Encoding techniques for Quantum Machine Learning

Nowadays, Quantum Computing (QC) and Machine Learning (ML) are two of the most innovative research fields of information technologies. Quantum Machine Learning (QML) merges these two topics, developing models for ML tasks whose computational complexity can be reduced with QC techniques. A relevant ML application is Classification, which identifies the class to which new input data belong, according to a model built during a preliminary learning process. This is achieved on a training dataset composed of features (numerical vectors describing data) and labels (the expected output class). The accuracy of a classifier can be quantified in terms of the total number of correctly predicted outcomes over the total number of processed data. For near-term applications, the limits of current quantum hardware, in terms of execution reliability and scalability, promote the definition of hybrid QML solutions making the best of quantum and classical processing. Among these, the Variational Quantum Circuit and the quantum-kernel-estimation-based Support Vector Machine can be mentioned. The former implements the classification model with a parameterized quantum circuit optimized classically to achieve better accuracy. The other tries to maximize the distinguishability of data belonging to two different classes with a classical optimizer, assisted by quantum computing, mapping features in a higher dimensional space. In both cases, a preliminary encoding operation to represent classical data onto a quantum system is required. Then, specific quantum and classical operations complete Classification according to the hybrid solution and how the information has been represented. This thesis aims to verify that the data encoding strategy influences the model’s accuracy, so it must be treated as an optimizable degree of freedom for QML algorithms. In particular, the Amplitude and Angle Encodings, which have the most promising scalability, have been considered. The first one maps data features to the probability amplitudes of the qubits state vector, while the other consists of embedding the data as the angle parameter for rotational gates. In this work, new Angle Encoding techniques have been explored and compared with those already present in the literature to observe the impact on accuracy, examining sixty different strategies. The derived models have been developed and simulated with the Pennylane QML library, while the tests have considered the Iris and Wine datasets to prove the dependence of classification accuracy on encoding. For each case study, the best encoding strategy has been identified as the best compromise between learning performance requirements and execution time. For each dataset, three different benchmarking classifications have been performed, considering the available classes: 1vsAll, where the model has to identify if new data belong to class 0; 1vs1, in which the classification is accomplished by taking just two among all classes; and Multi-class, for which all classes are evaluated concurrently. From the obtained results, it can be concluded that the best encoding strategy cannot be chosen from previous analyses but depends on the specific case study. Moreover, some encodings can be discarded because they do not separate data effectively. Therefore, the encoding choice is a crucial preliminary operation to be properly pondered for efficient QML model development.