In machine learning, classification algorithms often use statistical methods to build the correspondence between features (or attributes) and categories (or labels), that is, the statistical correlation between features and categories. In quantum theory, a large number of experimental results show that quantum correlation is far stronger than what can be explained by local hidden theory (i.e., classical or non-quantum theory), that is, quantum mechanics theory reveals a statistical correlation stronger than that described by classical theory. Based on this, this paper will use the strong statistical correlation revealed by Bell state to build a classification algorithm to verify the validity and superiority of the formal framework of quantum mechanics in specific classification tasks. Specifically, we use quantum joint probabilities derived from the measurement process of Bell state to model the quantum statistical correlation between features and categories. The paper first theoretically proves that the formal framework used has the ability to violate Bell inequality; moreover, a classification algorithm is implemented and verified on classic machine learning datasets. Experimental results show that the algorithm is significantly better than most mainstream machine learning algorithms.
In machine learning, classification algorithms often use statistical methods to build the correspondence between features (or attributes) and categories (or labels), that is, the statistical correlation between features and categories. In quantum theory, a large number of experimental results show that quantum correlation is far stronger than what can be explained by local hidden theory (i.e., classical or non-quantum theory), that is, quantum mechanics theory reveals a statistical correlation stronger than that described by classical theory. Based on this, this paper will use the strong statistical correlation revealed by Bell state to build a classification algorithm to verify the validity and superiority of the formal framework of quantum mechanics in specific classification tasks. Specifically, we use quantum joint probabilities derived from the measurement process of Bell state to model the quantum statistical correlation between features and categories. The paper first theoretically proves that the formal framework used has the ability to violate Bell inequality; moreover, a classification algorithm is implemented and verified on classic machine learning datasets. Experimental results show that the algorithm is significantly better than most mainstream machine learning algorithms.
In supervised learning, the generative approach is an important one, which obtains the generative model by learning the joint probability between features and categories. In quantum mechanics, Quantum Entanglement (QE) can provide a statistical correlation between subsystems (or attributes) that is stronger than what classical systems are able to produce. It inspires us to use entangled systems (states) to characterize this strong statistical correlation between features and categories, that is, to use the joint probability derived from QE to model the correlation. Based on the separability of the density matrix of entangled systems, this paper formally clarifies the manifestation of the strong statistical correlation revealed by QE, and implements a classification algorithm (called ECA) to verify the feasibility and superiority of the correlation in specific tasks. Since QE arises from the measurement process of entangled systems, the core of ECA is quantum measurement operations. In this paper, we use the GHZ [25] and W [22] states to prepare the entangled system and use a fully connected network layer to learn the measurement operator. It can also be understood as replacing the output layer of the Multi-Layer Perceptron (MLP) with a quantum measurement operation. The experimental results show that ECA is superior to most representative classification algorithms in multiple evaluation metrics.
Quantum theory has attracted people's attention since it was proposed. Due to its unique advantages in information storage and processing, quantum information processing has become the most popular research field. Quantum theory also provides us with new methods or concepts for information manipulation and processing. The basic problems of classical physics are basically trying to be solved in a situation of isolation from the surrounding environment to reduce the complexity of the analysis problem, but the quantum system inevitably produces decoherence and establishes a close relationship with the environment such as entanglement, so the formal framework of quantum mechanics is inherently capable of depicting complex relationships. Based on the principle of quantum open system, a classifier under the formal framework of quantum mechanics is established to simulate the evolution process of open systems, that is, the interaction process between the target system and the environment. Specifically, we regard the features (or attributes) of the sample as environmental factors that affect the decision-making of the target system, and the target system can obtain the categories (or labels) of the sample through measurement. Based on this, we use the formal framework of quantum mechanics to establish a more natural and tighter correspondence between attributes and labels. Limited by the limitations of simulating quantum operations on classical computers, we conducted experiments on two lightweight machine learning datasets and compared them with mainstream classification algorithms. Experimental results show that the classification algorithm is better than the comparison models, and it also reveals the potential of the algorithm.
It is one of the most remarkable features of quantum physics that measurements on spatially separated systems cannot always be described by a locally causal theory. In such a theory, the outcomes of local measurements are determined in advance solely by some unknown (or hidden) variables and the choice of local measurements. Correlations that are allowed within the framework of a locally causal theory are termed classical. Typically, the fact that quantum mechanics does not always result in classical correlations is revealed by the violation of Bell inequalities, which are constraints that have to be satisfied by any classical correlations. It has been known for a long time that entanglement is necessary to demonstrate nonclassical correlations, and hence a Bell inequality violation. However, since some entangled quantum states are known to admit explicit locally causal models, the exact role of entanglement in Bell inequality violation has remained obscure. This thesis provides both a comprehensive review on these issues as well as a report on new discoveries made to clarify the relationship between entanglement and Bell inequality violation. In particular, within the framework of a standard Bell experiment, i.e., a Bell inequality test that is directly performed on a single copy of a quantum state r, we have derived two algorithms to determine, respectively, a lower bound and an upper bound on the strength of correlations that r can offer for any given Bell inequality. Both of these algorithms make use convex optimization techniques in the form of a semidefinite program. By examples, we show that these algorithms can often be used in tandem, in conjunction with convexity arguments, to determine if a quantum state can offer nonclassical correlations and hence violates a given Bell inequality. On the other hand, since a standard Bell experiment typically involves measurements over many copies of the quantum systems, we have also investigated the possibility of enhancing the strength of nonclassical correlation by, instead, performing collective measurements on multiple copies of the quantum systems. Our findings show that even without postselection, such joint measurements may also lead to stronger nonclassical correlations, and hence a better Bell inequality violation. Meanwhile, previous studies have indicated that entangled state admitting locally causal models may still lead to observable nonclassical correlations if, prior to a standard Bell experiment, the state is subjected to some appropriate local preprocessing. This phenomenon of hidden nonlocality was discovered more than a decade ago, but to date, it is still not known if all entangled states can demonstrate nonclassical correlations through these more sophisticated Bell experiments. A key result in this thesis then consists of showing that for all bipartite entangled states, observable nonclassical correlations, in the form of a Bell-CHSH inequality violation, can indeed be derived if we allow both local preprocessing and the usage of shared ancillary state which by itself does not violate the Bell-CHSH inequality. This establishes a kind of equivalence between bipartite entanglement and states that cannot be simulated by classical correlations. In summary, for a standard Bell experiment where no local preprocessing on a quantum state r is allowed, we have provided two algorithms that can be used in tandem to determine if r can be simulated by a locally causal theory, whereas in the scenario where local preprocessing is allowed, we have demonstrated that bipartite entangled states are precisely those which cannot always be simulated classically.
The ability to witness nonlocal correlations lies at the core of foundational aspects of quantum mechanics and its application in the processing of information. Commonly, this is achieved via the violation of Bell inequalities. Unfortunately, however, their systematic derivation quickly becomes unfeasible as the scenario of interest grows in complexity. To cope with that, here, we propose a machine learning approach for the detection and quantification of nonlocality. It consists of an ensemble of multilayer perceptrons blended with genetic algorithms achieving a high performance in a number of relevant Bell scenarios. As we show, not only can the machine learn to quantify nonlocality, but discover new kinds of nonlocal correlations inaccessible with other current methods as well. We also apply our framework to distinguish between classical, quantum, and even postquantum correlations. Our results offer a novel method and a proof-of-principle for the relevance of machine learning for understanding nonlocality.
This paper introduces a novel feature selection algorithm based on quantum machine learning, designed to optimize the selection of relevant features for machine learning models. Traditional feature selection methods often rely on classical computational techniques, which can be limited in their ability to effectively handle complex feature spaces and intricate relationships. This research explores the potential of quantum mechanics to enhance feature selection by leveraging quantum properties, specifically superposition and entanglement, to efficiently explore and prioritize the most impactful features. We present a theoretical framework and initial experimental results demonstrating the algorithm's superior performance in selecting relevant features compared to existing classical methods. The core mechanism centers around quantum-enhanced feature representation and a novel quantum optimization process for feature ranking. This work holds promise for improving the accuracy and efficiency of machine learning models, particularly in high-dimensional datasets.
This paper investigates the potential of combining quantum machine learning with quantum feature selection to enhance the performance of machine learning models. The core idea is to frame the machine learning problem as a quantum feature selection problem, leveraging quantum phenomena such as entanglement and superposition to effectively identify the most informative features. Traditional feature selection methods often struggle with high-dimensional datasets and may not fully exploit the inherent correlations between features. Quantum feature selection, utilizing quantum computers, offers a fundamentally different approach, potentially capable of identifying subtle relationships and patterns that classical methods miss. This paper explores the theoretical framework, outlining the conversion process and the utilization of quantum mechanics to optimize feature selection. The proposed method aims to achieve superior classification and regression results compared to conventional machine learning algorithms. We present a detailed mathematical description of the process, emphasizing the key quantum concepts involved. The ultimate goal is to demonstrate a viable pathway for advancing machine learning capabilities through the integration of quantum computing principles.