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arXiv:quant-ph/0202016

Neural Networks with c-NOT Gated Nodes

Fariel Shafee

Published Feb 2, 2002• 9 citations
arXivHTMLPDF

Abstract

We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural lattice, it appears that the state of the system behaves in ways reflecting both the strengths of coupling between neurons as well as initial conditions. We find that depending whether there is a threshold for emission from excited to ground state, the system shows either aperiodic oscillations or coherent ones with periodicity depending on the strength of coupling.

DOI
10.48550/arxiv.quant-ph/0202016

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We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural lattice, it appears that the state of the system behaves in ways reflecting both the strengths of coupling between neurons as well as initial conditions. We find that depending whether there is a threshold for emission from excited to ground state, the system shows either aperiodic oscillations or coherent ones with periodicity depending on the strength of coupling.
We present some results from simulation of a network of nodes connected by c-NOT gates with nearest neighbors. Though initially we begin with pure states of varying boundary conditions, the updating with time quickly involves a complicated entanglement involving all or most nodes. As a normal c-NOT gate, though unitary for a single pair of nodes, seems to be not so when used in a network in a naive way, we use a manifestly unitary form of the transition matrix with c?-NOT gates, which invert the phase as well as flipping the qubit. This leads to complete entanglement of the net, but with variable coefficients for the different components of the superposition. It is interesting to note that by a simple logical back projection the original input state can be recovered in most cases. We also prove that it is not possible for a sequence of unitary operators working on a net to make it move from an aperiodic regime to a periodic one, unlike some classical cases where phase-locking happens in course of evolution. However, we show that it is possible to introduce by hand periodic orbits to sets of initial states, which may be useful in forming dynamic pattern recognition systems.
The approximation ability of neural networks plays an important role to the result when one uses neural networks to resolve problems.Unfortunately there is no ideal way to construct proper networks with strong approximation ability.A novel construction approach based on the multi-qubits controller-not gates is proposed for neural networks model in this paper.The proposed model consists of three layers where the hidden nodes are the quantum neurons and the output nodes are the common neurons.The quantum neuron consists of the quantum rotation gates and the multi-qubits controllednot gates.The overall memory of input sequences is captured from information feedback of target qubit from output to input in the multi-qubits controlled-not gate.The output of quantum neuron is obtained from the controlled relationship of the multi-qubits controlled-not gate.The L-M learning algorithms are designed in detail based on the basic principles of quantum computation.The features of input sequences can be effectively obtained in two ways of breadth and depth.The experimental results of solitaire forecast show that,when the number of input nodes is close to the length of sequences,the training set recognition rate of the proposed model increases about 8% than the common neural networks,which reveals the effectiveness of the quantum computation for enhancing the approximation capability of the common neural networks.
This paper introduces the Quantum Mechanics Simulation of Neurons Model (QMNN), a novel approach to simulating neuronal behavior based on fundamental principles of quantum mechanics. Traditional artificial neural networks (ANNs) often struggle to accurately replicate the complex dynamics observed in biological neurons due to their reliance on classical computational methods. QMNN leverages concepts such as superposition and entanglement, key features of quantum mechanics, to represent neuronal states and interactions. The model employs a discrete quantum system, where neuronal activity is represented by quantum states, allowing for inherent parallelism and potentially capturing phenomena currently inaccessible to classical neural simulations. This work details the core concepts of QMNN, outlining its mathematical formulation, key components, and potential advantages over conventional ANN approaches. We present a simplified model of a single neuron utilizing a quantum bit (qubit) to represent its state. The model's equations reflect the Schrödinger equation and the evolution of quantum states under influence of external stimuli. The simulation explores scenarios demonstrating the potential for increased computational efficiency and the ability to model phenomena like quantum coherence within neuronal networks. Further research will focus on scaling the model to multi-neuron networks and investigating the model's applicability to various neurological conditions.
Quantum reservoir computing is a promising approach for quantum neural networks, capable of solving hard learning tasks on both classical and quantum input data. However, current approaches with qubits suffer from limited connectivity. We propose an implementation for quantum reservoir that obtains a large number of densely connected neurons by using parametrically coupled quantum oscillators instead of physically coupled qubits. We analyse a specific hardware implementation based on superconducting circuits: with just two coupled quantum oscillators, we create a quantum reservoir comprising up to 81 neurons. We obtain state-of-the-art accuracy of 99 % on benchmark tasks that otherwise require at least 24 classical oscillators to be solved. Our results give the coupling and dissipation requirements in the system and show how they affect the performance of the quantum reservoir. Beyond quantum reservoir computing, the use of parametrically coupled bosonic modes holds promise for realizing large quantum neural network architectures, with billions of neurons implemented with only 10 coupled quantum oscillators.
Hardware neurons incorporating built-in memory components are critical technologies for implementing large scale neural networks that exhibit adaptive-itinerant behavior and produce biological-inspired spiking patterns that match neuroscience known operations (1). Moreover, neurons capable of full quantum information processing through their qubit states and quantum trajectory provides capability for hybrid quantum-classical operations through the level of coherence/entanglement and non-Markovianity (2,3). These attributes further contribute to solving complex quantum mechanical problems by providing a rich and diverse group for expressing quantum neural states. Upgrading these hardware neurons now with optical spin qubits excitable with pulsed laser excitation in the near infrared and designed from negatively charged silicon vacancies in semiconductor silicon carbide (4) and Neodymium rare earth ions in the superconducting Niobium/Niobium oxide film (5) that form the memory provides access to the unique spin Hamiltonian that considers electronic and nuclear interactions. In this manuscript, we experimentally measure opto-electronic quantum-classical neurons integrated with a optical spin qubit and examine how tailored neuronal spiking sequences drive the photoluminescence oscillations and modulate the quantum spin transitions. We derive a quantum model for the system that considers the interaction between the neuron and optical qubit spin and perform calculations to project how quantum computing operations are expandable across the state space in the quantum-classical neuron and spin qubit system. For example, the resulting impact on the neuron quantum states where the strength is adjustable due to dynamical memory changes. These results are critical for realizing hardware neurons with quantum optical capabilities and inspired by the existence in biology of biophotons.
It has been known that a variety of optimization problems can be solved with a neural network, and that a quantum computer executes real parallel computation. A quantum neural network has been proposed to incorporate quantum dynamics into a neural network. In this study, we test the possibility of actual implementation of a quantum neural network with a nuclear spin as a qubit. First, we introduce the relationship between a spin and a neuron, then describe the adiabatic Hamiltonian evolution applied for the state change. Next, we describe a real spin quantum system and show the simulation results. A proposed nuclear spin system behaves as a neuron with inhibitory interactions, as expected in analogy to a Hopfield network.