[Paper Review] Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory

Zohreh Davoudi, Ethan T. Neil+36 more|arXiv (Cornell University)|Sep 22, 2022

Particle physics theoretical and experimental studies8 citations

TL;DR

This Snowmass 2021 report outlines the strategic vision for lattice gauge theory in U.S. high-energy physics, advocating for continued investment in lattice QCD to enable precision calculations of quark masses, the muon g-2, electric dipole moments, and new physics signals in nucleons and nuclei. It emphasizes the integration of exascale computing, quantum simulations, and quantum computing to advance simulations of strongly interacting field theories and to prepare for future discoveries in particle physics.

ABSTRACT

Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report.

Motivation & Objective

• To advance lattice QCD as a cornerstone for precision flavor physics, including the muon anomalous magnetic moment and quark masses.
• To identify and calculate signals of new physics in nucleons and nuclei, such as electric dipole moments and lepton/baryon number violation.
• To prepare for the exascale computing era by improving algorithms, software, and computational frameworks for lattice field theory.
• To integrate quantum computing and quantum simulation into lattice field theory research, leveraging near-term noisy intermediate-scale quantum (NISQ) devices.
• To foster collaboration across academia, national labs, and industry to co-develop specialized hardware and software for lattice field theory and quantum simulations.

Proposed method

• Utilize lattice QCD simulations to compute hadronic matrix elements, quark masses, and strong coupling constants with controlled uncertainties.
• Apply improved actions, improved fermion formulations, and algorithmic advances (e.g., domain decomposition, multigrid solvers) to enhance computational efficiency.
• Develop protocols for preparing nontrivial quantum states and measuring observables such as scattering amplitudes, structure functions, and quantum information measures.
• Map quantum field theories onto analog quantum simulators (e.g., ultracold atoms, trapped ions, photonic systems) using tailored Hamiltonian engineering.
• Benchmark and implement lattice field theory algorithms on near-term NISQ devices to validate theoretical proposals against experimental constraints.
• Co-design special-purpose quantum hardware with industry partners, informed by past successes in HPC co-design for lattice QCD.

Experimental results

Research questions

• RQ1 How can lattice QCD improve precision in the muon anomalous magnetic moment and tau decay amplitudes?
• RQ2 What are the leading-order hadronic contributions to the muon g-2, and how can they be computed with sub-1% uncertainty?
• RQ3 Can lattice QCD calculations of electric dipole moments provide constraints on CP-violating phases in the Standard Model and beyond?
• RQ4 How can lattice simulations probe lepton-number violating processes such as neutrinoless double-beta decay?
• RQ5 What are the optimal quantum algorithms and hardware mappings for simulating QCD and other strongly coupled field theories on near-term quantum devices?

Key findings

• Lattice QCD has achieved sub-1% precision in key observables like the hadronic vacuum polarization contribution to the muon g-2, with ongoing improvements expected to reduce uncertainties further.
• Calculations of electric dipole moments in nucleons and nuclei are now feasible with controlled systematic errors, offering a sensitive probe of CP violation.
• Lattice simulations have provided quantitative evidence for the existence of exotic hadronic states and resonances, including those relevant to proton decay and n–n̄ oscillations.
• Near-term quantum devices are being used to benchmark quantum algorithms for scattering amplitudes and structure functions, with promising results in controlled simulations.
• The transition to exascale computing is expected to enable simulations of full-QCD with physical quark masses and fine lattices, reducing systematic errors.
• Collaborative co-design of quantum hardware and software is essential to meet the computational demands of simulating non-Abelian gauge theories on quantum processors.