For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementations of the quantum perceptron model have failed to fuse the two elegantly. This was due to a slow learning rule and a disregard for the unitary requirement. In this paper, we present a quantum perceptron that can compute functions uncomputable by the classical perceptron while analytically solving for parameters and preserving the unitary and dissipative requirements.
For the past two decades, researchers have attempted to create a Quantum Neural Network (QNN) by combining the merits of quantum computing and neural computing. In order to exploit the advantages of the two prolific fields, the QNN must meet the non-trivial task of integrating the unitary dynamics of quantum computing and the dissipative dynamics of neural computing. At the core of quantum computing and neural computing lies the qubit and perceptron, respectively. We see that past implementations of the quantum perceptron model have failed to fuse the two elegantly. This was due to a slow learning rule and a disregard for the unitary requirement. In this paper, we present a quantum perceptron that can compute functions uncomputable by the classical perceptron while analytically solving for parameters and preserving the unitary and dissipative requirements.
Abstract With the overwhelming success in the field of quantum computing, much attention has been paid to constructing a quantum neural network by combining a classical neural network with quantum computing. In this paper, we propose a novel quantum neural network model based on a quantum version of the sigmoid function, which skillfully combines the non-linear dissipation dynamics of neural computation with the linear unitary dynamics of quantum computation. Moreover, we also add connections from the input layer to the output layer to increase the non-linear expression ability of the network and the similarity to the human brain’s information processing. The specific steps and relevant formulas of the conjugate gradient algorithm in the learning stage of the quantum network parameters are also given in this paper. Finally, the feasibility and properties of the model are demonstrated by MATLAB simulation with a encryption and decryption experiment.
Quantum computing is one of the most exciting research areas of the last decades. At the same time, methods of machine learning have started to dominate science, industry and our everyday life. In this thesis we combine these two essential research topics of the 21st century and introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are capable of universal quantum computation and have low memory requirements while training. We start the discussion of this interdisciplinary topic by introducing artificial neural networks, which are a very common tool in classical machine learning. Next, we give an overview on quantum information. Here we focus on quantum algorithms and circuits, which are used to implement quantum neural networks. Moreover, we explain the opportunities and challenges arising with today's quantum computers. The discussion of the architecture and training algorithm of the DQNNs forms the core of this work. These networks are optimised with training data pairs in form of input and desired output states and therefore can be used for characterising unknown or untrusted quantum devices. We not only demonstrate the generalisation behaviour of these quantum neural networks using classical simulations, but also implement them successfully on actual quantum computers. To understand the ultimate limits for such quantum machine learning methods, we discuss the quantum no free lunch theorem, which describes a bound on the probability that a quantum device, which can be modelled as a unitary process and is optimised with quantum examples, gives an incorrect output for a random input. This gives us a tool to review the learning behaviour of quantum neural networks in general and the DQNNs in particular. Moreover we expand the area of applications of DQNNs in two directions. In the first case, we include additional information beyond just the training data pairs: since quantum devices are always structured, the resulting data is always structured as well. We modify the DQNN's training algorithm such that knowledge about the graph-structure of the training data pairs is included in the training process and show that this can lead to better generalisation behaviour. Both the original DQNN and the DQNN including graph structure are trained with data pairs in order to characterise an underlying relation. However, in the second extension of the algorithm we aim to learn characteristics of a set of quantum states in order to extend it to quantum states which have similar properties. Therefore we build a generative adversarial model where two DQNNs, called the generator and discriminator, are trained in a competitive way. Overall, we observe that DQNNs can not only be trained efficiently but also, similar to their classical counterparts, modified to suit different applications.
Recently, with the rapid development of technology, there are a lot of applications require to achieve low-cost learning. However the computational power of classical artificial neural networks, they are not capable to provide low-cost learning. In contrast, quantum neural networks may be representing a good computational alternate to classical neural network approaches, based on the computational power of quantum bit (qubit) over the classical bit. In this paper we present a new computational approach to the quantum perceptron neural network can achieve learning in low-cost computation. The proposed approach has only one neuron can construct self-adaptive activation operators capable to accomplish the learning process in a limited number of iterations and, thereby, reduce the overall computational cost. The proposed approach is capable to construct its own set of activation operators to be applied widely in both quantum and classical applications to overcome the linearity limitation of classical perceptron. The computational power of the proposed approach is illustrated via solving variety of problems where promising and comparable results are given.
In recent years, Quantum Computing witnessed massive improvements in terms of available resources and algorithms development. The ability to harness quantum phenomena to solve computational problems is a long-standing dream that has drawn the scientific community’s interest since the late ’80s. In such a context, we propose our contribution. First, we introduce basic concepts related to quantum computations, and then we explain the core functionalities of technologies that implement the Gate Model and Adiabatic Quantum Computing paradigms. Finally, we gather, compare, and analyze the current state-of-the-art concerning Quantum Perceptrons and Quantum Neural Networks implementations.
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.
Miniaturisation of computers components is taking us from classical to quantum physics domain. Further reduction in computer components size eventually will lead to the development of computer systems whose components will be on such a small scale that quantum physics intrinsic properties must be taken into account. The expression quantum computation and a first formal model of a quantum computer were first employed in the eighties. With the discovery of a quantum algorithm for factoring exponentially faster than any known classical algorithm in 1997, quantum computing began to attract industry investments for the development of a quantum computer and the design of novel quantum algorithms. For instance, the development of learning algorithms for neural networks. Some artificial neural networks models can simulate an universal Turing machine, and together with learning capabilities have numerous applications in real life problems. One limitation of artificial neural networks is the lack of an efficient algorithm to determine its optimal architecture. The main objective of this work is to verify whether we can obtain some advantage with the use of quantum computation techniques in a neural network learning and architecture selection procedure. We propose a quantum neural network, named quantum perceptron over a field (QPF). QPF is a direct generalisation of a classical perceptron which addresses some drawbacks found in previous models for quantum perceptrons. We also present a learning algorithm named Superposition based Architecture Learning algorithm (SAL) that optimises the neural network weights and architectures. SAL searches for the best architecture in a finite set of neural network architectures and neural networks parameters in linear time over the number of examples in the training set. SAL is the first quantum learning algorithm to determine neural network architectures in linear time. This speedup is obtained by the use of quantum parallelism and a non linear quantum operator.