What are Quantum Neural Networks (QNNs)?
by Stephen M. Walker II, CoFounder / CEO
What are Quantum Neural Networks (QNNs)?
Quantum Neural Networks (QNNs) are computational neural network models based on the principles of quantum mechanics. They are designed to leverage the power of quantum computing to improve the performance of classical neural networks, particularly in big data applications. QNNs are developed as feedforward networks, similar to their classical counterparts, and can be integrated into basic quantum machine learning (QML) workflows.
Key components of QNNs include:

Quantum Perceptron — This is the quantum analogue of classical perceptrons used in classical machine learning. It is an arbitrary unitary operator with m input qubits and n output qubits.

Quantum Circuit — The quantum circuit acts upon an initial state of input qubits and produces a mixed state of output qubits. It consists of layer unitaries, which are composed of a product of quantum perceptrons that act upon the qubits.

Training — QNNs can be trained using a quantum analogue of the classical backpropagation algorithm, which exploits completely positive layer transition matrices.
QNNs have shown promising results in various applications, such as image classification and data approximation. However, the convergence of QNN training is not fully understood, and further research is needed to better analyze the dynamics and performance of these networks.
How do QNNs work?
Quantum Neural Networks operate by using quantum bits, or qubits, which can exist in multiple states simultaneously, unlike classical bits that are either 0 or 1. This property allows qubits to perform multiple calculations at once, providing a theoretical speedup for certain computational tasks.
A QNN typically consists of a sequence of quantum gates that perform operations on qubits, analogous to the weights and activation functions in classical neural networks. These quantum gates are arranged in layers to form a circuit, and the output of the circuit is measured to obtain the result of the computation.
What are the potential advantages of QNNs?
Quantum Neural Networks (QNNs) hold several potential advantages over their classical counterparts. Firstly, they can achieve an exponential speedup for certain problems by exploiting quantum parallelism. Secondly, due to the highdimensional state space of qubits, QNNs can efficiently represent complex, highdimensional data using fewer resources. Lastly, QNNs can utilize quantum entanglement to capture correlations in data that might be inaccessible to classical systems.
What are the challenges associated with QNNs?
Quantum Neural Networks (QNNs), despite their potential, are currently facing several challenges. The high susceptibility of quantum systems to noise and the loss of quantum information over time, known as decoherence, can degrade the performance of QNNs. Additionally, the limitations of current quantum hardware, such as a restricted number of qubits and a propensity for errors, limit the size and complexity of QNNs that can be practically implemented. Furthermore, the field of QNNs is still in its infancy, leading to a lack of standardized models and training algorithms.
What is the current state of QNN research?
Current research in Quantum Neural Networks (QNNs), as of 2023, is primarily theoretical with a handful of experimental implementations on quantum hardware. The focus is on exploring diverse architectures, training methods, and potential applications for complex problemsolving. Significant strides have been made in error correction techniques and stabilizing qubits, both critical for QNNs' practical application. However, the widespread use of QNNs in realworld applications is expected to take several more years.
How could QNNs impact the future of AI and computing?
Overcoming technical challenges could allow Quantum Neural Networks (QNNs) to revolutionize artificial intelligence by efficiently processing vast datasets and solving complex optimization problems. This advancement could also impact fields like drug discovery and financial modeling, where large data processing and analysis are crucial.
QNNs, though in early development stages, represent an exciting frontier in the intersection of quantum computing and artificial intelligence. Their potential to transform computational capabilities makes them a pivotal research area for future technology.