Kernel methods for machine learning are widely used in pattern recognition and classification tasks. However, when a feature space becomes too large, computation of the kernel function becomes prohibitively expensive for classical computers. Quantum computers can perform computations in extremely large spaces, so what if we map our data into a quantum-enhanced feature space? In a paper recently published in Nature, IBM researchers propose using two quantum algorithms based on superconducting processors to provide a novel solution to classification problems.
Synced invited Maria Schuld, a researcher at Xanadu Quantum Computing and post-doc at the University of KwaZulu-Natal in South Africa, to share her thoughts on supervised learning with quantum-enhanced feature spaces.
Could you introduce quantum-enhanced feature space?
In the context of quantum machine learning, where researchers ask how quantum computers can enhance data mining, “quantum-enhanced” usually refers to algorithms that are improved by resources from quantum information processing. Oftentimes, this is done in a hybrid fashion: A small part of the algorithm is outsourced to quantum hardware, and the overall quantum-classical algorithm is in some sense better than a purely classical algorithm.
As many readers will know, the term “feature space” stems from the theory of kernel methods in machine learning. Here data gets implicitly mapped to a “proxy space” where it is represented by feature vectors. In such a feature space, patterns in data may become easier to find.
Put together, quantum-enhanced feature spaces would describe data analysis in a feature space that is the state space of a quantum system, such as a quantum computer. Other terms proposed for this idea are “quantum kernels” or “quantum feature maps” (Schuld and Killoran 2019, Phys. Rev. Lett. 122(4)).
Why does this research matter?
The idea of quantum feature spaces opens up new avenues of using near-term quantum technologies for machine learning. A rather simple exercise for a quantum computer, namely embedding information into a quantum state and then measuring an overlap (i.e., the similarity) with another quantum state, is sufficient to compute a “quantum kernel”. Such a kernel is a measure of similarity for data points in this quantum feature space. As much as quantum computing is expected to be faster for some computations, we expect there to be quantum kernels that are inefficient or even impossible to compute with classical hardware.
On the other hand, the idea also shows a new avenue for innovation in machine learning. Hardware-inspired algorithms, which are by definition very efficient to implement in physical devices, may be the next step in artificial intelligence. And if we speak of quantum hardware, some of the results may be very different from the algorithms known today.