This article deals with the problem of the uncertainty in rule-based systems (RBS), but from the perspective of quantum computing (QC). In this work we first remember the characteristics of Quantum Rule-Based Systems (QRBS), a concept defined in a previous article by one of the authors of this paper, and we introduce the problem of quantum uncertainty. We assume that the subjective uncertainty that affects the facts of classical RBSs can be treated as a direct consequence of the probabilistic nature of quantum mechanics (QM), and we also assume that the uncertainty associated with a given hypothesis is a consequence of the propagation of the imprecision through the inferential circuits of RBSs. This article does not intend to contribute anything new to the QM field: it is a work of artificial intelligence (AI) that uses QC techniques to solve the problem of uncertainty in RBSs. Bearing the above arguments in mind a quantum model is proposed. This model has been applied to a problem already defined by one of the authors of this work in a previous publication and which is briefly described in this article. Then the model is generalized, and it is thoroughly evaluated. The results obtained show that QC is a valid, effective and efficient method to deal with the inherent uncertainty of RBSs.
This article deals with the problem of the uncertainty in rule-based systems (RBS), but from the perspective of quantum computing (QC). In this work we first remember the characteristics of Quantum Rule-Based Systems (QRBS), a concept defined in a previous article by one of the authors of this paper, and we introduce the problem of quantum uncertainty. We assume that the subjective uncertainty that affects the facts of classical RBSs can be treated as a direct consequence of the probabilistic nature of quantum mechanics (QM), and we also assume that the uncertainty associated with a given hypothesis is a consequence of the propagation of the imprecision through the inferential circuits of RBSs. This article does not intend to contribute anything new to the QM field: it is a work of artificial intelligence (AI) that uses QC techniques to solve the problem of uncertainty in RBSs. Bearing the above arguments in mind a quantum model is proposed. This model has been applied to a problem already defined by one of the authors of this work in a previous publication and which is briefly described in this article. Then the model is generalized, and it is thoroughly evaluated. The results obtained show that QC is a valid, effective and efficient method to deal with the inherent uncertainty of RBSs.
In this paper, we illustrate that inaccurate knowledge can be efficiently implemented in a quantum environment. For this purpose, we analyse the correlation between certainty factors and quantum probability. We first explore the certainty factors approach for inexact reasoning from a classical point of view. Next, we introduce some basic aspects of quantum computing, and we pay special attention to quantum rule-based systems. In this context, a specific use case was built: an inferential network for testing the behaviour of the certainty factors approach in a quantum environment. After the design and execution of the experiments, the corresponding analysis of the obtained results was performed in three different scenarios: (1) inaccuracy in declarative knowledge, or imprecision, (2) inaccuracy in procedural knowledge, or uncertainty, and (3) inaccuracy in both declarative and procedural knowledge. This paper, as stated in the conclusions, is intended to pave the way for future quantum implementations of well-established methods for handling inaccurate knowledge.
Abstract Quantum Mechanics and Computation has a major problem called the measurement problem. This has given physicists a very hard time over the years when I first looked into the problem my approach was simple find a new number system that can go with the uncertainty of a Quantum particle the paper deals with the mathematics of uncertainty which has solved 2 millenium prize problems [4], [5] and quantum mea- surement problem very efficiently. We divide chaos into two parts low chaos and high chaos then we find the desired value [18] inside the inter- section of both. This helps us find something in a ℵ3 >>> ∞ this takes the problems around us to the next level if we are able to control a chaos then we can achieve pretty much anything.
In the twenty-first century, humanity is compelled to face global challenges. Such challenges involve complex systems. However, science has some cognitive and predictive limits in dealing with complex systems. Some of these limits are related to computational complexity and the recognition of variable patterns. To overcome these limits, artificial intelligence (AI) and quantum computing (QC) appear to be helpful. Even more promising is quantum AI (QAI), which emerged from the combination of AI and QC. The combination of AI and QC produces reciprocal, synergistic effects. This work describes some of these effects. It shows that QC offers new materials for implementing AI and innovative algorithms for solving optimisation problems and enhancing machine learning algorithms. Additionally, it demonstrates how AI algorithms can help overcome many of the experimental challenges associated with implementing QC. It also outlines several perspectives for the future development of quantum artificial intelligence.
Quantum computing presents a paradigm shift in computation, offering the potential to solve problems intractable for classical computers. However, the inherent complexity of quantum mechanics poses a significant challenge: the lack of interpretability. This paper introduces an Explainable Quantum Computing Model (EQCM), built upon the foundations of probability logic and information theory, designed to provide a transparent understanding of quantum computation processes and outcomes. The model aims to bridge the gap between the abstract nature of quantum algorithms and human intuition. We propose a framework where quantum operations are represented and interpreted within a probabilistic logic framework, allowing for the tracing and explanation of quantum state transformations. The core of the EQCM lies in quantifying uncertainty and leveraging information theory to derive explanations for observed quantum behaviors. This work contributes to the growing field of quantum explainability, paving the way for improved debugging, validation, and ultimately, wider adoption of quantum computing technologies. The model's key features include a probabilistic representation of quantum states, a formal method for tracking quantum operations, and a mechanism for quantifying the degree of uncertainty associated with quantum outcomes. We demonstrate how this framework can be applied to simple quantum algorithms, providing insights into their underlying mechanisms.
The article is devoted to the study of the possibility of uncertainty processing using quantum algorithms. Uncertainty processing is one of the most important tasks in artificial intelligence. The quality of knowledge used by the intelligent system depends on the solution of this problem. Domain knowledge contains uncertainty. The paper considers the possibility of uncertainty handling using quantum computing. Tensor method is used to represent uncertainty. The tensor method provides an object representation of fuzzy knowledge. This approach allows to investigate the properties of uncertainty which are not available in representing fuzzy knowledge by traditional methods such as fuzzy sets, Bayesian networks, Stanford confidence factor, neural networks. Tensor processing on a classical computer is a computationally complex task. Quantum algorithms provide exponential acceleration in solving such problems. The article discusses the possibility of using quantum algorithms to process fuzzy knowledge represented by tensors.
Quantum computing is an emerging technology that has the potential to change the perspectives and applications of computing in general. A wide range of applications are enabled: from faster algorithmic solutions of classically still difficult problems to theoretically more secure communication protocols. A quantum computer uses the quantum mechanical effects of particles or particle-like systems, and a major similarity between quantum and classical computers consists of both being abstracted as information processing machines. Whereas a classical computer operates on classical digital information, the quantum computer processes quantum information, which shares similarities with analog signals. One of the central differences between the two types of information is that classical information is more fault-tolerant when compared to its quantum counterpart. Faults are the result of the quantum systems being interfered by external noise, but during the last decades quantum error correction codes (QECC) were proposed as methods to reduce the effect of noise. Reliable quantum circuits are the result of designing circuits that operate directly on encoded quantum information, but the circuit’s reliability is also increased by supplemental redundancies, such as sub-circuit repetitions. Reliable quantum circuits have not been widely used, and one of the major obstacles is their vast associated resource overhead, but recent quantum computing architectures show promising scalabilities. Consequently the number of particles used for computing can be more easily increased, and that the classical control hardware (inherent for quantum computation) is also more reliable. Reliable quantum circuits haev been investigated for almost as long as general quantum computing, but their limited adoption (until recently) has not generated enough interest into their systematic design. The continuously increasing practical relevance of reliability motivates the present thesis to investigate some of the first answers to questions related to the background and the methods forming a reliable quantum circuit design stack. The specifics of quantum circuits are analysed from two perspectives: their probabilistic behaviour and their topological properties when a particular class of QECCs are used. The quantum phenomena, such as entanglement and superposition, are the computational resources used for designing quantum circuits. The discrete nature of classical information is missing for quantum information. An arbitrary quantum system can be in an infinite number of states, which are linear combinations of an exponential number of basis states. Any nontrivial linear combination of more than one basis states is called a state superposition. The effect of superpositions becomes evident when the state of the system is inferred (measured), as measurements are probabilistic with respect to their output: a nontrivial state superposition will collapse to one of the component basis states, and the measurement result is known exactly only after the measurement. A quantum system is, in general, composed from identical subsystems, meaning that a quantum computer (the complete system) operates on multiple similar particles (subsystems). Entanglement expresses the impossibility of separating the state of the subsystems from the state of the complete system: the nontrivial interactions between the subsystems result into a single indivisible state. Entanglement is an additional source of probabilistic behaviour: by measuring the state of a subsystem, the states of the unmeasured subsystems will probabilistically collapse to states from a well defined set of possible states. Superposition and entanglement are the building blocks of quantum information teleportation protocols, which in turn are used in state-of-the-art fault-tolerant quantum computing architectures. Information teleportation implies that the state of a subsystem is moved to a second subsystem without copying any information during the process. The probabilistic approach towards the design of quantum circuits is initiated by the extension of classical test and diagnosis methods. Quantum circuits are modelled similarly to classical circuits by defining gate-lists, and missing quantum gates are modelled by the single missing gate fault. The probabilistic approaches towards quantum circuits are facilitated by comparing these to stochastic circuits, which are a particular type of classical digital circuits. Stochastic circuits can be considered an emulation of analogue computing using digital components. A first proposed design method, based on the direct comparison, is the simulation of quantum circuits using stochastic circuits by mapping each quantum gate to a stochastic computing sub-circuit. The resulting stochastic circuit is compiled and simulated on FPGAs. The obtained results are encouraging and illustrate the capabilities of the proposed simulation technique. However, the exponential number of possible quantum basis states was translated into an exponential number of stochastic computing elements. A second contribution of the thesis is the proposal of test and diagnosis methods for both stochastic and quantum circuits. Existing verification (tomographic) methods of quantum circuits were targeting the reconstruction of the gate-lists. The repeated execution of the quantum circuit was followed by different but specific measurement at the circuit outputs. The similarities between stochastic and quantum circuits motivated the proposal of test and diagnosis methods that use a restricted set of measurement types, which minimise the number of circuit executions. The obtained simulation results show that the proposed validation methods improve the feasibility of quantum circuit tomography for small and medium size circuits. A third contribution of the thesis is the algorithmic formalisation of a problem encountered in teleportation-based quantum computing architectures. The teleportation results are probabilistic and require corrections represented as quantum gates from a particular set. However, there are known commutation properties of these gates with the gates used in the circuit. The corrections are not applied as dynamic gate insertions (during the circuit’s execution) into the gate-lists, but their effect is tracked through the circuit, and the corrections are applied only at circuit outputs. The simulation results show that the algorithmic solution is applicable for very large quantum circuits. Topological quantum computing (TQC) is based on a class of fault-tolerant quantum circuits that use the surface code as the underlying QECC. Quantum information is encoded in lattice-like structures and error protection is enabled by the topological properties of the lattice. The 3D structure of the lattice allows TQC computations to be visualised similarly to knot diagrams. Logical information is abstracted as strands and strand interactions (braids) represent logical quantum gates. Therefore, TQC circuits are abstracted using a geometrical description, which allows circuit input-output transformations (correlations) to be represented as geometric sub-structures. TQC design methods were not investigated prior to this work, and the thesis introduces the topological computational model by first analysing the necessary concepts. The proposed TQC design stack follows a top-down approach: an arbitrary quantum circuit is decomposed into the TQC supported gate set; the resulting circuit is mapped to a lattice of appropriate dimensions; relevant resulting topological properties are extracted and expressed using graphs and Boolean formulas. Both circuit representations are novel and applicable to TQC circuit synthesis and validation. Moreover, the Boolean formalism is broadened into a formal mechanism for proving circuit correctness. The thesis introduces TQC circuit synthesis, which is based on a novel logical gate geometric description, whose formal correctness is demonstrated. Two synthesis methods are designed, and both use a general planar representation of the circuit. Initial simulation results demonstrate the practicality and performance of the methods. An additional group of proposed design methods solves the problem of automatic correlation construction. The methods use validity criteria which were introduced and analysed beforehand in the thesis. Input-output correlations existing in the circuit are inferred using both the graph and the Boolean representation. The thesis extends the TQC state-of-the-art by recognising the importance of correlations in the validation process: correlation construction is used as a sub-routine for TQC circuit validation. The presented cross-layer validation procedure is useful when investigating both the QECC and the circuit, while a second proposed method is QECC-independent. Both methods are scalable and applicable even to very large circuits. The thesis completes with the analysis of TQC circuit identities, where the developed Boolean formalism is used. The proofs of former known circuit identities were either missing or complex, and the presented approach reduces the length of the proofs and represents a first step towards standardising them. A new identity is developed and detailed during the process of illustrating the known circuit identities. Reliable quantum circuits are a necessity for quantum computing to become reality, and specialised design methods are required to support the quest for scalable quantum computers. This thesis used a twofold approach towards this target: firstly by focusing on the probabilistic behaviour of quantum circuits, and secondly by considering the requirements of a promising quantum computing architecture, namely TQC. Both approaches resulted in a set of design methods enabling the investigation of reliable quantum circuits. The thesis contributes with the proposal of a new quantum simulation technique, no