Machine learning for quantum states in embedding data

Quantum computing to process large quantities of data together with complementary and versatile quantum processors.

Quantum computers are fundamentally different from their classical counterparts, with the potential to solve many problems even faster than the world’s fastest supercomputers.

But a fundamental question within the field is whether quantum computers can overcome the current limitations of standard machine learning algorithms, such as memory and computational resource overloads.

Machine learning is a data analysis technique that, in a sense, mimics the processes of human intelligence as a software learner learns data, identifies patterns, and makes decisions automatically. Nowadays, its applications range from domotic systems to autonomous cars, to face and voice recognition to medical diagnostics.

Quantum computers and machine learning

One is the fields where machine learning may be very efficient and big data processing, where a typical problem is classification – that is, breaking down data into separate categories.

In this type of problems, it is convenient to first achieve a data of geometric representation. For example, if there are only two classes of objects located on a plane, using machine learning, the objects can be arranged in such a way that they are separated by a line where all the points are seated. class. If the objects are defined in a higher dimensional space, the line is replaced by a plane, or its multi-dimensional counterpart known as a hyperplane.

However, the data is not geometrically and its distribution in the original set can be quite erratic, making the division into classes not explicit and hard. In these cases, it is useful to first map (ie, embed) the data into a high-dimensional space where the separator is easier to find and draw.

In a 2020 study, scientists proposed a specific embedding technique that maps the original data into a quantum computer using high-dimensional space. The space, known as a Hilbert space, is used to describe quantum mechanics, and the corresponding map is called the quantum embedding.

To test these theoretical considerations, a team of physicists led by Filippo Caruso, professor at the European Laboratory for Nonlinear Spectroscopy (LENS) and the Department of Physics and Astronomy at Florence University, designed and tested two different engineered experimental quantities. A cloud-available quantum processor is provided by the Rigetti computing company, using platforms and what the results are.

“Quantum computers are not just the most powerful versions of current computers,” said Ilaria Gianani, one of the study’s authors from the Roma Tre University. “They interpret information in radically different ways, and this difference is what makes them ‘look’ patterns that a standard machine could not. This study is aimed to test and compare experimentally a protocol with quantitative data into classical data, where the latter could be processed more efficiently and quickly. ”

Quantum data is much more convenient than the process of machine learning given the original classical data given by exploiting superposition states or quantum parallelism, and properties such as entanglement, that do not exist in the classical domain. But in the new study, even the first step in solving the classification problem, namely the mapping of classical objects into a larger space using a larger quantum technique.

“The embedding of classical data into a series of quantum operations (also called quantum gates) allows for some free parameters that allow ‘learn’ how to represent any classical data and possibly classify them by a higher dimensional space. of more efficient and feasible linear separators, ”explained Lorenzo Buffoni, another of the study’s authors.

Quantum embedding put to the test

The two steps in the application of quantum embedding were: First, the physicists determined the optimal parameters to achieve better quantum embedding and simplifying the data classification problem. This step was done offline as a classical computer with a relatively easy numerical optimization.

Next, the reality of theoretically proposed method of using the latter is to determine how efficient the circuit is for the quantum machines. This two-step scheme is called hybrid quantum computing.

Quantum bits or qubits – Quantum version of bits – Quantum optics, ultracold atoms, and superconducting qubits. The study showed that all the architectures actually gave satisfactory results in realizing quantum embedding.

The fact is that all three quantum systems are based on hybrid architectures that promise very good results, with the benefit of storage, processing, and distribution of quantum data.

“The most significant outcome of our study is that real-world problems with hybrid quantum technologies represent the future of exploiting the different features and advantages of complementary and versatile physics platforms. , and using new algorithms developed in the young but increasingly promising research field of quantum AI and quantum machine learning, ”Caruso added.

Moreover, the advantages of the quantum embedding algorithm include not only the simplification of a classification problem – but also the ability to remarkably speed up any processing of classical data, such as searching through a database, feature extraction, image segmentation, edge detection, and many others, especially in the case of large volumes of data generated in various domains ranging from sociology to economics, to geography to biomedicine.

Reference: Filippo Caruso, et al., Experimental Quantum Embedding for Machine Learning, Advanced Quantum Technologies (2022). DOI: 10.1002 / qute.202100140

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