# From Quantum Links to D-Theory: A Resource Efficient Framework for the Quantum Simulation of Gauge Theories

- Institution: CERN
- Department: TH institutes
- Speaker: Uwe-Jens Wiese
- Year: 2021
- Language: English
- Subjects: Physics, Computer science
- Source: [CERN](https://videos.cern.ch/record/3013558)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

Quantum link models provide an extension of Wilson's lattice gauge theory in which the link variables have operator-valued entries. For example, in a U(1) quantum link model the link variables are raising and lowering operators of quantum spins that belong to a link-based SU(2) embedding algebra. For non-Abelian SU(N), Spin(N), or Sp(N) quantum link models, the embedding algebras are SU(2N), Spin(2N), and Sp(2N), respectively. In contrast to Wilson's framework, quantum link models can be realized in a finite-dimensional link Hilbert space corresponding to a representation of the embedding algebra. This is well suited for a resource efficient implementation of quantum link models in quantum simulation experiments. The quantum link dynamics can be embodied with a finite number of well-controlled states of ultra-cold matter, including atoms in an optical lattice, ions in a trap, or quantum circuits. For example, using dual variables, a densely encoded quantum circuit has recently been constructed for a (2+1)-d U(1) quantum link model on a triangular lattice that shows qualitatively new nematic phases with rich confining dynamics. Quantum spins and quantum links are discrete quantum variables which give rise to collective low-energy excitations. In (2+1)-d, SU(N) quantum spins give rise to massless Goldstone bosons which undergo dimensional reduction to (1+1)-d asymptotically free CP(N-1) models. This can be realized in quantum simulation experiments with alkaline-earth atoms in an optical lattice. In (3+1)-d, Abelian quantum links give rise to massless photons which undergo dimensional reduction to (2+1)-d confining U(1) gauge theory, which can be embodied with spin-ice. In (4+1)-d, non-Abelian quantum links give rise to massless gluons which undergo dimensional reduction to (3+1)-d Yang-Mills theory. Quarks are naturally included as domain wall fermions. The dimensional reduction of discrete quantum variables defines D-theory, in which quantum field theories emerge…

## Lectures

1. [From Quantum Links to D-Theory: A Resource Efficient Framework for the Quantum Simulation of Gauge Theories](https://invisiblenetwork.ai/learn/cern/3013558/a8879df5a325), 1 h 14 min (CERN's player)