In the Noisy Intermediate-Scale Quantum (NISQ) era, efficient quantum circuit synthesis is essential for optimizing limited qubit resources and mitigating noise effects. Quantum Linear Reversible Circuits (QLRCs) are a fundamental class of circuits with applications in quantum compilation or quantum error correction. They are composed exclusively of CX and SWAP gates, which are among the noisiest operations on current quantum hardware. Therefore, their efficient synthesis is pivotal for executing QLRCs on NISQ processors, which have restricted connectivity between qubits. In this direction, we introduce a Reinforcement Learning (RL)-based synthesis approach using Proximal Policy Optimization (PPO) to synthesize QLRCs on generic topologies of up to five qubits. This work extends previous work that did not handle different topologies of quantum processors. Our method dynamically adapts to hardware constraints, learning optimal or near-optimal gate decompositions. We compare our approach against Qiskit’s synthesis methods for QLRCs, demonstrating that our RL-based synthesizer consistently achieves lower CX gate depth. These results highlight the potential of RL-driven quantum circuit synthesis as a powerful alternative to traditional heuristic-based techniques, paving the way for more efficient AI-based quantum compilation strategies in the NISQ era.

The nuclear shell model is one of the most adopted many-body methods for the description of atomic nuclei whose main ingredient is the effective Hamiltonian. One of the approaches widely used to derive it is of phenomenological type, where its matrix elements are considered parameters to be fixed to reproduce the experimental data. However, the number of parameters as well as the number of experimental data dramatically increases with the mass of the nuclei under investigation and the commonly adopted procedures such as least-square fitting become computationally prohibitive. Therefore, there is a strong emergence in finding alternative approaches to construct effective Hamiltonians for heavy nuclei. To pave the way in this direction, the proposed work exploits for the very first time Genetic Algorithms. Indeed, their ability to simultaneously examine and manipulate sets of possible solutions could be crucial to deal with the above issues. The suitability of Genetic Algorithms in computing effective Hamiltonians is evaluated experimentally for the p - shell interaction, where the obtained results, without any physical constraint on the parameters, outperform the current widely-adopted description represented by the Cohen and Kurath solution.

The regulation of traffic lights in a signalised urban network requires optimizing objective functions that represent performance indicators of one or more intersections (such as delay or queue length). In this scenario, evolutionary algorithms are adopted to find suitable approximate solutions, in cases when no deterministic algorithm for finding the exact solution is known. This paper attempts to further improve the performance of evolutionary approaches by using a hybrid quantum-classical genetic algorithm to find the optimal configuration of the green signal timing regulating the traffic flow across two interacting junctions. The adopted algorithm, run on IBM quantum computer simulators, is shown to be suitable for the optimization problem at hand. Indeed, the experimental results highlight some of the strengths of the proposed technique with respect to the purely evolutionary approach, and encourage the application of this approach to more complex and close-to-real application scenarios.

In recent years, quantum computing is finding strong application in the development of new evolutionary algorithms. This is mainly due to the intrinsic parallelism induced by this new computational paradigm, which fits well with the structure of population-based optimization algorithms. However, the pioneering nature of quantum hardware makes quantum computations still suffer from noise that affects their accuracy and precision. This study aims to analyze the effect of this noise on quantum genetic algorithms and to quantify how much this can destroy or enhance the guided search of these algorithms in the search space. In detail, the proposed paper introduces a systematic study that assess the effects of quantum noise in a genetic algorithm equipped with a quantum recombination operator, formally known as the Quantum Mating Operator, when applied to solving a well-known optimization problem such as the 01 knapsack.

Quantum computers can be a revolutionary tool to implement inference engines for fuzzy rule-based systems. In fact, the use of quantum mechanical principles can enable parallel execution of fuzzy rules and allow them to be used efficiently in complex contexts such as distributed and big data environments. This article introduces the very first quantum-based fuzzy inference engine that is capable of providing exponential acceleration in fuzzy rule execution compared to its classical counterpart, and allows a quantum computer to be programmed by fuzzy linguistic rules. The proposed inference engine was implemented using a quantum algorithm design scheme based on the oracle notion. This scheme allows the modeling of a fuzzy rule-based system as a Boolean function, the oracle, which is able to reconstruct the relationships between the antecedent and consequent parts of fuzzy rules, and can be efficiently computed on a quantum computer. The suitability of the proposed quantum algorithm for use as a fuzzy inference engine was tested in a typical benchmark scenario, such as that provided by inverted pendulum control.

Genetic Algorithms (GAs) are optimization methods that search near-optimal solutions by applying well-known operations such as selection, crossover and mutation. In particular, crossover and mutation are aimed at creating new solutions from selected parents with the goal of discovering better and better solutions in the search space. In literature, several approaches have been defined to create new solutions from the mating pool to try to improve the performance of genetic optimization. In this paper, the literature is enriched by introducing a new mating operator that harnesses the stochastic nature of quantum computation to evolve individuals in a classical genetic workflow. This new approach, named Quantum Mating Operator, acts as a multi-parent operator that identifies alleles' frequency patterns from a collection of individuals selected by means of conventional selection operators, and encodes them through a quantum state. This state is successively mutated and measured to generate a new classical chromosome. As shown by experimental results, GAs equipped with the proposed operator outperform those equipped with traditional crossover and mutation operators when used to solve well-known benchmark functions.

Due to the built-in parallelism of quantum computing, there is an unexplored potential for some complex fuzzy logic computations to take the advantage of the future quantum computers. Recently, it has been introduced a novel representation of fuzzy sets and implementations of some basic fuzzy logic operators (union, intersection, alpha-cut and maximum) based on solving a Quadratic Unconstrained Binary Optimization (QUBO) problems, on a type of quantum computers known as quantum annealers. In this paper, this work is extended by presenting an implementation of centroid defuzzification on quantum annealer machines, based on binary quadratic model (BQM) but this time using Ising model. Having the basic operations and defuzzification implemented on quantum computers, this paper paves the way towards the implementation of a whole fuzzy inference engine on enhanced devices, such as quantum annealers.

Quantum computation is going to revolutionize the world of computing by enabling the design of massive parallel algorithms that solve hard problems in an efficient way, thanks to the exploitation of quantum mechanics effects, such as superposition, entanglement, and interference. These computational improvements could strongly influence the way how fuzzy systems are designed and used in contexts, such as Big Data, where computational efficiency represents a nonnegligible constraint to be taken into account. In order to pave the way toward this innovative scenario, this article introduces a novel representation of fuzzy sets and operators based on quadratic unconstrained binary optimization problems, so as to enable the implementation of fuzzy inference engines on a type of quantum computers known as quantum annealers.

This paper introduces a study on fuzzy-based approaches aimed at addressing a crucial task in quantum computation: the evaluation of the similarity between quantum states. A quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement of a quantum algorithm. Because quantum computers are still characterized by high noise in computation, output quantum states generated by quantum algorithms could be very far to be close to the ideal output quantum state computed by a noiseless quantum computer. As a consequence, there is a strong emergence for measures capable of assessing the similarity level of two quantum states, one ideal and the other real, to infer the quality of a quantum device in performing precise calculations and design appropriate quantum error correction schemes. This research proves that fuzzy methods are fully suitable to face this crucial challenge in a pioneering scenario such as that of quantum computing, as proved by their application on well-known quantum algorithms, such as Bernstein-Vazirani and Grover's algorithm.

Abstract Quantum computers have become reality thanks to the effort of some majors in developing innovative technologies that enable the usage of quantum effects in computation, so as to pave the way towards the design of efficient quantum algorithms to use in different applications domains, from finance and chemistry to artificial and computational intelligence. However, there are still some technological limitations that do not allow a correct design of quantum algorithms, compromising the achievement of the so-called quantum advantage. Specifically, a major limitation in the design of a quantum algorithm is related to its proper mapping to a specific quantum processor so that the underlying physical constraints are satisfied. This hard problem, known as circuit mapping, is a critical task to face in quantum world, and it needs to be efficiently addressed to allow quantum computers to work correctly and productively. In order to bridge above gap, this paper introduces a very first circuit mapping approach based on deep neural networks, which opens a completely new scenario in which the correct execution of quantum algorithms is supported by classical machine learning techniques. As shown in experimental section, the proposed approach speeds up current state-of-the-art mapping algorithms when used on 5-qubits IBM Q processors, maintaining suitable mapping accuracy.