Google’s AlphaGo represents the impressive performance of deep learning and the backbone of deep learning is the workhorse of highly versatile neural networks. Each network is made up of layers of interconnected neur...Google’s AlphaGo represents the impressive performance of deep learning and the backbone of deep learning is the workhorse of highly versatile neural networks. Each network is made up of layers of interconnected neurons and the nonlinear activation function inside each neuron is one of the key factors that account for the unprecedented achievement of deep learning. Learning how to create quantum neural networks has been a long time pursuit since 1990’s from many researchers, unfortunately without much success. The main challenge is to know how to design a nonlinear activation function inside the quantum neuron, because the laws in quantum mechanics require the operations on quantum neurons be unitary and linear. A recent discovery uses a special quantum circuit technique called repeat-until-success to make a nonlinear activation function inside a quantum neuron, which is the hard part of creating this neuron. However, the activation function used in that work is based on the periodic tangent function. Because of this periodicity, the input to this function has to be restricted to the range of [0, π/2), which is a serious constraint for its applications in real world problems. The function’s periodicity also makes its neurons not suited for being trained with gradient descent as its derivatives oscillate. The purpose of our study is to propose a new nonlinear activation function that is not periodic so it can take any real numbers and its neurons can be trained with efficient gradient descent. Our quantum neuron offers the full benefit as a quantum entity to support superposition, entanglement, interference, while also enjoys the full benefit as a classical entity to take any real numbers as its input and can be trained with gradient descent. The performance of the quantum neurons with our new activation function is analyzed on IBM’s 5Q quantum computer and IBM’s quantum simulator.展开更多
A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is...A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which （1） is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects： convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.展开更多
To enhance the approximation ability of neural networks, by introducing quantum rotation gates to the traditional BP networks, a novel quantum-inspired neural network model is proposed in this paper. In our model, the...To enhance the approximation ability of neural networks, by introducing quantum rotation gates to the traditional BP networks, a novel quantum-inspired neural network model is proposed in this paper. In our model, the hidden layer consists of quantum neurons. Each quantum neuron carries a group of quantum rotation gates which are used to update the quantum weights. Both input and output layer are composed of the traditional neurons. By employing the back propagation algorithm, the training algorithms are designed. Simulation-based experiments using two application examples of pattern recognition and function approximation, respectively, illustrate the availability of the proposed model.展开更多
To enhance the approximation and generalization ability of artificial neural network (ANN) by employing the principles of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is...To enhance the approximation and generalization ability of artificial neural network (ANN) by employing the principles of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-not gate after being rotated by the quantum rotation gates, control the target qubit for reverse. The model output is described by the probability amplitude of state in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the sequence input-based quantum-inspired neurons to the hidden layer and the classical neurons to the output layer, and a learning algorithm is derived by employing the Levenberg-Marquardt algorithm. Simulation results of benchmark problem show that, under a certain condition, the QNNSI is obviously superior to the ANN.展开更多
A general definition of quantum coherence is developed from analysis of superposition, entanglement, chemical bonding behavior, and basic phenomena of classical mechanics. Various properties of atoms can be better exp...A general definition of quantum coherence is developed from analysis of superposition, entanglement, chemical bonding behavior, and basic phenomena of classical mechanics. Various properties of atoms can be better explained if these particles are matter waves that embody a spectrum ranging from relatively coherent to decoherent states. It is demonstrated that quantum coherence so defined can comprehensively explain signal transmission in neurons and dynamics of the brain’s emergent electric field, including potential support for the claim that conscious volition is to some degree real rather than an illusion. Recent research in a physiological context suggests that electromagnetic radiation interacts with molecular structure to comprise integrated energy fields. A mechanism is proposed by which quantum coherence as accelerating electric currents in neurons may result in a broadened spectrum of electromagnetic radiation capable of interacting with molecular complexes in the brain and perhaps elsewhere in an organism to influence vibrational and structural properties. Research should investigate whether a consequent energy field is the basic perceptual substrate, with at least some additive electromagnetic wavelengths of this field involved in generating image percepts insofar as they arise from the body, and electromagnetic vibrations the signature of a more diverse phenomenon by which somewhat nondimensional features of perception such as sound, touch, taste, smell, interoceptive sensations, etc. partially arise. If examination of the brain reveals this organ to be composed of a coherence field, structured at least in part by broadened spectrums of EM radiation interacting with molecular components, this has major implications for furthering our model of the matter/mind interface and possibly physical reality in total.展开更多
文摘Google’s AlphaGo represents the impressive performance of deep learning and the backbone of deep learning is the workhorse of highly versatile neural networks. Each network is made up of layers of interconnected neurons and the nonlinear activation function inside each neuron is one of the key factors that account for the unprecedented achievement of deep learning. Learning how to create quantum neural networks has been a long time pursuit since 1990’s from many researchers, unfortunately without much success. The main challenge is to know how to design a nonlinear activation function inside the quantum neuron, because the laws in quantum mechanics require the operations on quantum neurons be unitary and linear. A recent discovery uses a special quantum circuit technique called repeat-until-success to make a nonlinear activation function inside a quantum neuron, which is the hard part of creating this neuron. However, the activation function used in that work is based on the periodic tangent function. Because of this periodicity, the input to this function has to be restricted to the range of [0, π/2), which is a serious constraint for its applications in real world problems. The function’s periodicity also makes its neurons not suited for being trained with gradient descent as its derivatives oscillate. The purpose of our study is to propose a new nonlinear activation function that is not periodic so it can take any real numbers and its neurons can be trained with efficient gradient descent. Our quantum neuron offers the full benefit as a quantum entity to support superposition, entanglement, interference, while also enjoys the full benefit as a classical entity to take any real numbers as its input and can be trained with gradient descent. The performance of the quantum neurons with our new activation function is analyzed on IBM’s 5Q quantum computer and IBM’s quantum simulator.
基金the National Natural Science Foundation of China (50138010)
文摘A quantum BP neural networks model with learning algorithm is proposed. First, based on the universality of single qubit rotation gate and two-qubit controlled-NOT gate, a quantum neuron model is constructed, which is composed of input, phase rotation, aggregation, reversal rotation and output. In this model, the input is described by qubits, and the output is given by the probability of the state in which （1） is observed. The phase rotation and the reversal rotation are performed by the universal quantum gates. Secondly, the quantum BP neural networks model is constructed, in which the output layer and the hide layer are quantum neurons. With the application of the gradient descent algorithm, a learning algorithm of the model is proposed, and the continuity of the model is proved. It is shown that this model and algorithm are superior to the conventional BP networks in three aspects： convergence speed, convergence rate and robustness, by two application examples of pattern recognition and function approximation.
文摘To enhance the approximation ability of neural networks, by introducing quantum rotation gates to the traditional BP networks, a novel quantum-inspired neural network model is proposed in this paper. In our model, the hidden layer consists of quantum neurons. Each quantum neuron carries a group of quantum rotation gates which are used to update the quantum weights. Both input and output layer are composed of the traditional neurons. By employing the back propagation algorithm, the training algorithms are designed. Simulation-based experiments using two application examples of pattern recognition and function approximation, respectively, illustrate the availability of the proposed model.
文摘To enhance the approximation and generalization ability of artificial neural network (ANN) by employing the principles of quantum rotation gate and controlled-not gate, a quantum-inspired neuron with sequence input is proposed. In the proposed model, the discrete sequence input is represented by the qubits, which, as the control qubits of the controlled-not gate after being rotated by the quantum rotation gates, control the target qubit for reverse. The model output is described by the probability amplitude of state in the target qubit. Then a quantum-inspired neural network with sequence input (QNNSI) is designed by employing the sequence input-based quantum-inspired neurons to the hidden layer and the classical neurons to the output layer, and a learning algorithm is derived by employing the Levenberg-Marquardt algorithm. Simulation results of benchmark problem show that, under a certain condition, the QNNSI is obviously superior to the ANN.
文摘A general definition of quantum coherence is developed from analysis of superposition, entanglement, chemical bonding behavior, and basic phenomena of classical mechanics. Various properties of atoms can be better explained if these particles are matter waves that embody a spectrum ranging from relatively coherent to decoherent states. It is demonstrated that quantum coherence so defined can comprehensively explain signal transmission in neurons and dynamics of the brain’s emergent electric field, including potential support for the claim that conscious volition is to some degree real rather than an illusion. Recent research in a physiological context suggests that electromagnetic radiation interacts with molecular structure to comprise integrated energy fields. A mechanism is proposed by which quantum coherence as accelerating electric currents in neurons may result in a broadened spectrum of electromagnetic radiation capable of interacting with molecular complexes in the brain and perhaps elsewhere in an organism to influence vibrational and structural properties. Research should investigate whether a consequent energy field is the basic perceptual substrate, with at least some additive electromagnetic wavelengths of this field involved in generating image percepts insofar as they arise from the body, and electromagnetic vibrations the signature of a more diverse phenomenon by which somewhat nondimensional features of perception such as sound, touch, taste, smell, interoceptive sensations, etc. partially arise. If examination of the brain reveals this organ to be composed of a coherence field, structured at least in part by broadened spectrums of EM radiation interacting with molecular components, this has major implications for furthering our model of the matter/mind interface and possibly physical reality in total.
