Abstract
Quantum machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by these developments, we present an embedding-based framework for supervised learning with trainable quantum circuits. We introduce both explicit and implicit approaches. The aim of these approaches is to map data from different classes to separated locations in the Hilbert space via the quantum feature map. We will show that the implicit approach is a generalization of a recently introduced strategy, so-called \textit{quantum metric learning}. In particular, with the implicit approach, the number of separated classes (or their labels) in supervised learning problems can be arbitrarily high with respect to the number of given qubits, which surpasses the capacity of some current quantum machine learning models. Compared to the explicit method, this implicit approach exhibits certain advantages over small training sizes. Furthermore, we establish an intrinsic connection between the explicit approach and other quantum supervised learning models. Combined with the implicit approach, this connection provides a unified framework for quantum supervised learning. The utility of our framework is demonstrated by performing both noise-free and noisy numerical simulations. Moreover, we have conducted classification testing with both implicit and explicit approaches using several IBM Q devices.
Highlights
Quantum computation has been intensively studied over the past few decades and is expected to outperform its classical counterpart in certain computational tasks [1,2,3]
We argue that previous traditional quantum classification methods [15,27,28,29] essentially achieve a certain well separation of data points, which implies that quantum classification models could be conceptually merged into a common framework
In our framework for quantum supervised learning, the main conceptual tool of our method is the idea that the input data x are “forwarded” to the classifying vector f, and their classification can be done
Summary
Quantum computation has been intensively studied over the past few decades and is expected to outperform its classical counterpart in certain computational tasks [1,2,3] In this novel approach for computation, information is stored in the quantum states of an appropriately chosen and designed physical system, which resides in a complex Hilbert space H, and quantum bits (qubits) are used as the underlying building blocks and processing units. ML has been successful in computer vision [8,9,10], natural language processing [11], and drug discovery [12] Building on this history, a natural application of quantum computers may provide substantial speedup [13,14,15,16].
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