Digital lattice gauge theories

Abstract

We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a ${\mathbb{Z}}_3$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.

References in corpus (21)

• Many-Body Physics with Ultracold Gases
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Optical Abelian Lattice Gauge Theories
• Simulating 2+1d Lattice QED with dynamical matter using ultracold atoms
• Gauging quantum states: from global to local symmetries in many-body systems
• Tensor Networks for Lattice Gauge Theories with continuous groups
• Towards Quantum Simulating QCD
• Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Quantum simulation of the Schwinger model: A study of feasibility
• Lattice Gauge Tensor Networks
• Discrete Abelian Gauge Theories for Quantum Simulations of QED
• Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study
• Topological Wilson-loop area law manifested using a superposition of loops
• Half a state, half an operator: a general formulation of stators

Cited by in corpus (10)

• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Gauge Theories with Ultracold Atoms
• Selected topics of quantum computing for nuclear physics
• Local Manipulation and Measurement of Nonlocal Many-Body Operators in Lattice Gauge Theory Quantum Simulators
• ${\mathbb{Z}}_N$ lattice gauge theory in a ladder geometry
• Kibble-Zurek mechanism in quantum link model
• Self-dual criticality in three-dimensional ${\mathbb{Z}}_2$ gauge theory with matter