Encoding classical data into a quantum is some of the most crucial steps to get to a fully functioning quantum computer but to this day there is no data encoding which is optimal for every use case this paper tries to show different data encodings for different use cases with their advantages and disadvantages the paper also shows algorithms that are used to implement those encodings in reality the paper divides the encoding in two different categories fixed and trainable encodings we discuss both the encoding in detail along with their respective use cases we also discuss about data encoding on NISQ(noisy intermediate quantum) computers the paper also discuss the machine learning approach to quantum embedding of data and its advantages along with its use cases in classification tasks and other machine learning tasks
Encoding classical data into a quantum is some of the most crucial steps to get to a fully functioning quantum computer but to this day there is no data encoding which is optimal for every use case this paper tries to show different data encodings for different use cases with their advantages and disadvantages the paper also shows algorithms that are used to implement those encodings in reality the paper divides the encoding in two different categories fixed and trainable encodings we discuss both the encoding in detail along with their respective use cases we also discuss about data encoding on NISQ(noisy intermediate quantum) computers the paper also discuss the machine learning approach to quantum embedding of data and its advantages along with its use cases in classification tasks and other machine learning tasks
In this paper, we focus on providing insights into various data encoding techniques for solving real-life problems using quantum machine learning, specifically for gate based quantum computers. At present, quantum computers have small qubits numbers, are noisy and are termed as NISQ (Noisy Intermediate Scale Quantum) computers. Generally, there are four steps involved in solving quantum machine learning problems. First is to encode data into a quantum computer using various data encoding techniques. The second step is to create a model of the system being addressed which is essentially the development of a quantum circuit using 1- and 2- qubit quantum gates. The third step is to train the model using gradient based or other optimization techniques. The fourth step is measurement and analysis of classical outputs of the model and improve various metrics of the model to make it robust for providing accurate results. In this research work, we evaluate and provide the mathematical underpinnings of different data encoding techniques which are used in today's NISQ quantum computers. Further, we discuss performance and efficiency of the various data encoding techniques.
This study explores the integration of quantum data embedding techniques into classical machine learning (ML) algorithms; to assess performance enhancements and computational implications across a spectrum of models. We explored various classical-to-quantum mapping methods; ranging from basis encoding and angle encoding to amplitude encoding; for encoding classical data. We conducted an extensive empirical study encompassing popular ML algorithms, including Logistic Regression, K-Nearest Neighbors, Support Vector Machines, and ensemble methods like Random Forest, LightGBM, AdaBoost, and CatBoost. Our findings reveal that quantum data embedding contributes to improved classification accuracy and F1 scores, particularly notable in models that inherently benefit from enhanced feature representation. We observed nuanced effects on running time, with low-complexity models exhibiting moderate increases and more computationally intensive models experiencing discernible changes. Notably, ensemble methods demonstrated a favorable balance between performance gains and computational overhead. This study underscores the potential of quantum data embedding to enhance classical ML models and emphasizes the importance of weighing performance improvements against computational costs. Future research may involve refining quantum encoding processes to optimize computational efficiency and explore scalability for real-world applications. Our work contributes to the growing body of knowledge on the intersection of quantum computing and classical machine learning, offering insights for researchers and practitioners seeking to harness the advantages of quantum-inspired techniques in practical scenarios.
Harnessing the potential computational advantage of quantum computers for machine learning tasks relies on the uploading of classical data onto quantum computers through what are commonly referred to as quantum encodings. The choice of such encodings may vary substantially from one task to another, and there exist only a few cases where structure has provided insight into their design and implementation, such as symmetry in geometric quantum learning. Here, we propose the perspective that category theory offers a natural mathematical framework for analyzing encodings that respect structure inherent in datasets and learning tasks. We illustrate this with pedagogical examples, which include geometric quantum machine learning, quantum metric learning, topological data analysis, and more. Moreover, such a perspective provides a language in which to ask meaningful and mathematically precise questions for the design of quantum encodings and circuits for quantum machine learning tasks.
Data representation is crucial for the success of machine-learning models. In the context of quantum machine learning with near-term quantum computers, equally important considerations of how to efficiently input (encode) data and effectively deal with noise arise. In this paper, we study data encodings for binary quantum classification and investigate their properties both with and without noise. For the common classifier we consider, we show that encodings determine the classes of learnable decision boundaries as well as the set of points which retain the same classification in the presence of noise. After defining the notion of a robust data encoding, we prove several results on robustness for different channels, discuss the existence of robust encodings, and prove a lower bound on the number of robust points in terms of fidelities between noisy and noiseless states. Numerical results for several example implementations are provided to reinforce our findings.
Abstract The classification of big data usually requires a mapping onto new data clusters which can then be processed by machine learning algorithms by means of more efficient and feasible linear separators. Recently, Lloyd et al. have advanced the proposal to embed classical data into quantum ones: these live in the more complex Hilbert space where they can get split into linearly separable clusters. Here, these ideas are implemented by engineering two different experimental platforms, based on quantum optics and ultra‐cold atoms, respectively, where we adapt and numerically optimize the quantum embedding protocol by deep learning methods, and test it for some trial classical data. A similar analysis is also performed on the Rigetti superconducting quantum computer. Therefore, it is found that the quantum embedding approach successfully works also at the experimental level and, in particular, we show how different platforms could work in a complementary fashion to achieve this task. These studies might pave the way for future investigations on quantum machine learning techniques especially based on hybrid quantum technologies.
In recent years, many generation-based machine learning algorithms such as generative adversarial networks, Boltzmann machine, auto-encoder, etc. are widely used in data generation and probability distribution simulation. On the other hand, the combined algorithms of quantum computation and classical machine learning algorithms are proposed in various styles. Especially, there exist many relevant researches about quantum generative models, which are regarded as the branch of quantum machine learning. Quantum generative models are hybrid quantum-classical algorithms, in which parameterized quantum circuits are introduced to obtain the cost function of the task as well as its gradient, and then classical optimization algorithms are used to find the optima. Compared with its classical counterpart, quantum generative models map the data stream to high-dimensional Hilbert space with parameterized quantum circuits. In the mapping space, data features are easier to learn, which can surpass classical generative models in some tasks. Besides, quantum generative models are potential to realize the quantum advantage in noisy intermediate-scale quantum devices.