This paper introduces the first implementation of fuzzy rule-based systems for quantum computers. Quantum computers are incredibly powerful machines that use principles of quantum mechanics, such as superposition and entanglement, to process information in a more efficient way than classical computers. Currently, several companies and academic research groups are focusing their efforts on the development of quantum algorithms for artificial intelligence but, so far, no significant contribution in the area of the fuzzy inference for quantum machines has been proposed. This article bridges this gap by introducing a quantum implementation of a fuzzy rule-based system through a synergistic usage of the well-known Grover's algorithm and look-up tables. As shown by a case study, the behaviour of the quantum implementation of the fuzzy rule-based system is comparable to its classical version, but with a quadratic asymptotic speed-up than a fuzzy rule-based system implemented by a classical look-up table.
This paper introduces the first implementation of fuzzy rule-based systems for quantum computers. Quantum computers are incredibly powerful machines that use principles of quantum mechanics, such as superposition and entanglement, to process information in a more efficient way than classical computers. Currently, several companies and academic research groups are focusing their efforts on the development of quantum algorithms for artificial intelligence but, so far, no significant contribution in the area of the fuzzy inference for quantum machines has been proposed. This article bridges this gap by introducing a quantum implementation of a fuzzy rule-based system through a synergistic usage of the well-known Grover's algorithm and look-up tables. As shown by a case study, the behaviour of the quantum implementation of the fuzzy rule-based system is comparable to its classical version, but with a quadratic asymptotic speed-up than a fuzzy rule-based system implemented by a classical look-up table.
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.
Quantum computers can potentially perform certain types of optimisation problems much more efficiently than classical computers, making them a promising tool for solving complex fuzzy logic problems. In two recent developments, based on solving Quadratic Unconstrained Binary Optimization (QUBO) problems on a type of quantum computers known as quantum annealers, we have introduced novel representations of a) fuzzy sets; b) implementations of some basic fuzzy logic operators (union, intersection, alpha-cut and maximum) and; c) the centroid defuzzification. In this paper, the previous works are further extended by presenting an implementation of Mamdani inference on the quantum annealer machines. We first present how the fuzzy rules can be formulated for such an implementation, then we present how to cascade different quantum-fuzzy operators in order to implement the quantum-fuzzy inference, and finally, a sample implementation of the inference on a real quantum computer is demonstrated. Having the main components of a rule-based fuzzy logic system implemented on quantum computers, this paper provides an integrated solution for implementing a whole fuzzy rule-based system on quantum computers.
The increasing need to work in environments characterized by a large number of variables and data is driving the development of ad hoc fuzzy reasoners. Recently, the first quantum fuzzy inference engine (QFIE) has been proposed to evaluate fuzzy rules in parallel on quantum computers, whose design hardware is based on different technologies such as superconductors, photonics, trap-ion, cold atoms, and so on. Although the theoretical potential of this approach is very promising, its practical usage is still limited by the current quantum hardware, in term of dimension and noise. This paper attempts to bridge this theoretical/practical gap and pave the way for the execution of fuzzy rule-based systems on real quantum hardware by presenting a comparative study between two of the most promising quantum computing platforms, superconducting and trap-ion devices. The comparison is carried out by using QFIE for the control of a simulated particle accelerator system inspired by a real facility at the European Organization for Nuclear Research (CERN). The result of this original study allow to establish the ideal running backend for the practical use case of quantum fuzzy systems.
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.
The complexity of searching algorithms in classical computing is a perpetual researched field. Quantum computers and quantum algorithms can compute these problems faster, and, in addition, machine learning implementation could provide a prominent way to boost quantum technology. We call quantum machine learning to this novel set of tools coming from artificial intelligence and quantum mechanics. To achieve our purpose, we focus on applications on quantum machine learning; in particular, we propose a review and exploration of topics such as variational quantum algorithms, kernel methods, and a review of Grover’s algorithm (GA) as a quantum classifier. We start with the GA exploration to achieve this goal, which is a quantum search algorithm that achieves quadratic speedup over optimal classical search implementation. This paper implements a GA exploration that includes a concept summary and implementation, considering only AND, XOR, and OR gates. We also discuss potential in quantum machine learning.
Quantum Machine Learning (QML) has emerged as a groundbreaking approach within the rapidly evolving field of Quantum Computing (QC), leveraging quantum phenomena such as superposition and entanglement to surpass classical models in representational power, optimization speed, and computational efficiency. This paradigm shift paves the way for transformative applications across diverse domains while simultaneously confronting the inherent complexities of quantum mechanics and hardware limitations. Among the powerful computational models used for decision-making and pattern recognition, Fuzzy Cognitive Maps (FCMs) have demonstrated exceptional capabilities in modeling complex systems. Researchers have continually refined the traditional FCM framework by integrating novel features to enhance its effectiveness. However, despite its potential, the integration of quantum computing with FCMs remains largely unexplored, with only a limited number of studies addressing this intersection. This work provides a comprehensive theoretical algorithmic evaluation of the integration between Quantum Computing and FCMs, investigating potential advancements, challenges, and novel applications. Additionally, we present a systematic review of existing research on Quantum Fuzzy Cognitive Maps (QFCMs), offering new insights into their theoretical foundations and future directions. By bridging the gap between quantum computing and cognitive modeling, this study aims to unlock new possibilities for intelligent decision-making systems in the quantum era.