Quantum computers could revolutionize information theory

New prospects for storage and data transfer are discussed during an event by the São Paulo School of Advanced Science program.

By Diego Freire

Agência FAPESP – The prospect of quantum computing, which will offer higher processing capacity than that available from today’s computers, has led to advances in information theory, one of the most versatile fields of scientific research, with applications in a wide variety of knowledge areas. An event called SPCoding School was held in São Paulo State, Brazil, on January 19-30 to discuss this and other prospects. It was organized by the Mathematics, Statistics & Scientific Computation Institute (IMECC) of the University of Campinas (UNICAMP).

The event took place under the aegis of FAPESP’s São Paulo School of Advanced Science (SPSAS) program, which offers funds for the organization of short courses on advanced topics in science and technology in São Paulo State.

The information that is processed by the most widely used computers is made up of bits. A bit (short for binary digit) is the smallest unit of data that can be stored or processed by a computer. A quantum bit, or qubit, is the equivalent in quantum computing, which is based on quantum mechanics, a branch of physics that addresses physical phenomena close to or below the atomic scale. Quantum computers will be able to perform a far greater number of simultaneous calculations than conventional computers.

“The quantum-based view of information makes coding extremely complex,” said Sueli Irene Rodrigues, a professor at IMECC. “Although a complex analysis that would take an ordinary computer decades, centuries or even millennia to process could be completed in minutes by a quantum computer, this technology would also threaten the confidentiality of information not properly protected against this kind of innovation,” she told Agência FAPESP.

The greatest threat from quantum computing to today’s cryptography is its ability to break the codes used to protect important information such as credit card data. To prevent this from happening, it will be necessary to develop much more secure encryption systems that recognize the processing capacity of quantum computers. “Information theory and coding must stay a step ahead of the commercial use of quantum computing,” said Rodrigues Costa, one of the lead investigators for the Thematic Project “Security and reliability of Information: theory and practice”, supported by FAPESP.

“What we’re talking about is post-quantum cryptography. As long ago as the late 1990s, it was demonstrated that current encryption procedures won’t outlast the advent of quantum computing because they aren’t secure enough. The urgent need to develop quantum computing-ready solutions is also increasingly driving information theory forward in several directions,” Rodrigues Costa said.

Some of these solutions were addressed at the SPCoding School. Many of them are designed to produce more efficient systems for classical computing applications, such as error-correcting codes and lattices for cryptography. For Rodrigues Costa, the ascent of information theory alongside the development of quantum computing will revolutionize several knowledge areas.

“As with the multiple applications of information theory today, quantum coding would also take several areas of science to higher levels by enabling even more precise computational simulations of the physical world and dealing with an exponentially larger number of variables compared with classical computing,” Rodrigues Costa said.

Information theory is a branch of applied mathematics, electrical engineering, and computer science involving the quantification of information. It was pioneered by American engineer and mathematician Claude Shannon (1916-2001), the first person to treat communication as a mathematical problem.

Ongoing revolutions

While preparing for quantum computers, information theory is making significant changes to information coding and transmission. Amin Shokrollahi, a professor at EPFL, the Swiss Federal Institute of Technology in Lausanne, attended the SPCoding School, where he presented new coding techniques to solve such problems as noisy channels in data transfer and high energy consumption in data processing, including chip-to-chip communication inside a device.

Shokrollahi is well known in the field as the inventor of Raptor codes and the co-inventor of Tornado codes, which are used in mobile and satellite communications, with implementations in wireless systems and the delivery of digital television content over IP networks (IPTV).

“Growing volumes of digital data and the need for ever-faster communication increase the susceptibility of these systems to various kinds of noise and higher power consumption to combat the noise. New solutions are needed to solve these problems,” Shokrollahi said.

Shokrollahi also presented innovations developed by Kandou Bus, a Swiss company where he is head of research. “We use special algorithms to encode signals, which are all transferred simultaneously until a decoder retrieves the original signals. All this is done without allowing adjacent wires to interfere with each other, so that the noise levels generated are significantly lower. The systems also reduce chip size, increase transfer rates and reduce power consumption,” he explained. According to Rodrigues Costa, similar solutions are also being developed for several technologies in widespread societal use.

“Cell phone processing capacity and versatility have increased significantly, for example, but users frequently complain that batteries run low too quickly. One strategy is to discover ways of coding more efficiently to save power,” she said.

Biological applications

Information theory is not only useful for addressing or solving technological problems. The SPCoding School culminated in a panel session entitled “Information Theory, Coding Theory and the Real World”, where participants discussed the various uses of coding throughout society, including biological applications. The session was chaired by Vinay Vaishampayan, a professor at City University of New York (CUNY) in the United States.

“There isn’t only one information theory. All kinds of approaches, from computational to probabilistic, can be applied to practically every knowledge area. The panel session discussed the many research opportunities available to anyone interested in studying these interfaces between codes and the real world,” Vaishampayan told Agência FAPESP.

One knowledge area with outstanding potential in this respect is biology. “Neuroscience presents important questions that can be answered with the aid of information theory. We don’t yet know very much about how neurons communicate with each other or about how the brain works in all its plenitude. Neural networks are a very rich field of study from the mathematical standpoint. So is molecular biology,” Vaishampayan said.

This is because living beings are made of information, added Max Costa, a professor at UNICAMP’s School of Electrical Engineering & Computing and one of the speakers at the SPCoding School.

“We humans are encoded by the DNA in our cells. Discovering the secret of this code, the mechanism underlying the maps made and recorded in this context, is a problem of enormous interest for a deeper understanding of life as a process,” Costa said.

For Marcelo Firer, a professor at IMECC and coordinator of the SPCoding School, the event opened up new research opportunities for students and researchers in several fields.

“The participants shared opportunities for engagement with these and many other applications of information theory and coding,” Firer said. “The offering ranged from introductory courses for students with a consistent background in mathematics but not necessarily familiar with coding, to more complex courses, presentations and panel sessions.”

The event was attended by some 120 students from 70 universities and 25 countries. Foreign speakers included researchers from the California Institute of Technology (Caltech) and the University of Maryland in the United States, the Chinese University of Hong Kong in China, Nanyang Technological University in Singapore, Eindhoven University of Technology in the Netherlands, the University of Porto in Portugal, and Tel Aviv University in Israel.

More information can be found at www.ime.unicamp.br/spcodingschool.