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arXiv:1808.10561

A Quantum Model for Multilayer Perceptron

Changpeng Shao

Published Aug 31, 2018• 14 citations
arXivHTMLPDF

Abstract

Multilayer perceptron is the most common used class of feed-forward artificial neural network. It contains many applications in diverse fields such as speech recognition, image recognition, and machine translation software. To cater for the fast development of quantum machine learning, in this paper, we propose a new model to study multilayer perceptron in quantum computer. This contains the tasks to prepare the quantum state of the output signal in each layer and to establish the quantum version of learning algorithm about the weights in each layer. We will show that the corresponding quantum versions can achieve at least quadratic speedup or even exponential speedup over the classical algorithms. This provide us an efficient method to study multilayer perceptron and its applications in machine learning in quantum computer. Finally, as an inspiration, an exponential fast learning algorithm (based on Hebb's learning rule) of Hopfield network will be proposed.

DOI
10.48550/arxiv.1808.10561

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Multilayer perceptron is the most common used class of feed-forward artificial neural network. It contains many applications in diverse fields such as speech recognition, image recognition, and machine translation software. To cater for the fast development of quantum machine learning, in this paper, we propose a new model to study multilayer perceptron in quantum computer. This contains the tasks to prepare the quantum state of the output signal in each layer and to establish the quantum version of learning algorithm about the weights in each layer. We will show that the corresponding quantum versions can achieve at least quadratic speedup or even exponential speedup over the classical algorithms. This provide us an efficient method to study multilayer perceptron and its applications in machine learning in quantum computer. Finally, as an inspiration, an exponential fast learning algorithm (based on Hebb's learning rule) of Hopfield network will be proposed.
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.
Abstract The field of artificial neural networks is expected to strongly benefit from recent developments of quantum computers. In particular, quantum machine learning, a class of quantum algorithms which exploit qubits for creating trainable neural networks, will provide more power to solve problems such as pattern recognition, clustering and machine learning in general. The building block of feed-forward neural networks consists of one layer of neurons connected to an output neuron that is activated according to an arbitrary activation function. The corresponding learning algorithm goes under the name of Rosenblatt perceptron. Quantum perceptrons with specific activation functions are known, but a general method to realize arbitrary activation functions on a quantum computer is still lacking. Here, we fill this gap with a quantum algorithm which is capable to approximate any analytic activation functions to any given order of its power series. Unlike previous proposals providing irreversible measurement–based and simplified activation functions, here we show how to approximate any analytic function to any required accuracy without the need to measure the states encoding the information. Thanks to the generality of this construction, any feed-forward neural network may acquire the universal approximation properties according to Hornik’s theorem. Our results recast the science of artificial neural networks in the architecture of gate-model quantum computers.
Abstract Quantum computing is a new mode that follows the laws of quantum mechanics. It performs computational tasks based on the control of quantum units. From the view of computable problems, quantum computers can only solve the problems that traditional computers can solve, but considering the efficiency of computation, due to the existence of quantum superposition, some known quantum algorithms are exponentially faster than traditional general-purpose computers. In this article, we combine quantum computing with a classical neural network to design a quantum Hopfield network. Each neuron is initialized to a specified state and evolved into a steady state. The output result is one of patterns in a training set. We also present an application of this protocol in image recognition. The simulation results show that this network works in the quantum environment and the output images are correct, therefore the feasibility of this protocol is verified.
Artificial neural networks, usually just called neural networks, computing systems indefinitely inspired by the biological neural networks and they are extensive in both research as well as industry. It is critical to design quantum Neural Networks for complete quantum learning tasks. In this project, we suggest a computational neural network model based on principles of quantum mechanics which form a quantum feed-forward neural network proficient in universal quantum computation. This structure takes input from one layer of qubits and drives that input onto another layer of qubits. This layer of qubits evaluates this information and drives on the output to the next layer. Eventually, the path leads to the final layer of qubits. The layers do not have to be of the same breadth, meaning they need not have the same number of qubits as the layer before and/or after it. This assembly is trained on which path to take identical to classical ANN. The intended project can be compiled by the subsequent points provided here: 1. The expert training of the quantum neural network utilizing the fidelity as a cost function, providing both conventional and efficient quantum implementations. 2. Use of methods that enable quick optimization with reduced memory requirements. 3. Benchmarking our proposal for the quantum task of learning an unknown unitary and find extraordinary generality and a remarkable sturdiness to noisy training data.
Quantum information and quantum computers have enabled us to write algorithms, - quantum algorithms - that in some cases display a speedup with respect to their classical counterpart. As machine learning is becoming of upmost importance not only for our every-day-life and for scientific research, it is natural to inquire if we could use methods from quantum information to speed up machine learning’s processes. In this Thesis, we review a model of a quantum perceptron, a key component for modern neural networks, and simulate its time evolution to characterize behavior.
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where quantum computer may offer significant speedup. Several quantum algorithms for discriminative machine learning have been found based on efficient solving of linear algebraic problems, with potential exponential speedup in runtime under the assumption of effective input from a quantum random access memory. In machine learning, generative models represent another large class which is widely used for both supervised and unsupervised learning. Here, we propose an efficient quantum algorithm for machine learning based on a quantum generative model. We prove that our proposed model is exponentially more powerful to represent probability distributions compared with classical generative models and has exponential speedup in training and inference at least for some instances under a reasonable assumption in computational complexity theory. Our result opens a new direction for quantum machine learning and offers a remarkable example in which a quantum algorithm shows exponential improvement over any classical algorithm in an important application field.