Boixo & Isakov 2018 ), where it is shown that a fully working universal quantum computer with only 50 qubits will outperform any near-term realizable classical supercomputer on certain tasks. This publication was followed up by Google revealing Bristlecone ( Kelly 2018 ), a quantum processor consisting of 72 qubits. While many interesting quantum algorithms have proven to run polynomially or even exponentially faster than their classical analogons ( Montanaro 2016 ), these results only hold true for a decoherence-free machine. Therefore, to actually achieve quantum supremacy , quantum error correction schemes need to be implemented, requiring several physical qubits to make up a single logical qubit suitable for computation.
Artificial neural networks (ANN) proved to be efficient in solving many problems for big data analytics using machine learning. The complex and non-linear features of the input data can be learned and generalized by ANN. In the big data era, enormous amounts of data arrive from multiple sources. A stage is expected to be reached where even supercomputers are likely inundated with the big data. Training an ANN in such a situation is a challenging task due to the size and dimension of the big data. Also, a large number of parameters are to be used and optimized in the network to learn the patterns and analyze such data. Quantum computing is emerging as a field that provides a solution to this problem as a quantum computer can represent data differently using qubits. Qubits on quantum computers can be used to detect the hidden patterns in data that are difficult for a classical computer to find. Hence, there exists a huge scope for application in the area of artificial neural networks. In this work, we primarily focused on training an artificial neural network using qubits as artificial neurons. The simulation results show that our quantum computing approach for ANN (QC ANN) is efficient when compared to classical ANN. The model with qubits as artificial neurons can learn the features of data using fewer parameters for a binary classification task. We demonstrate our experiment using a quantum simulator and optimization of the quantum parameters used in QC ANN is carried out on a classical computer.
The field of quantum chemistry has long been defined by the central computational challenge of the quantum many-body fermionic system problem, main the electronic Schrödinger equation. This exponential scaling makes it computationally intractable to solve, the exact governing electronic Schrödinger equation. Approximation methods have been developed, ranging from the widely used Density Functional Theory (DFT) to Coupled Cluster (CC) theory. While powerful, these conventional approaches often involve controlled truncations which caused a trade-off between accuracy, leaving many systems—particularly those with strong electron correlation—beyond the reach of ab initio simulation. Furthermore, the famous fermionic sign oscillation problem is particularly severe in stochastic methods like Quantum Monte Carlo (QMC). 1 Traditional Ansätze are also frequently engineered specifically for particular systems, which results in a fragmentation of results and fundamentally limits the transferability. Recent research demonstrates that with carefully designed architectures, ANNs can not only represent ground states of model systems with high precision but also tackle the sign problem, offering a promising path forward for strongly correlated electronic structure calculations.2,3 This review charts the paradigm shift driven by Neural Network Quantum States (NNQS), which leverage the representational power of deep learning to overcome these barriers. We detail the architectural evolution from Restricted Boltzmann Machines to autoregressive models like RNNs and Transformers, which enable exact, uncorrelated sampling and bypass critical bottlenecks.2,4,5Furthermore, we explore the geometric foundation of high-efficiency optimization via the neural networks, which decouples optimization cost from model complexity.6 The frontier of the field is marked by the integration of operator learning and hybrid quantum-classical frameworks, such as Reinforcement Learning for contracted quantum eigen-solvers and Quantum-Enhanced Neural Networks, which leverage quantum processors to enhance expressivity for hardware-efficient Ansätze.7,8 By framing the problem through the lens of computational resource allocation—specifically, trading exponential memory demands for polynomialcomplexity optimization and sampling—this review elucidates how recent advances at the intersection of artificial neural networks and quantum computing have evolved. The emergence of those methods not merely progress into a powerful simulation-tools, but also a hybrid computational interface.9 This convergence offers a versatile and systematically improvable framework for potentially addressing some of the most challenging problems in quantum physics and chemistry.
The field of quantum chemistry has long been defined by the central computational challenge of the quantum many-body fermionic system problem, main the electronic Schrödinger equation. This exponential scaling makes it computationally intractable to solve, the exact governing electronic Schrödinger equation. Approximation methods have been developed, ranging from the widely used Density Functional Theory (DFT) to Coupled Cluster (CC) theory. While powerful, these conventional approaches often involve controlled truncations which caused a trade-off between accuracy, leaving many systems—particularly those with strong electron correlation—beyond the reach of ab initio simulation. Furthermore, the famous fermionic sign oscillation problem is particularly severe in stochastic methods like Quantum Monte Carlo (QMC). 1 Traditional Ansätze are also frequently engineered specifically for particular systems, which results in a fragmentation of results and fundamentally limits the transferability. Recent research demonstrates that with carefully designed architectures, ANNs can not only represent ground states of model systems with high precision but also tackle the sign problem, offering a promising path forward for strongly correlated electronic structure calculations.2,3 This review charts the paradigm shift driven by Neural Network Quantum States (NNQS), which leverage the representational power of deep learning to overcome these barriers. We detail the architectural evolution from Restricted Boltzmann Machines to autoregressive models like RNNs and Transformers, which enable exact, uncorrelated sampling and bypass critical bottlenecks.2,4,5Furthermore, we explore the geometric foundation of high-efficiency optimization via the neural networks, which decouples optimization cost from model complexity.6 The frontier of the field is marked by the integration of operator learning and hybrid quantum-classical frameworks, such as Reinforcement Learning for contracted quantum eigen-solvers and Quantum-Enhanced Neural Networks, which leverage quantum processors to enhance expressivity for hardware-efficient Ansätze.7,8 By framing the problem through the lens of computational resource allocation—specifically, trading exponential memory demands for polynomialcomplexity optimization and sampling—this review elucidates how recent advances at the intersection of artificial neural networks and quantum computing have evolved. The emergence of those methods not merely progress into a powerful simulation-tools, but also a hybrid computational interface.9 This convergence offers a versatile and systematically improvable framework for potentially addressing some of the most challenging problems in quantum physics and chemistry.