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Quantum computer simulates spontaneous symmetry breaking at zero temperature

For the first time, an international team of scientists has experimentally simulated spontaneous symmetry breaking (SSB) at zero temperature using a superconducting quantum processor. This achievement, which was accomplished with over 80% fidelity, represents a milestone for quantum computing and condensed matter physics.

The results are in the journal Nature Communications.

The system began in a classical antiferromagnetic state, in which particles have spins that alternate between one direction and the opposite direction. It then evolved into a ferromagnetic quantum state, in which all particles have spins that point in the same direction and establish quantum correlations.

"The system began with a flip-flop configuration of alternating spins and evolved spontaneously, reconfiguring itself with spins aligned in the same direction. This phase transition is due to symmetry breaking," summarizes Alan Santos, a physicist currently researching at the Institute of Fundamental ÌÇÐÄÊÓƵics of the Spanish National Research Council (CSIC) and co-organizer of the theoretical team involved in the study.

At the time the work was developed, Santos was a FAPESP postdoctoral fellow at the Department of ÌÇÐÄÊÓƵics of the Federal University of São Carlos (UFSCar) in the state of São Paulo, Brazil. The research was conducted by scientists from the Southern University of Science and Technology in Shenzhen, China; Aarhus University in Aarhus, Denmark; and UFSCar.

"The crucial point was simulating dynamics at zero temperature. There had already been previous studies on this type of transition, but always at temperatures other than zero. What we showed was that by setting the temperature to zero, it's possible to observe symmetry breaking even in local particle interactions, between first neighbors," says Santos.

It is worth remembering that absolute zero cannot be physically achieved, because it is equivalent to the total immobility of a material system. The researchers simulated what would happen to the system at zero temperature through quantum computing. The experiment used a quantum circuit of seven qubits arranged in a configuration that allows interactions only between immediate neighbors. They applied an algorithm to simulate adiabatic evolution at zero temperature.

"We designed the circuit, and the experimenters in China implemented it physically," says Santos.

The phase transition was identified using correlation functions and Rényi entropy, which revealed the formation of ordered patterns and quantum entanglement. Entanglement is one of the most important and distinctive properties of quantum mechanics. It refers to a situation in which two sets of particles are correlated such that the state of one particle instantly determines the state of another, even if they are separated by large distances.

Introduced by Hungarian mathematician Alfréd Rényi (1921–1970) in the 1960s, Rényi entropy is used to quantify the degree of entanglement and its distribution among parts of a quantum system. It allows us to measure the degree to which the subsystems are entangled.

Santos points out that entanglement and superposition are two central features of quantum computing: "Superposition allows a system to exist in multiple states simultaneously, called quantum parallelism. Entanglement is a type of correlation that cannot be reproduced on classical computers.

"To give you an intuitive idea, imagine you have a bunch of keys and need to find out which one opens the lock. A classical computer tests the keys one by one. A quantum computer, on the other hand, can test several of them at the same time, which speeds up processing," explains Santos.

In practical terms, the difference between a classical computer and a quantum computer comes down to performance. Both can solve the same mathematically formulable problems in theory. The question is how long it takes them to do so. Some calculations, such as factoring huge numbers into two prime numbers, would take classical computers millions of years but can be performed much faster on quantum computers.

It would be counterintuitive to use a classical computer to simulate quantum systems. Sometimes it is an impossible task. The study in question showed that it is possible to use quantum computing resources for such simulations.

The experiment was conducted at the Southern University of Science and Technology in Shenzhen. Shenzhen is currently one of the most advanced scientific, technological, and industrial hubs on the planet. Selected in 1980 as China's first "special economic zone," the city has evolved from a fishing village of about 30,000 people into a metropolis of over 17 million. It is home to giant companies that lead the global market.

The implementation used superconducting qubits based on aluminum and niobium alloys that operate at temperatures around one millikelvin. "The advantage of superconducting qubits is their scalability. It's technically possible to build chips with hundreds of them," says Santos.

The concept of symmetry breaking is present in all areas of physics. All of physics is structured around symmetries and their breaking.

"Symmetry gives us the laws of conservation. Symmetry breaking allows complex structures to emerge," says Santos.