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.

“A core element in the computational speed-ups enabled by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here we propose and experimentally implement two quantum algorithms on a superconducting processor. A key component in both methods is the use of the quantum state space as feature space. The use of a quantum-enhanced feature space that is only efficiently accessible on a quantum computer provides a possible path to quantum advantage. The algorithms solve a problem of supervised learning: the construction of a classifier. One method, the quantum variational classifier, uses a variational quantum circuit1,2 to classify the data in a way similar to the method of conventional SVMs. The other method, a quantum kernel estimator, estimates the kernel function on the quantum computer and optimizes a classical SVM. The two methods provide tools for exploring the applications of noisy intermediate-scale quantum computers3 to machine learning.” (Nature).

Synced invited Dr. 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. (For more on this, check out here.)

What impact might this research bring to the research community?

Just to be clear, quantum machine learning is an emerging discipline. The results may point us towards directions that may not directly yield practical applications for several years yet. In that sense, the idea of quantum feature spaces may guide a new line of research and development with potential future impact, but in the near-term the research ideas still outpace the hardware.

Can you identify any bottlenecks in the research?

A central question is wide open: Where is the “enhancement” of quantum-enhanced feature spaces? Merely being hard to do with classical computers does not make an algorithm worthwhile. The task of the next couple of years will be to find cases in which one can show advantages of this and other quantum machine learning protocols.

This is notoriously difficult. It takes a lot of computational resources to simulate quantum computers on classical hardware, while “real” quantum devices are still small and noisy – more a physical experiment than a industrial-strength machine. Data analysis is therefore limited to proof-of-principle experiments, and even something like the MNIST is out of reach for most benchmarks. On the other hand, mathematical analysis, which has been quantum computing’s tool of choice, easily evades us in machine learning, where most results are empirical. This methodological challenge has to be overcome in order to show quantum enhancements.

Can you predict any potential future developments related to this research?

In my view, what we as researchers have to focus on are domain-related applications. We cannot expect a very special physical setup to be good for any problem in machine learning. We have to understand our quantum algorithms – for example the type of feature spaces quantum devices give rise to – and find the application where these structures are useful. The power of quantum computing may only play a role in real applications of a very certain kind.

One crucial ingredient is to get the “conventional” machine learning community interested in quantum machine learning, and to exchange knowledge to improve the ideas that physicists came up with, to bring them to a different level.

The paper Supervised learning with quantum-enhanced feature spaces is on Nature.

Maria Schuld works at Xanadu, a Toronto-based quantum computing startup, and for the University of KwaZulu-Natal in Durban, South Africa. For over six years her research has been driven by the question of how quantum information could be useful for machine learning. She co-authored the book “Supervised Learning with Quantum Computers” (Springer 2018).

Xanadu builds a photonic quantum computer and is one of the leading companies in quantum machine learning research. The startup recently released the software framework PennyLane (pennylane.ai) which can be used to train real quantum devices to learn from data.

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