Quantum Technologies For LAttice Gauge theories (QTFLAG)

In the past decades, quantum technologies have been fast developing from proof-of-principle experiments to ready-to-the-market solutions. Applications in this far-reaching field include for examples quantum sensors for high precision measurements, secure communication systems and quantum simulations. Recently, the study of gauge theories has been recognised as an unexpected field of application of quantum technologies. Gauge theories describe some of the most fundamental and intriguing processes occurring in Nature, ranging from the interaction of elementary particles described by the Standard Model to condensed matter models displaying exotic quantum behaviour such as topological order. Despite being at the heart of our understanding of these fundamental processes, these theories elude most of our investigative approaches whenever dynamics and finite fermionic densities are involved and the infamous sign problem hinders the effectiveness of Monte Carlo methods. Thus, developing novel approaches without such limitations will pave the way to unprecedented research possibilities. This is the projects goal: to develop a new quantum-based sign-problem-free technology to simulate strongly correlated many-body quantum systems and to apply them to the study of gauge theories, ultimately aiming at Quantum Chromodynamics. The results of this project will bring the first generation of quantum simulators to live and will have far reaching consequences in different fundamental and applied fields of science ranging from materials science, quantum chemistry to astrophysics.

Calculations involving quantum particles quickly become intractably complex. Using quantum systems for performing computations i.e., a "quantum computer," circumvents this difficulty: the quantumness of the computing device matches the quantumness of the problem. The quantum interactions of fundamental particles are understood through gauge theories. In 2016, the University of Innsbruck presented the first quantum computation for a gauge theory for particle physics. This experiment was selected by Physics World as one of the "Top 10 breakthroughs in physics in 2016" , but it applied only to a subset of gauge theories. There are two different types, Abelian and non-Abelian gauge theories. Abelian theories describe electrical forces and are not sufficient to explain even something as simple as the nucleus of a hydrogen atom. Non-Abelian theories are needed to explain how baryons such as protons are formed. Simulating non-Abelian matter has been widely recognized by the scientific community as a key challenge to unlocking the potential of quantum simulations of gauge theories. In 2021, QTFLAGs project team achieved the first quantum computation involving non-Abelian matter. Since current quantum computers are small and lack error correction, realizing non-Abelian matter calculations had proven to be too complex prior to this work. The team overcame the challenge by extending their earlier work, and by introducing a new method that identifies parts of a quantum circuit that do not need to be performed quantumly and relegates them to a regular computer. This rendered an experiment on a superconducting quantum computer possible, that demonstrated the conceptual framework for simulating non-Abelian matter by calculating the masses of the lightest hadrons in a one-dimensional benchmarking model. The paper represents the first quantum simulation of a baryon, which cannot exist in Abelian theories. This is a landmark advance: first, it provides the understanding of how non-Abelian matter can be simulated using hybrid quantum-enhanced computing. Second, it demonstrates the power of this framework in a proof-of-concept experiment. Impact: Vast classes of problems in particle physics are insurmountable using traditional approaches, but not for quantum computers. Examples include real-time dynamics (e.g., particle collisions or pair creation), and matter under high density (such as in neutron stars or the early universe). The team's breakthrough results demonstrate the utility of quantum-enhanced computing for our understanding of nature at the most fundamental level, and a practical approach for its realization.