Lattice QCD calculations have been conducted using large-scale classical computers based on the Lagrangian formalism of field theory for the past 40 years. On the other hand, the advent of quantum computers has brought increasing attention to first-principles computational methods based on the Hamiltonian formalism compatible with these machines. In this talk, we discuss recent results on how to calculate hadronic properties using the Hamiltonian formalism.
Lattice QCD calculations have been conducted using large-scale classical computers based on the Lagrangian formalism of field theory for the past 40 years. On the other hand, the advent of quantum computers has brought increasing attention to first-principles computational methods based on the Hamiltonian formalism compatible with these machines. In this talk, we discuss recent results on how to calculate hadronic properties using the Hamiltonian formalism.
<!--HTML-->There are many fundamental questions in particle and nuclear physics that cannot be addressed via classical computing techniques. These include the equation of state for finite density nuclear matter, real-time dynamics of quantum field theories from first-principles and non-perturbative aspects of chiral gauge theories. In recent years quantum computing hardware has seen dramatic advancements, which have brought with them the possibility to apply quantum computing to these and other open problems in high energy physics. In this talk, after a brief introduction to quantum computing, I will discuss my recent work towards the quantum simulation of lower-dimensional lattice gauge theories, focusing on the interplay between Gauss’ law, gauge redundancies and (un)favourable resource scaling.
Abstract: Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract:
One goal in understanding quantum chromodynamics (QCD) includes solving how quarks and gluons combine to form the hadrons and nuclei seen in nature. With lattice QCD, progress has been made regarding the calculation of masses and couplings. However, the real-time evolution and the critical behavior at finite density of strong particles in colliders, stars, or after the big bang remain a challenging problem despite their potential to detect the existence of new physics. The tensor methods for lattice field theories provide a route to handle strongly correlated systems across different subfields using renormalization group methods or quantum computing.
This thesis develops advanced Tensor Network (TN) methods to address Hamiltonian Lattice Gauge Theories (LGTs), overcoming limitations in real-time dynamics and finite-density regimes. A novel dressed-site formalism is introduced, enabling efficient truncation of gauge fields while preserving gauge invariance for both Abelian and non-Abelian theories. This formalism is successfully applied to SU(2) Yang-Mills LGTs in two dimensions, providing the first TN simulations of this system and revealing critical aspects of its phase diagram and non-equilibrium behavior, such as a Quantum Many-Body (QMB) scarring dynamics. A generalization of the dressed-site formalism is proposed through a new fermion-to-qubit mapping for general lattice fermion theories, revealing powerful for classical and quantum simulations. Numerical innovations, including the use of optimal space-filling curves such as the Hilbert curve to preserve locality in high-dimensional simulations, further enhance the efficiency of these methods. Together with high-performance computing techniques, these advances open current and future development pathways toward optimized, efficient, and faster simulations on scales comparable to Monte Carlo state-of-the-art.
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum chromodynamics. Yet, some very relevant problems remain inherently challenging, such as real time evolution, or the presence of a chemical potential, cases in which Monte Carlo simulations are hindered by a sign problem. In the last few years, a number of possible alternatives have been put forward, based on quantum information ideas, which could potentially open the access to areas of research that have so far eluded more standard methods. They include tensor network calculations, quantum simulations with different physical platforms and quantum computations, and constitute nowadays a vibrant research area. Experts from different fields, including experimental and theoretical high energy physics, condensed matter, and quantum information, are turning their attention to these interdisciplinary possibilities, and driving the progress of the field. The aim of this article is to review the status and perspectives of these new avenues for the exploration of lattice gauge theories.
Abstract Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one long-term goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented – a classical simulation approach – applied to the study of lattice gauge theories together with some results on Abelian and non-Abelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proof-of-principle trapped ions experimental quantum simulations of the Schwinger model are reviewed. Graphical abstract