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Quantum Simulations of Gauge Theories
Last Updated: 2026-06-03 00:07:40
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
Does not take place this semester.
|
No time listed | 2 h weekly |
| exercise |
Quantum Simulations of Gauge Theories
Does not take place this semester.
|
No time listed | 1 h weekly |
Offered In
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Electives (In the ‘electives’ subcategory, at least two course units must be successfully completed. All courses listed as core courses (not electives) for one of the following ETH MSc programmes, MSc Statistics, MSc Physics, MSc Computer Science, MSc (Applied) Mathematics, MSc Neural Systems and Computation, MSc Robotics, Systems, and Control, MSc Data Science, MSc Electrical Engineering and Information Technology, can be taken as an elective course in the MSc CSE without prior permission.)
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Doctorate Physics (More Information at: )
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Subject Specialisation (Please note that this is an INCOMPLETE list of courses.)
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