Eliminating fermionic matter fields in lattice gauge theories

Abstract

We devise a unitary transformation that replaces the fermionic degrees of freedom of lattice gauge theories by (hard-core) bosonic ones. The resulting theory is local and gauge invariant, with the same symmetry group. The method works in any spatial dimensions and can be directly applied, among others, to the gauge groups $G=U(N)$ and $SU(2N)$, where $N\in \mathbb{N}$. For $SU(2N+1)$ one can also carry out the transformation after introducing an extra idle ${\mathbb{Z}}_2$ gauge field, so that the resulting symmetry group trivially contains ${\mathbb{Z}}_2$ as a normal subgroup. Those results have implications in the field of quantum simulations of high-energy physics models.

11 pages, 3 figures

References in corpus (3)

• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Tapering off qubits to simulate fermionic Hamiltonians
• Two-dimensional Lattice Gauge Theories with Superconducting Quantum Circuits

Cited by in corpus (52)

• SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers
• Review on novel methods for lattice gauge theories
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Digitization of Scalar Fields for Quantum Computing
• General Methods for Digital Quantum Simulation of Gauge Theories
• Search for Efficient Formulations for Hamiltonian Simulation of non-Abelian Lattice Gauge Theories
• Gluon Field Digitization for Quantum Computers
• A resource efficient approach for quantum and classical simulations of gauge theories in particle physics
• Quantum Simulation of Lattice Gauge Theories in more than One Space Dimension -- Requirements, Challenges, Methods
• Lattice Quantum Electrodynamics in (3+1)-dimensions at finite density with Tensor Networks
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Removing Staggered Fermionic Matter in $U(N)$ and $SU(N)$ Lattice Gauge Theories
• Gluon Field Digitization via Group Space Decimation for Quantum Computers
• Gauge protection in non-Abelian lattice gauge theories
• A gauge redundancy-free formulation of compact QED with dynamical matter for quantum and classical computations
• Quantum codes for quantum simulation of Fermions on a square lattice of qubits
• Real-time-dynamics quantum simulation of (1+1)-D lattice QED with Rydberg atoms
• Primitive Quantum Gates for Dihedral Gauge Theories
• Toward Quantum Simulations of ${\mathbb{Z}}_2$ Gauge Theory Without State Preparation
• Lattice Renormalization of Quantum Simulations
• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss' Law and Fermion Elimination
• Simulating (2+1)D SU(2) Yang-Mills Lattice Gauge Theory at finite density with tensor networks
• Variational quantum simulation of U(1) lattice gauge theories with qudit systems
• Quantum Simulation of Z2 Lattice Gauge theory with minimal resources
• Selected topics of quantum computing for nuclear physics
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Duality as a Feasible Physical Transformation
• Exponential improvements in the simulation of lattice gauge theories using near-optimal techniques
• Loop-string-hadron approach to SU(3) lattice Yang-Mills theory: I. Hilbert space of a trivalent vertex
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Bosonization based on Clifford algebras and its gauge theoretic interpretation
• Simulating ${\mathbb{Z}}_2$ Lattice Gauge Theory with the Variational Quantum Thermalizer
• Gauss Law, Minimal Coupling and Fermionic PEPS for Lattice Gauge Theories
• Protecting local and global symmetries in simulating 1+1-D non-abelian gauge theories
• A relativistic discrete spacetime formulation of 3+1 QED
• Loop-Free Tensor Networks for High-Energy Physics
• Constraints of kinematic bosonization in two and higher dimensions
• Analysis of Superfast Encoding Performance for Electronic Structure Simulations
• Quantum algorithms for disordered physics
• Bosonization of Majorana modes and edge states
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Digital quantum simulation of lattice fermion theories with local encoding
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Fault-tolerant simulation of Lattice Gauge Theories with gauge covariant codes
• Towards Quantum Simulating Non-Abelian Gauge Theories
• Local Jordan-Wigner transformations on the torus
• Basis set convergence of Wilson basis functions for electronic structure
• Eigenstate Thermalization in 1+1-Dimensional SU(2) Lattice Gauge Theory Coupled with Dynamical Fermions
• Introducing Fermionic Link Models
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model
• Counting gauge-invariant states with matter fields and finite gauge groups