Ensembles of Quantum Classifiers

TL;DR

An implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models.

Abstract

In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubits requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, the ensembles have turned out to be able to mitigate both unsuitable data normalizations and repeated measurement inaccuracies, making quantum classifiers more stable.

Figures (12)

• Figure 1: High-level view of the interaction between classical and quantum components in the proposed hybrid scheme.
• Figure 2: Quantum circuit example for the quantum cosine classifier (a), the quantum distance classifier (b), and the quantum $k$-NN classifier; the dataset and the test instance considered are $X = \{([1, 0, 0, 0], -1), ([0, 1, 0, 0], -1), ([0, 0, 1, 0], 1), ([0, 0, 0, 1], 1)\}$ and $x = [1,0,0,0]$, respectively.
• Figure 3: Accuracy comparison for the bootstrap technique, varying the number of internal classifiers $N$ (left) and the number of training samples for each classifier $S$ (right) while keeping fixed the other parameter ($S=6$ in the left plot, $N=30$ in the right plot). Each box contains 990 points, with each data point being the accuracy obtained in a run on a certain dataset by a combination of quantum classifier and normalization technique.
• Figure 4: Accuracy comparison for the boosting technique, varying the number of internal classifiers $N$ (left) and the number of training samples for each classifier $S$ (right) while keeping fixed the other parameter ($S=6$ in the left plot, $N=30$ in the right plot). Each box contains 990 points, with each data point being the accuracy obtained in a run on a certain dataset by a combination of quantum classifier and normalization technique.
• Figure 5: Accuracy achieved by local simulation with 8192 shots, for all combinations of ensemble, base classifier, and data normalization technique. Each box contains 110 points (one for each run on each dataset).