Tensor network methods are numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories that approach relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. This work reviews the state-of-the-art tensor network methods and discusses a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories. Tensor networks are a powerful complementary approach to Monte Carlo methods for simulating lattice gauge theories, enabling access to challenging regimes such as real-time dynamics and finite-density systems. This work reviews the state of the art, outlines a roadmap for algorithmic developments, and provides resource estimates to guide large-scale applications in high-energy physics.
Tensor network methods are numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice gauge theories that approach relevant problems in high-energy physics. Compared to Monte Carlo methods, they do not suffer from the sign problem, allowing them to explore challenging regimes such as finite chemical potentials and real-time dynamics. Further development is required to tackle fundamental challenges, such as accessing continuum limits or computations of large-scale quantum chromodynamics. This work reviews the state-of-the-art tensor network methods and discusses a possible roadmap for algorithmic development and strategies to enhance their capabilities and extend their applicability to open high-energy problems. We provide tailored estimates of the theoretical and computational resource scaling for attacking large-scale lattice gauge theories. Tensor networks are a powerful complementary approach to Monte Carlo methods for simulating lattice gauge theories, enabling access to challenging regimes such as real-time dynamics and finite-density systems. This work reviews the state of the art, outlines a roadmap for algorithmic developments, and provides resource estimates to guide large-scale applications in high-energy physics.
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.
Tensor Network States are ans\'atze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation of real time evolution, have turned them into one of the most promising techniques to study strongly correlated systems. In the realm of Lattice Gauge Theories they can offer an alternative to standard lattice Monte Carlo calculations, which are suited for static properties and regimes where no sign problem appears. The application of Tensor Networks to this kind of problems is a young but rapidly evolving research field. This paper reviews some of the recent progress in this area, and how, using one dimensional models as testbench, some fundamental milestones have been reached that may pave the way to more ambitious goals.
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential.So far, there is no universal method to overcome this problem.However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent.In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model.We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics.In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential.We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
Tensor network methods are becoming increasingly important for high-energy physics, condensed matter physics and quantum information science (QIS). We discuss the impact of tensor network methods on lattice field theory, quantum gravity and QIS in the context of High Energy Physics (HEP). These tools will target calculations for strongly interacting systems that are made difficult by sign problems when conventional Monte Carlo and other importance sampling methods are used. Further development of methods and software will be needed to make a significant impact in HEP. We discuss the roadmap to perform quantum chromodynamics (QCD) related calculations in the coming years. The research is labor intensive and requires state of the art computational science and computer science input for its development and validation. We briefly discuss the overlap with other science domains and industry.
Tensor Network States are ansaetze for the efficient description of quantum many-body systems. Their success for one dimensional problems, together with the fact that they do not suffer from the sign problem and can address the simulation of real time evolution, have turned them into one of the most promising techniques to study strongly correlated systems. In the realm of Lattice Gauge Theories they can offer an alternative to standard lattice Monte Carlo calculations, which are suited for static properties and regimes where no sign problem appears. The application of Tensor Networks to this kind of problems is a young but rapidly evolving research field. This paper reviews some of the recent progress in this area, and how, using one dimensional models as testbench, some fundamental milestones have been reached that may pave the way to more ambitious goals.