Federated learning is a paradigm that proposes protecting data privacy by sharing local models instead of raw data during each iteration of model training. However, these models can be large, with many parameters, provoking a substantial communication cost and having a notable environmental impact. Reducing communication overhead is paramount but conflictual to maintaining the model’s accuracy. Most research has dealt with the different factors influencing communication reduction separately without addressing their correlations. Moreover, most of them do not consider the heterogeneity of clients’ hardware. Finding the optimal configuration to fulfil all these training aspects can become intractable for classical techniques. This work explores the add-in that multi-objective evolutionary algorithms can provide for solving the communication overhead problem while achieving high accuracy. We do this by 1) realistically modelling and formulating this task as a multi-objective problem by considering the devices’ heterogeneity, 2) including all the communication-triggering aspects, and 3) applying a multi-objective evolutionary algorithm with an intensification operator to solve the problem. A simulated client–server architecture of four devices with four different processing speeds is studied. Both fully connected and convolutional neural network models are investigated with 33,400 and 887,530 weights, respectively. The experiments are performed using the MNIST and Fashion-MNIST datasets. A comparison is made between three approaches using an extensive set of metrics. Results prove that our approach obtains solutions with better accuracy than the full-communication setting and other methods while getting reductions in communications by around 1,000 times in most cases and up to 10,000 times in some cases compared to the maximum communication setting.

Discrete-variable gate-model quantum machines are promising quantum systems considering their wide applicability. Being in their noisy-intermediate-scale era, they allow executing only circuits of limited complexity and fitting the machines' features. Thus, such systems implement a key and unavoidable tailoring process to produce the most possible compact and device-compliant circuit. The qubits' initialisation is a primary and complex step that can ease/jeopardise the tailoring process and restrict/extend the machine's computational capacities. Ultimately, this bottleneck can be responsible of making quantum leaps like quantum supremacy. As a step towards the former, this work investigates how evolutionary algorithms can enhance the qubits' initialisation by tackling it as a single-objective problem using a genetic algorithm. The experiments used instances representing 19 real IBM quantum machines with 7 to 65 qubits and 9 different qubit topologies. Also, 76 GHZ circuits of sizes 7-65 qubits and 25%-100% of entanglement were created and studied. Extensive standard and statistical comparisons have been made against the IBM qubit initialiser that is currently used in real quantum machines. Results showed that the proposal outperforms IBM in 64 instances and is similar to it in 10 ones, with an average circuit-compression gain up to 46%.

Quantum-inspired metaheuristics are solvers that incorporate principles inspired from quantum mechanics into classical-approximate algorithms using non-quantum machines. Due to the uniqueness of quantum principles, the inspiration of quantum phenomena and the way it is done in fundamentally different non-quantum systems rather than real or simulated quantum computers raise important questions about these algorithms’ design and the reproducibility of their results in real or simulated quantum devices. Thus, this work’s contribution stands in a first step towards answering those questions as an attempt to identify key findings in the existing literature that should be considered or adapted in order to build hybrid or fully-quantum algorithms that can be used in quantum machines. This is done by proposing and studying four inspired, simulated and real quantum cellular genetic algorithms that, as far as the authors’ knowledge, are the first quantum structured metaheuristics studied in the three quantum realms using a quantum simulator with 32 quantum bits and a real quantum machine employing 15 superconducting quantum bits. The users’ mobility management in cellular networks is taken as a validation problem using 13 real-world instances. The comparisons have been made against 6 diverse algorithms using 9 comparison metrics. Thorough statistical tests and parameters’ sensitivity analysis have been also conducted. The experiments allowed answering several questions, including how quantum hardware influences the studied-algorithms’ search process. They also enabled opening new perspectives in quantum metaheuristics’ design.