[Paper Review] Tensor networks for High Energy Physics: contribution to Snowmass 2021

Yannick Meurice, Xiao-Yong Jin+4 more|arXiv (Cornell University)|Mar 9, 2022

Computational Physics and Python Applications4 citations

TL;DR

This paper advocates for tensor network methods—particularly Tensor Lattice Field Theory (TLFT)—as a promising alternative to Monte Carlo simulations in high-energy physics, especially for solving sign problems in lattice QCD. By reformulating field theories using translationally invariant tensors that preserve symmetries, TLFT enables classical and quantum simulations of strongly correlated systems, offering a path toward first-principles calculations in four-dimensional quantum field theories.

ABSTRACT

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.

Motivation & Objective

• Address the limitations of Monte Carlo methods in high-energy physics, particularly the sign problem in strongly interacting systems.
• Develop tensor network-based formulations of lattice field theories that preserve local and global symmetries.
• Enable mapping of quantum field theories onto quantum hardware for simulation using digital circuits or analog simulators.
• Advance classical simulation of quantum circuits to test and optimize quantum algorithms for near-term NISQ devices.
• Establish a roadmap for applying tensor networks to quantum chromodynamics (QCD) and other non-perturbative HEP problems within the next decade.

Proposed method

• Reformulate lattice gauge theories using translationally invariant, local tensors as building blocks of exact path integral discretizations.
• Use tensor network contractions and decompositions (e.g., PEPS, MERA) to represent and compute quantum states and amplitudes efficiently.
• Implement truncations that preserve gauge and global symmetries, ensuring the correct universal continuum limit is maintained.
• Map lattice field theories to quantum circuits or analog quantum simulators using tensor network representations.
• Perform classical simulations of quantum circuits via tensor networks to test algorithms without full state-vector storage.
• Leverage high-performance computing (HPC) and software development to validate and scale tensor network methods for complex 4D theories.

Experimental results

Research questions

• RQ1 Can tensor network methods provide a viable alternative to Monte Carlo simulations in lattice QCD, particularly in the presence of sign problems?
• RQ2 How can tensor networks be used to systematically preserve gauge and global symmetries in discretized field theories?
• RQ3 What is the optimal way to map lattice field theories onto quantum hardware using tensor network representations?
• RQ4 How can tensor networks enable efficient classical simulation of quantum circuits relevant to HEP applications?
• RQ5 What are the key methodological and software developments needed to make tensor networks competitive with Monte Carlo in 4D quantum field theories?

Key findings

• Tensor Lattice Field Theory (TLFT) provides a new, symmetric, and general framework for formulating lattice field theories using local, translationally invariant tensors that encode both local and global symmetries.
• Tensor network methods avoid statistical sampling and thus offer a potential solution to the sign problem that plagues traditional Monte Carlo approaches in HEP.
• Truncations in tensor networks can be designed to preserve symmetries generically, ensuring that the universal continuum limit of the original theory is retained.
• TLFT enables a smooth connection between Lagrangian and Hamiltonian formulations and supports both classical and quantum simulation of quantum field theories.
• Classical simulations of quantum circuits using tensor networks allow for efficient testing and development of quantum algorithms, especially for NISQ-era devices.
• The application of tensor networks to QCD-related problems is feasible in the next decade, but requires significant investment in HPC, software, and interdisciplinary collaboration.