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Machine learning unlocks mysteries of quantum physics

Understanding electrons’ intricate behaviour has led to discoveries that transformed society, such as the revolution in computing made possible by the invention of the transistor.

Today, through advances in technology, electron behaviour can be studied much more deeply than in the past, potentially enabling scientific breakthroughs as world-changing as the personal computer. However, the data these tools generate are too complex for humans to interpret.

A Cornell-led team has developed a way to use machine learning to analyze the data generated by scanning tunnelling microscopy (STM) – a technique that produces subatomic scale images of electronic motions in material surfaces at varying energies, providing information unattainable by any other method.

“Some of those images were taken on materials that have been deemed important and mysterious for two decades,” said Eun-Ah Kim, professor of physics. “You wonder what kinds of secrets are buried in those images. We would like to unlock those secrets.”

Kim is senior author of “Machine Learning in Electronic Quantum Matter Imaging Experiments,” which published in Nature June 19. First authors are Yi Zhang, formerly a postdoctoral researcher in Kim’s lab and now at Peking University in China, and Andrej Mesaros, a former postdoctoral researcher in Kim’s lab now at the Université Paris-Sud in France.

Co-authors include J.C. Séamus Davis, Cornell’s James Gilbert White Distinguished Professor in the Physical Sciences, an innovator in STM-driven studies.

The research yielded new insights into how electrons interact – and showed how machine learning can be used to drive further discovery in experimental quantum physics.

At the subatomic scale, a given sample will include trillion trillions of electrons interacting with each other and the surrounding infrastructure. Electrons’ behaviour is determined partly by the tension between their two competing tendencies: to move around, associated with kinetic energy; and to stay far away from each other, associated with repulsive interaction energy.

In this study, Kim and collaborators set out to discover which of these tendencies is more important in a high-temperature superconductive material.

Using STM, electrons tunnel through a vacuum between the conducting tip of the microscope and the surface of the sample being examined, providing detailed information about the electrons’ behaviour.

“The problem is, when you take data like that and record it, you get image-like data, but it’s not a natural image, like an apple or a pear,” Kim said. The data generated by the instrument is more like a pattern, she said, and about 10,000 times more complicated than a traditional measurement curve. “We don’t have a good tool to study those kinds of data sets.”

To interpret this data, the researchers simulated an ideal environment and added factors that would cause changes in electron behaviour. They then trained an artificial neural network – a kind of artificial intelligence that can learn a specific task using methods inspired by how the brain works – to recognize the circumstances associated with different theories. When the researchers input the experimental data into the neural network, it determined which of the theories the actual data most resembled.

This method, Kim said, confirmed the hypothesis that the repulsive interaction energy was more influential in the electrons’ behaviour.

A better understanding of how many electrons interact on different materials and under different conditions will likely lead to more discoveries, she said, including the development of new materials.

“The materials that led to the initial revolution of transistors were actually pretty simple materials. Now we have the ability to design much more complex materials,” Kim said. “If these powerful tools can reveal important aspects leading to the desired property, we would like to be able to make a material with that property.”

Also contributing were researchers at Brookhaven National Laboratory, Stanford University, Harvard University, San Jose State University, the National Institute of Advanced Industrial Science in Japan, the University of Tokyo and Oxford University.

Materials provided by Cornell University

Quantum network

Establishing the ultimate limits of quantum communication networks

At the moment, sensitive data is typically encrypted and then sent across fibre-optic cables and other channels together with the digital “keys” needed to decode the information. However, the data can be vulnerable to hackers.

Quantum communication takes advantage of the laws of quantum physics to protect data. These laws allow particles—typically photons of light —to transmit the data using quantum bits, or qubits.

Superior capabilities

Multinational corporations, such as IBM and Google, are now building intermediate-size quantum computers with increasing number of quantum units or qubits.

Once they scaled up to larger sizes, these devices will have far-superior capabilities than current classical computers. For instance, they may process extremely large numbers in just a few seconds, speed-up many fundamental mathematical operations, and perfectly simulate molecular and biological processes.

One challenge will be to connect quantum computers together, in order to create a quantum-version of the Internet or " quantum Internet".

However, an important but unanswered question remains: what is the ultimate rate at which one can transmit secret messages or quantum systems from one remote quantum computer to another?

Notoriously difficult

Writing in the journal Communications PhysicsProfessor Stefano Pirandola, from the University of York’s Department of Computer Science, said scientists have answered the question.

Prof Pirandola studied the optimal working mechanism of a future quantum Internet, and also provided the ultimate secret-key capacities that can potentially be achieved.

He said: “Studying quantum networks is notoriously difficult, but recent mathematical tools developed in quantum information theory have allowed us to completely simplify the analysis.

Qubits

“An outstanding question was to compute the maximum number of elementary quantum systems (known as qubits) that could be reliably transmitted from one user of the network to another, or similarly, the maximum number of completely secret bits that these remote users could share.

“This number has now a precise analytical formula.”

Furthermore, the study reveals that the classical-inspired strategy of simultaneously sending qubits through multiple routes of the network can remarkably boost the rate, i.e., the speed of the quantum communication between any two remote users.

Materials required University of York