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402-0836-16L 6 Credits DR , MSC D-MATH , D-PHYS
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Quantum Simulations of Gauge Theories

Lecturers & Examiners: Prof. Dr. Marina Krstic Marinkovic, Dr. Joao Carlos Pinto Barros
VVZ CR n/a

Last Updated: 2026-06-01 11:31:00

Abstract

Divided into three parts, the course introduces various aspects of lattice quantum field theory (QFT), gauge symmetries, quantum simulators, and implementation schemes. Other than highlighting the strengths and weaknesses of the lattice formulation of QFTs suitable for Monte Carlo simulations, the course discusses practical realization of quantum simulators for gauge theories.

Objective

After acquiring the foundations on lattice formulation of gauge theories, and challenges of conventional Monte Carlo simulation approaches, the students will learn about different strategies for quantum simulation of gauge theories and their implementation on digital and analog quantum devices.

Content

1. Background and Motivation 1.1 From Quantum Field Theories to Lattice field theories; 1.2 Lattice Gauge Theories - Lagrangian formulation, gauge symmetries, observables; 1.3 Monte Carlo simulations, sign problems, and complex actions. 2. Road-map for Quantum Simulation of Gauge Theories 2.1 Hamiltonian formulation, Wilson’s formulation, and the infinite Hilbert spaces; 2.2 Finite Hilbert spaces: Z(N) gauge theories. Dualizing the Ising model and relation with the toric code; 2.3 Finite Hilbert spaces: Quantum link models for Abelian gauge theories; 2.4 Finite Hilbert spaces: Quantum link models for non-Abelian gauge theories; 2.5 Exploring the physics of gauge theories - phases, dynamics, and thermalization; 2.6 Exploring methods for gauge theories - exact diagonalization, tensor networks, Monte Carlo. 3. Quantum Simulation Approaches and Platforms 3.1 Digital vs. analog quantum simulations; 3.2 Proposals for simulations of gauge theories, realization, and perspectives.

Resources

Literature

Quantum chromodynamics on the lattice (Christof Gattringer, Christian B. Lang. Series Title: Lecture Notes in Physics. DOI: https://doi.org/10.1007/978-3-642-01850-3 ) From Quantum Link Models to D-Theory: A Resource Efficient Framework for the Quantum Simulation and Computation of Gauge Theories, U. J. Wiese

General Information

Language
English
Levels
DR , MSC
Frequency
Every two years

Examination

Type
graded semester performance

Course Components

Type Title Time & Place Hours
lecture Quantum Simulations of Gauge Theories
  • Fri 09:45-11:30 (HCI H 2.1)
2 h weekly
exercise Quantum Simulations of Gauge Theories
  • Fri 11:45-12:30 (HCI D 8)
1 h weekly

Offered In