A Scalable Quantum Neural Network for Approximate SRBB-Based Unitary Synthesis

In this work, scalable quantum neural networks are introduced to approximate unitary evolutions through the Standard Recursive Block Basis (SRBB) and, subsequently, redesigned with a reduced number of CNOTs. This algebraic approach to the problem of unitary synthesis exploits Lie algebras and their topological features to obtain scalable parameterizations of unitary operators. First, the recursive algorithm that builds the SRBB is presented, framed in the original scalability scheme already known to the literature only from a theoretical point of view. Unexpectedly, 2-qubit systems emerge as a special case outside this scheme. Furthermore, an algorithm to reduce the number of CNOTs is proposed, thus deriving a new implementable scaling scheme that requires one single layer of approximation. From the mathematical algorithm, the scalable CNOT-reduced quantum neural network is implemented and its performance is assessed with a variety of different unitary matrices, both sparse and dense, up to 6 qubits via the PennyLane library. The effectiveness of the approximation is measured with different metrics in relation to two optimizers: a gradient-based method and the Nelder-Mead method. The approximate SRBB-based synthesis algorithm with CNOT-reduction is also tested on real hardware and compared with other valid approximation and decomposition methods available in the literature.

Multi-Class Quantum Convolutional Neural Networks

Classification is particularly relevant to Information Retrieval, as it is used in various subtasks of the search pipeline. In this work, we propose a quantum convolutional neural network (QCNN) for multi-class classification of classical data. The model is implemented using PennyLane. The optimization process is conducted by minimizing the cross-entropy loss through parameterized quantum circuit optimization. The QCNN is tested on the MNIST dataset with 4, 6, 8 and 10 classes. The results show that with 4 classes, the performance is slightly lower compared to the classical CNN, while with a higher number of classes, the QCNN outperforms the classical neural network.

Demonstration of Envariance and Parity Learning on the IBM 16 Qubit Processor

Recently, IBM has made available a quantum computer provided with 16 qubits, denoted as IBM Q16. Previously, only a 5 qubit device, denoted as Q5, was available. Both IBM devices can be used to run quantum programs, by means of a cloud-based platform. In this paper, we illustrate our experience with IBM Q16 in demonstrating entanglement assisted invariance, also known as envariance, and parity learning by querying a uniform quantum example oracle. In particular, we illustrate the non-trivial strategy we have designed for compiling $n$-qubit quantum circuits ($n$ being an input parameter) on any IBM device, taking into account topological constraints.

Measuring the Complexity of Ultra-Large-Scale Adaptive Systems

Ultra-large scale (ULS) systems are becoming pervasive. They are inherently complex, which makes their design and control a challenge for traditional methods. Here we propose the design and analysis of ULS systems using measures of complexity, emergence, self-organization, and homeostasis based on information theory. These measures allow the evaluation of ULS systems and thus can be used to guide their design. We evaluate the proposal with a ULS computing system provided with adaptation mechanisms. We show the evolution of the system with stable and also changing workload, using different fitness functions. When the adaptive plan forces the system to converge to a predefined performance level, the nodes may result in highly unstable configurations, that correspond to a high variance in time of the measured complexity. Conversely, if the adaptive plan is less "aggressive", the system may be more stable, but the optimal performance may not be achieved.