Information conservation is perhaps one of the main challenges in the development of quantum computing. In the early 1960s, IBM physicist Rolf Landauer (1927-1999) showed that there is an intimate connection between information and heat. Data processing produces thermal energy, and information is corrupted as a result. Information cannot be stored forever or even for a sufficiently long time.

The great irony is that over the course of history, the development of material substrates and the increase in the amount of information they can hold have been accompanied by a steady loss of durability.

The inscriptions engraved in stone on Egyptian monuments have lasted for thousands of years. Paper books can last several centuries in ideal conditions. Today’s hard disks are expected to have working lives of three to five years, while flash memory sticks, CDs and DVDs last less than a decade. As systems are miniaturized to the quantum scale, this problem will become even more pronounced as energy dissipation in the form of heat increases.

A new study has identified a phenomenon that can enable quantum systems to retain information longer than expected. Albeit developed in the context of pure science with a highly abstract mathematical apparatus, the proposed model offers an idea that could serve as a paradigm for technologists and engineers involved in building components of future quantum computers.

The model is described in an article published in the Journal of High Energy Physics by Pramod Padmanabhan, Soo-Jong Rey, Daniel Teixeira and Diego Trancanelli.

“This study is an example of how ideas that originate in completely different fields can transcend their origins and offer the prospect of unforeseen applications. At the outset we weren’t thinking of quantum computing. Padmanabhan, who was then doing postdoctoral research at the University of São Paulo, was interested in applying an unusual supersymmetry construction to the classification of the phases of matter. I saw the possibility of creating a simple model to try to understand some aspects of quantum gravitation, which is my research field. The way this all developed took us far from the starting point,” said Trancanelli, a professor at the University of São Paulo’s Physics Institute (IF-USP), in an interview with Agência FAPESP.

The study was supported by **FAPESP** as part of the Thematic Project “Gauge/Gravity duality”, by a regular research grant for “High precision tests of the AdS/CFT correspondence”, and by a postdoctoral scholarship for “Applications of Hopf algebras in physics”.

Trancanelli explained that the initial aim was to build a simplified model that could function as an analogue of a black hole – not an astrophysical black hole produced by the gravitational collapse of a high-mass star, but a quantum black hole, a tiny object with which scientists want to establish a theory of quantum gravitation.

“One of the features often attributed to quantum black holes is that they’re chaotic. It’s been thought that any information inserted into a quantum black hole would be ‘forgotten’ in no time at all, faster than anything else in nature,” he said. “However, when we built the simplified model we found that the constraints imposed by supersymmetry are so strong that what happens is actually the opposite. Instead of chaos, what we see is an order in which information isn’t destroyed and wasted, but conserved. We found the opposite of what we were looking for: a system that’s able to preserve information very efficiently.”

This is one of the desired properties of a quantum computer, where information preservation without the so-called “decoherence” that results from interactions between the system and its environment is a fundamental necessity.

“We’re not proposing a quantum memory device. Our research was a pure science project, with no expectations of technological applications, but some of the ideas we developed might ultimately provide useful avenues,” said PhD student Daniel Teixeira, a co-author of the article.

To understand what is at stake in more depth, it is necessary to consider the concept of quantum black holes and what the simplified model under discussion set out to reproduce. A key aspect is the idea of an “event horizon”, a threshold beyond which nothing can return. If a given quantity of matter crosses the event horizon, it is captured by the black hole and cannot be brought back.

In many respects, the event horizon behaves like a membrane. Just as a pebble cast into a pond makes ripples that gradually dissipate, any information that falls into a black hole produces disturbances in the event horizon. The disturbances dissipate very rapidly but scramble the information, which cannot be retrieved. Information scrambling and loss occurs in the system in connection with an increase in entropy.

“What we discovered from our new model is that the constraints of supersymmetry play a role analogous to that of thermal insulators, which delay heat exchange and hence information exchange between the system and the environment. Our model doesn’t reproduce a black hole, which is a far more complex reality. Instead of rapid dissipation, the behavior it displays is prolonged conservation of information – a surprising result, and a very interesting outcome if you’re ultimately thinking about the creation of quantum memory devices,” Trancanelli said.

**Supersymmetry**

Supersymmetry is a mathematical structure proposed by theoretical physicists that has not yet been observed experimentally. In short, the basic idea is that every elementary particle has a supersymmetrical partner equal in energy but statistically different.

In the so-called Standard Model, for example, all particles are fermions or bosons. Fermions are particles with semi-integer spin that obey the Fermi-Dirac statistic – electrons, for example. Bosons are particles with integer spin that obey the Bose-Einstein statistic – photons, for example. Extensions of the Standard Model that include supersymmetry incorporate a boson partner for every fermion and vice-versa.

“Supersymmetry is useful because it makes the theories much simpler,” the researchers explained. “It’s easy to understand this using an analogy. Compare two geometric bodies, a sphere and a cube. Both have symmetry, but the sphere is more symmetrical. How we see a sphere doesn’t depend on our angle of view because it’s symmetrical in all directions, whereas how we see a cube does depend on the angle. So the more symmetrical a system, the simpler the theory needed to describe it. In the case of some quantum systems, such as the one we studied, supersymmetry constrains the theory so much that it becomes solvable. You can calculate it with pen and paper. You don’t need numerical simulations and powerful computers. That’s how we did all our calculations.”

Using the mathematical principles of supersymmetry, Trancanelli and collaborators designed a hypothetical material endowed with a kind of “barrier” that delays information loss. The “barrier” is possible because in the structure of the material, electrons occupy the lower energy levels and no upper levels are available. As a result, the energy exchanged between the system and environment is also minimized.

Ultimately, entropy always wins, and the information is scrambled. However, the information retention time becomes exponentially longer than that of today’s silicon-based memory devices.

Although the material does not yet exist, the idea can be taken up by technologists and engineers involved in developing quantum computers.

Source : **By José Tadeu Arantes | Agência FAPESP**

FAPESP