Abstract Although the studies on quantum algorithms have been progressing, it is still necessary to broaden the investigation of open quantum systems. In this study, we present the use of an open quantum system to implement a quantum classifier algorithm. Zhang et al. propose a one QuBit system interacting with the environment through a unitary operator that comes from the Hamiltonian. In our proposal, the input data is loaded into the amplitude of the environment instead of being in the unitary operator. This change positively impacts the performance of different databases tested and causes a difference in the system entanglement behavior. For evaluation, both the Zhang et. al model and the proposed model were tested in four real-world datasets and seven other toy problems. The results are evaluated according to accuracy and F1-Score. A deeper analysis of the Iris dataset is also done, checking the creation of entanglement and an extensive random search for better parameters on the proposed model. The results show that for most real-world datasets configurations, the proposed model, although having a simpler decision area, performed better than the one inspired by the Zhang et. al model, and that there is no pattern for the system entanglement in the Iris Dataset.
Abstract Although the studies on quantum algorithms have been progressing, it is still necessary to broaden the investigation of open quantum systems. In this study, we present the use of an open quantum system to implement a quantum classifier algorithm. Zhang et al. propose a one QuBit system interacting with the environment through a unitary operator that comes from the Hamiltonian. In our proposal, the input data is loaded into the amplitude of the environment instead of being in the unitary operator. This change positively impacts the performance of different databases tested and causes a difference in the system entanglement behavior. For evaluation, both the Zhang et. al model and the proposed model were tested in four real-world datasets and seven other toy problems. The results are evaluated according to accuracy and F1-Score. A deeper analysis of the Iris dataset is also done, checking the creation of entanglement and an extensive random search for better parameters on the proposed model. The results show that for most real-world datasets configurations, the proposed model, although having a simpler decision area, performed better than the one inspired by the Zhang et. al model, and that there is no pattern for the system entanglement in the Iris Dataset.
Although the studies on quantum algorithms have been progressing, it is still necessary to broaden the investigation of open quantum systems. In this study, we present the use of an open quantum system to implement a quantum classifier algorithm. Zhang et al. propose a one QuBit system interacting with the environment through a unitary operator that comes from the Hamiltonian. In our proposal, the input data is loaded into the amplitude of the environment instead of being in the unitary operator. This change positively impacts the performance of different databases tested and causes a difference in the system entanglement behavior. For evaluation, the Zhang et al. model and the proposed model were tested in four real-world datasets and seven other toy problems. The results are evaluated according to accuracy and F1-Score. A deeper analysis of the Iris dataset is also done, checking the creation of entanglement and an extensive random search for better parameters on the proposed model. The results show that for most real-world dataset configurations, the proposed model, although having a simpler decision area, performed better than the one inspired by the Zhang et al. model, and that there is no pattern for the system entanglement in the Iris Dataset. Due to an underperform for both models in a linearly separable problem, an exponential kernel was introduced. It resulted in an improvement in the accuracy of both models in most of the evaluated situations.
We implement a quantum binary classifier where given a dataset of pairs of training inputs and target outputs our goal is to predict the output of a new input. The script is based in a hybrid scheme inspired in an existing PennyLane's variational classifier and to encode the classical data we resort to PennyLane's amplitude encoding embedding template. We use the quantum binary classifier applied to the well known Iris dataset and to a car traffic dataset. Our results show that the quantum approach is capable of performing the task using as few as 2 qubits. Accuracies are similar to other quantum machine learning research studies, and as good as the ones produced by classical classifiers.
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.
Quantum Machine Learning (QML) is a newly emerging research area at the intersection of classical machine learning (CML) and quantum computing (QC). Data is becoming voluminous rapidly, so it is challenging for classical computers to train Machine Learning (ML) models over massive datasets. The hope is that quantum physics' intrinsic features, such as entanglement, superposition, and interference, could be exploited as resources for training ML models on big datasets that would otherwise be relatively impossible for classical computers. It is theoretically proven that quantum computers have an exponential-time advantage over their classical counterparts in solving several problems, e.g., complex large dimensional matrix multiplication, factorization problem, unstructured database search, etc. QML models attempt to find a quantum advantage over their classical counterparts. Variational Quantum Classifiers (VQC) are hybrid quantum neural networks to perform the task of classification using QML models. VQC models in the present NISQ (Noisy Intermediate Scale Quantum — 50 to 100 qubits) era can produce comparable and even better results than Classical models. In this article, we examined the performance of a VQC while performing a simple binary classification task. In this article, we use a VQC to evaluate this method's performance empirically. We constructed a VQC to predict the label of fresh input for the typical Iris dataset comprising pairings of target outputs and training inputs. Our quantum classifier can reasonably predict species labels using only four qubits. These levels are fairly good compared to the accuracy levels attained by classical classifiers.
The development of artificial intelligence today is marked with increased computational power, new algorithms, and big data. One such milestone impressive achievement in this area is Google’s AlphaGo. However, this advancement is beginning to face increasing challenges and the major bottleneck of AI today is the lack of adequate computing power in the processing of big data. Quantum computing offers a new and viable solution to deal with these challenges. A recent work designed a quantum classifier that runs on IBM’s five qubit quantum computer and tested its performance on the Iris data set as well as a circles data set. As quantum machine learning is still an emerging discipline, it may be enlightening to conduct an empirical analysis of this quantum classifier on some artificial datasets to help learn its unique features and potentials. Our work on the quantum classifier can be summarized in three parts. The first is to run its original version as a binary classifier on some artificial datasets using visualization to reveal the quantum nature of this algorithm, and the second is to analyze the swap operation utilized in its original circuit due to the hardware constraint and investigate its impact on the performance of the classifier. The last part is to extend the original circuit for binary classification to a circuit for multiclass classification and test its performance. Our findings shed new light on how this quantum classifier works.
In this article, we investigate the applicability of quantum machine learning for classification tasks using two quantum classifiers from the Qiskit Python environment: the variational quantum circuit and the quantum kernel estimator (QKE). We provide a first evaluation on the performance of these classifiers when using a hyperparameter search on six widely known and publicly available benchmark datasets and analyze how their performance varies with the number of samples on two artificially generated test classification datasets. As quantum machine learning is based on unitary transformations, this paper explores data structures and application fields that could be particularly suitable for quantum advantages. Hereby, this paper introduces a novel dataset based on concepts from quantum mechanics using the exponential map of a Lie algebra. This dataset will be made publicly available and contributes a novel contribution to the empirical evaluation of quantum supremacy. We further compared the performance of VQC and QKE on six widely applicable datasets to contextualize our results. Our results demonstrate that the VQC and QKE perform better than basic machine learning algorithms, such as advanced linear regression models (Ridge and Lasso). They do not match the accuracy and runtime performance of sophisticated modern boosting classifiers such as XGBoost, LightGBM, or CatBoost. Therefore, we conclude that while quantum machine learning algorithms have the potential to surpass classical machine learning methods in the future, especially when physical quantum infrastructure becomes widely available, they currently lag behind classical approaches. Our investigations also show that classical machine learning approaches have superior performance classifying datasets based on group structures, compared to quantum approaches that particularly use unitary processes. Furthermore, our findings highlight the significant impact of different quantum simulators, feature maps, and quantum circuits on the performance of the employed quantum estimators. This observation emphasizes the need for researchers to provide detailed explanations of their hyperparameter choices for quantum machine learning algorithms, as this aspect is currently overlooked in many studies within the field. To facilitate further research in this area and ensure the transparency of our study, we have made the complete code available in a linked GitHub repository.