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Particle physics, as well as many relevant phenomena in condensed matter, is described by the so-called gauge theories, characterized by the presence of local non-Abelian symmetries. Some of these theories, such as quantum chromodynamics – the theory of strong interactions that explains the existence and properties of hadrons like protons and neutrons – are strongly coupled and must be studied numerically through lattice gauge theory, an approach in which space-time is described by a network of discrete values, often using the Monte Carlo method (a widely used mathematical tool for solving complex problems). However, this method has different limitations, such as the so-called sign problem and critical slowing down.

With the development of quantum technologies, researchers around the world are considering the use of quantum computers and quantum-inspired algorithms to complement Monte Carlo methods, to shed light on the mechanism of confinement of quarks – the constituents of protons and neutrons – and on hadron collisions, which produce the so-called quark-gluon plasma.

Despite the first promising results in models in one spatial dimension, the presence of local non-Abelian symmetries has so far been a formidable obstacle, even for proposing the study of models in two and three spatial dimensions, such as quantum chromodynamics, using quantum computers and methods. Although there already exist approximations that can overcome these difficulties in certain regimes, to connect lattice simulations with the real world – which is continuous – it is essential to have methods that work across the full range of coupling constant values.

Our work presents a method that overcomes this obstacle and allows for the simulation of high-energy physics theories across all coupling regimes. The proposal is based, on one hand, on a reformulation of gauge theory directly in terms of invariant states under local symmetry and, on the other hand, on an optimal representation of these states that minimizes the computational resources required for the simulation.

The proposal has been successfully applied to a non-Abelian gauge theory known as SU(2) gauge theory. Numerical results show that, with a very small number of resources – such as those available in current quantum computers – it is possible to obtain highly precise, physically relevant information. 

Our theoretical work, carried out by the researchers Pierpaolo Fontana and Marc Miranda-Riaza under the supervision of Alessio Celi, has recently been recognized through its publication in Physical Review X, a multidisciplinary, peer-reviewed scientific journal that features high-impact studies, as it enables the study of hadrons using quantum computers.