Advancements in quantum computing have increased the expectation for its future influence in real-world applications. However, how will quantum computers impact machine learning? Significant efforts are being undertaken to examine the use of quantum computing in machine learning, as it might provide a quantum edge in the NISQ era. Furthermore, the application of enhancement techniques may help improve the training methods of the present classical models. Yet another technique uses quantum models to create correlations between difficult to describe variables by classical computation (for example, quantum neural networks).
Quantum computers can handle correlations and input complexities well beyond those of a ‘classical’ computer, and this has been proved recently through numerous researches. A recent example is the collaboration between the Institute for Quantum Computing (IQC) and the University of Innsbruck. They have proposed an efficient computing method for pairing the reliability of a classical computer with the strength of a quantum system. It shows that quantum computer learning models can be considerably stronger for selective applications– quicker processing and greater generalisation of fewer data, or both. With the rapid development of quantum technologies, it becomes crucial to understand which applications can profit from the power of these devices.
In a recently published article titled ‘Power of data in quantum machine learning’, published in Nature Communications, researchers analyse the problem of quantum advantage in machine learning. In the paper, researchers have tried to illustrate quantitatively how the complexity of a problem varies formally with the availability of data and how that is sometimes able to increase the competitiveness of traditional learning models with quantum methods. Although the quantum circuits generating the data are difficult to compute traditionally, the data can elevate classical models to rival quantum models.
Firstly, they demonstrated how classical algorithms with data could match quantum output. Following that, they presented rigorous prediction error bounds for training classical and quantum machine learning algorithms based on kernel functions to learn quantum mechanical models. They took these steps because kernel methods provide verifiable guarantees and are also highly versatile in terms of the functions they can learn.
(source: Power of data in quantum machine learning – Scientific Figure on ResearchGate)
Power of data
The concept of quantum advantage over a traditional computer is sometimes expressed in terms of computational complexity classes. Factoring big numbers and modelling quantum systems are examples of Bounded Quantum Polynomial (BQP) time problems expected to be easier for quantum computers to handle than classical systems. On the other hand, bounded probabilistic polynomial (BPP) problems are easily solved on traditional computers.
The researchers demonstrated that learning algorithms equipped with data from a quantum process, such as fusion or chemical reactions, form a new class of problems called BPP/Samp that can efficiently perform tasks that traditional algorithms without data cannot. It is a subclass of problems efficiently solvable with polynomial sized advice (P/poly). This illustrates that comprehending the quantum advantage for various machine learning tasks necessitates an analysis of accessible data as well.
Projected Quantum Kernel
Quantum machine learning is frequently divided into two parts– a quantum embedding of the data (an embedding map for the feature space using a quantum computer) and evaluating a function applied to the data. A procedure was created for assessing the possibility for advantage within a kernel learning framework. The most potent and instructive of which was the creation of a new geometric test. A geometric proof showed that existing quantum kernels had easier geometry that fostered memorising instead of understanding.
This inspired to development of a projected quantum kernel in which the quantum embedding is projected back to a classical representation. While this representation is still difficult to compute directly with a conventional computer, it has several practical advantages over remaining entirely in the quantum space.
(Source:Power of data in quantum machine learning. Nature Communications. 12. 10.1038/s41467-021-22539-9)
Overall, the fundamental contribution of the research is the invention of quantum kernels and the construction of a handbook that generates machine learning problems with a considerable separation between quantum and classical models. The usage of prediction error bounds quantifies the difference in prediction errors between quantum and classical machine learning models for a given quantity of training data.
Typically, the comparison is based on the geometric difference specified by the nearest efficient classical machine learning model; however, in practice, one should consider the geometric difference concerning a suite of optimised classical machine learning models. When the geometric difference is minor, a traditional machine learning method is guaranteed to deliver equivalent or higher performance prediction on the data set, regardless of function values or labels. When the geometry differs significantly, a data set displays a significant prediction advantage when employing the quantum machine learning model.
The research demonstrates that the availability of data profoundly changes the question when assessing the capabilities of quantum computers to aid in machine learning. While a comprehensive computational advantage on a real-world application needs to be observed, this research lays the groundwork for the future.
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Ritika Sagar is currently pursuing PDG in Journalism from St. Xavier's, Mumbai. She is a journalist in the making who spends her time playing video games and analyzing the developments in the tech world.