# A Statistical Model for Identifying Potential Defects in Quantum Computers

## A Spanish student’s internship in Bilbao, Spain, has led to a paper where the author claims to have helped create a universal model that can predict the number distribution of topological defects in non-equilibrium systems.

Unfortunately, it’s all too common that internships, even at the most prestigious institutions and companies, lead to nothing of note. Most of the time, they have exaggerated HR exercises. However, that was not the case for Jack Mayo, a master’s student in nanoscience at the University of Groningen. He claims to have created a universal model that can help predict the distribution number of topological defects in non-equilibrium systems.

### Solving a Big Challenge in Quantum Computing

The study was conducted to solve a significant challenge in quantum computing. Still, it has much broader implications in other areas such as nanoscale magnets and, due to its roots in theoretical physics, for the Universe itself. In all these systems, the onset of order, such as that induced by cooling, is almost always accompanied by defects. *“Take a system in which particles have a magnetic moment that can flip between up and down. If you increase their attractive interaction, they will start to align with each other,”* Mayo explains.

This alignment will begin at uncorrelated points in a medium and then grow uncontrollably, much like ice crystals in water. Each alignment (for example, “up” or “down” for magnetic moments) is a matter of random chance. Local alignments will grow outwards, and at a certain stage, domains will meet and interact. If, for example, an up domain meets a down one, the result will be a domain wall at their interface. This is a symmetry-breaking defect in the ordered structure and leaves behind an artifact of the material in its higher-symmetry phase.

This annealing of a medium is described by the Kibble-Zurek mechanism, originally designed to explain how a phase transition resulted in ordered structures in the early Universe. It was subsequently discovered that it could be used to describe the transition of liquid helium from a fluid to a superfluid phase. It is a universal method and is used in quantum computing based on quantum annealing. *“This technology is already on the market and can solve complex puzzles such as the traveling salesman problem. However, a problem with this type of work is that defects that occur during the annealing process will distort the results,”* said Mayo.

*A model detailing how quantum defects can be detected in energy phases. In the case displayed in the model, a straight-chain decay into a zig-zag when the anisotropy passes a critical value. Where two consecutive ions fall onto the same side, a state of higher energy locally, we can observe a defect. Image credited to Fernando Gómez-Ruiz*

### Developing the Statistical Model

Any number of defects can show up in quantum annealing; it is mostly down to the time taken to pass the phase transition. If it takes place over millions of years, interactions slowly change and you do not get defects.

This, of course, is not very practical. As Mayo put it, the trick is in designing finite-time schedules that are inherently more practical. This results in an acceptable number of defects with high probability. This is what Mayo’s research focused on—creating a model that could accurately estimate the number of defects and guide the design of optimized quantum systems.

To achieve this, Mayo and his team used theoretical tools to describe phase transitions. These were coupled up with numerical simulations to estimate the defect distribution during cooling. Since each domain can only have one of two values (in this case, “up” or “down”), the team could estimate the chances of two opposite domains meeting and thus creating a defect. This led to a statistical model that could predict how a system should be cooled to result in the fewest number of defects.

Verified against independent numerical simulations, the statistical model could have considerable ramifications in quantum computing and lead to more robust and better-optimized systems.

0 Comments