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arXiv:2205.01514 · Electronic Proceedings in Theoretical Computer Science

Tunable Quantum Neural Networks in the QPAC-Learning Framework

Viet Pham Ngoc, David Tuckey, Herbert Wiklicky

Published Nov 14, 2023• 0 citations
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Abstract

In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By tuning the set of controls these circuits are able to approximate any Boolean functions. This architecture is particularly suited to be used in the QPAC-learning framework as it can handle the superposition produced by the oracle. In order to tune the network so that it can approximate a target concept, we have devised and implemented an algorithm based on amplitude amplification. The numerical results show that this approach can efficiently learn concepts from a simple class.

DOI
10.4204/eptcs.394.13

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In this paper, we investigate the performances of tunable quantum neural networks in the Quantum Probably Approximately Correct (QPAC) learning framework. Tunable neural networks are quantum circuits made of multi-controlled X gates. By tuning the set of controls these circuits are able to approximate any Boolean functions. This architecture is particularly suited to be used in the QPAC-learning framework as it can handle the superposition produced by the oracle. In order to tune the network so that it can approximate a target concept, we have devised and implemented an algorithm based on amplitude amplification. The numerical results show that this approach can efficiently learn concepts from a simple class.
In this paper we propose a new approach to quantum neural networks. Our multi-layer architecture avoids the use of measurements that usually emulate the non-linear activation functions which are characteristic of the classical neural networks. Despite this, our proposed architecture is still able to learn any Boolean function. This ability arises from the correspondence that exists between a Boolean function and a particular quantum circuit made out of multi-controlled NOT gates. This correspondence is built via a polynomial representation of the function called the algebraic normal form. We use this construction to introduce the idea of a generic quantum circuit whose gates can be tuned to learn any Boolean functions. In order to perform the learning task, we have devised an algorithm that leverages the absence of measurements. When presented with a superposition of all the binary inputs of length nnn, the network can learn the target function in at most n+1n+1n+1 updates.
In this paper, we study the tunable quantum neural network architecture in the quantum exact learning framework with access to a uniform quantum example oracle. We present an approach that uses amplitude amplification to correctly tune the network to the target concept. We applied our approach to the class of positive kkk-juntas and found that O(n22k)O(n^22^k)O(n22k) quantum examples are sufficient with experimental results seemingly showing that a tighter upper bound is possible.
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.
Quantum machine learning has established as an interdisciplinary field to overcome limitations of classical machine learning and neural networks. This is a field of research which can prove that quantum computers are able to solve problems with complex correlations between inputs that can be hard for classical computers. This suggests that learning models made on quantum computers may be more powerful for applications, potentially faster computation and better generalization on less data. The objective of this paper is to investigate how training of quantum neural network (QNNs) can be done using quantum optimization algorithms for improving the performance and time complexity of QNNs. A classical neural network can be partially quantized to create a hybrid quantum-classical neural network which is used mainly in classification and image recognition. In this paper, a QNN structure is made where a variational parameterized circuit is incorporated as an input layer named as Variational Quantum Neural Network (VQNNs). We encode the cost function of QNNs onto relative phases of a superposition state in the Hilbert space of the network parameters. The parameters are tuned with an iterative quantum approximate optimisation (QAOA) mixer and problem hamiltonians. VQNNs is experimented with MNIST digit recognition (less complex) and crack image classification datasets (more complex) which converges the computation in lesser time than QNN with decent training accuracy.
This paper explores the integration of adaptive quantum computing principles into neural network architecture optimization. Traditional neural network training relies heavily on manual parameter tuning, often requiring extensive experimentation. We propose a novel framework, "Quantum-Adaptive Optimization," that dynamically adjusts network parameters based on quantum computation's inherent parallelism and probabilistic nature. This framework aims to automate the optimization process, enhancing model performance and efficiency through targeted parameter adjustments. The core mechanism leverages quantum-inspired algorithms to guide the adjustment of neural network weights and biases, leading to improved generalization and robustness. The paper details the framework's design, explores its implementation with a simplified quantum simulation, and analyzes its potential impact on various machine learning tasks. The results demonstrate a significant improvement in model accuracy and reduced training time compared to conventional methods.
Quantum neural networks (QNN) have been proposed as a promising architecture for quantum machine learning. There exist a number of different quantum circuit designs being branded as QNNs, however no clear candidate has presented itself as more suitable than the others. Rather, the search for a ``quantum perceptron" -- the fundamental building block of a QNN -- is still underway. One candidate is quantum perceptrons designed to emulate the nonlinear activation functions of classical perceptrons. Such sigmoid quantum perceptrons (SQPs) inherit the universal approximation property that guarantees that classical neural networks can approximate any function. However, this does not guarantee that QNNs built from SQPs will have any quantum advantage over their classical counterparts. Here we critically investigate both the capabilities and performance of SQP networks by computing their effective dimension and effective capacity, as well as examining their performance on real learning problems. The results are compared to those obtained for other candidate networks which lack activation functions. It is found that simpler, and apparently easier-to-implement parametric quantum circuits actually perform better than SQPs. This indicates that the universal approximation theorem, which a cornerstone of the theory of classical neural networks, is not a relevant criterion for QNNs.