Motivated by the fact that biological neuron change its content in time and the dynamics of a neuron with internal state can mimic neuronal behaviour such as chaos and bifurcation, neural networks composed of classical artificial neuron models that consider internal information modification after their operation, were introduced in the 90’s. Here we study a quantum version of these networks. We introduced the quantum perceptron with internal memory state that can be changed during the neuron execution. For that, we use the quantum perceptron which reproduces the step function of the inner product between input and weights and extend it with a memory that can be updated during its own execution.
Motivated by the fact that biological neuron change its content in time and the dynamics of a neuron with internal state can mimic neuronal behaviour such as chaos and bifurcation, neural networks composed of classical artificial neuron models that consider internal information modification after their operation, were introduced in the 90’s. Here we study a quantum version of these networks. We introduced the quantum perceptron with internal memory state that can be changed during the neuron execution. For that, we use the quantum perceptron which reproduces the step function of the inner product between input and weights and extend it with a memory that can be updated during its own execution.
This paper investigates the potential of quantum neural networks (QNNs) enhanced by non-Markovian dynamics. Traditional Markovian QNNs suffer from limitations in capturing long-range dependencies, a crucial aspect in complex data processing. We propose a novel QNN architecture that incorporates quantum memory and entanglement to facilitate non-Markovian information processing. This approach allows the network to retain and utilize the entire past history of the input, fundamentally altering the dynamics of information flow. Through theoretical analysis and mathematical formulations, we demonstrate how this architecture can significantly improve the network's ability to learn and represent complex patterns, particularly those exhibiting long-range correlations. Specifically, we introduce a modified update rule leveraging the concept of quantum memory and entanglement, expressed as: $ \Delta w_{ij} = \alpha \cdot E[\rho(t)|x_1, x_2, ..., x_K] \cdot \langle \psi_i | \rho(t) | \psi_j \rangle - (1 - \alpha) \cdot w_{ij}$ Where: * $ \Delta w_{ij}$ is the change in the synaptic weight between neurons *i* and *j*. * α is the learning rate. * E[ρ(t)∣x1,x2,...,xK] represents the expected state of the quantum memory at time *t*, given the entire input sequence x1,x2,...,xK. * ρ(t) is the density matrix representing the quantum state at time *t*. * ⟨ψi∣ρ(t)∣ψj⟩ is the inner product between the quantum states ψi and ψj within the density matrix ρ(t). * wij is the current synaptic weight between neurons *i* and *j*. The core of our innovation lies in the utilization of quantum memory, modeled as a quantum state ρ(t), which retains information about the entire past sequence. The entanglement between neurons further enables correlated updates, bypassing the limitations of Markovian models that only consider immediate dependencies. We explore the impact of varying the strength of entanglement and the capacity of the quantum memory on the network's performance using mathematical models. The results suggest a significant improvement in accuracy and convergence speed compared to standard Markovian QNNs when dealing with datasets exhibiting long-range dependencies. Further investigation into the scalability and practical implementation of this architecture is warranted.
Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.
Abstract Artificial neural networks are the heart of machine learning algorithms and artificial intelligence. Historically, the simplest implementation of an artificial neuron traces back to the classical Rosenblatt’s “perceptron”, but its long term practical applications may be hindered by the fast scaling up of computational complexity, especially relevant for the training of multilayered perceptron networks. Here we introduce a quantum information-based algorithm implementing the quantum computer version of a binary-valued perceptron, which shows exponential advantage in storage resources over alternative realizations. We experimentally test a few qubits version of this model on an actual small-scale quantum processor, which gives answers consistent with the expected results. We show that this quantum model of a perceptron can be trained in a hybrid quantum-classical scheme employing a modified version of the perceptron update rule and used as an elementary nonlinear classifier of simple patterns, as a first step towards practical quantum neural networks efficiently implemented on near-term quantum processing hardware.
An artificial neural network, consisting of many neurons in different layers, is an important method to simulate the human brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is the inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of a quantum neural network in which the weights between neurons are all quantum states. We also construct a quantum circuit to realize this quantum neural network model. A learning algorithm is proposed meanwhile. We show the validity of the learning algorithm theoretically and demonstrate the potential of the quantum neural network numerically.
This paper proposes a novel approach to biological information processing by leveraging the principles of quantum memory. The core idea is to mimic the memory function of biological neurons using quantum memory models, thereby accelerating and enhancing the efficiency of biological information handling. This research explores the potential of quantum memory to emulate key aspects of neuronal operation, specifically focusing on the rapid processing and storage of biological information. The theoretical framework developed herein outlines a computational model based on quantum memory interactions, demonstrating a pathway towards achieving significant improvements in biological information processing speed and capacity. This work presents a fundamental investigation into the intersection of quantum mechanics and neuroscience, offering a new perspective on the mechanisms underlying biological memory and potentially paving the way for advanced bio-computing architectures. The presented model utilizes the following key equations to illustrate the core concepts: (Δs) = (H(s) * ∇s) + (G(s, s') * s') where: Δs represents the change in state of the quantum memory. H(s) is the Hamiltonian operator describing the quantum memory's energy levels. ∇s is the gradient operator, representing the influence of external stimuli. G(s, s') is the coupling strength between neighboring quantum memories. s and s' represent the states of the quantum memories. Further equations exploring the dynamics include: (ds/dt) = (H(s) * s) - (∑G(s, s') * s') and the state update rule: s(t+Δt) = U(Δt) * s(t) where: U(Δt) is the time evolution operator, describing the quantum dynamics over a small time interval Δt. This research contributes to the nascent field of quantum biology and provides a foundational model for future investigations into quantum-enhanced biological systems. ---
A Perceptron is a fundamental building block of a neural network. The flexibility and scalability of perceptron make it ubiquitous in building intelligent systems. Studies have shown the efficacy of a single neuron in making intelligent decisions. Here, we examined and compared two perceptron’s with distinct mechanisms, and developed a quantum version of one of those perceptron’s. As a part of this modelling, we implemented the quantum circuit for an artificial perception, generated a dataset, and simulated the training. Through these experiments, we show that there is an exponential growth advantage and test different qubit versions. Our findings show that this quantum model of an individual perceptron can be used as a pattern classifier. For the second type of model, we provide an understanding to design and simulate a spike-dependent quantum perceptron. Our code is available at https://github.com/ashutosh1919/quantum-perceptron