Non-Abelian gauge invariance from dynamical decoupling
- URL: http://arxiv.org/abs/2012.08620v2
- Date: Tue, 29 Jun 2021 09:39:31 GMT
- Title: Non-Abelian gauge invariance from dynamical decoupling
- Authors: Valentin Kasper, Torsten V. Zache, Fred Jendrzejewski, Maciej
Lewenstein, Erez Zohar
- Abstract summary: We employ a coherent quantum control scheme to enforce non-Abelian gauge invariance.
We discuss this idea in detail for a one dimensional SU(2) lattice gauge system.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Lattice gauge theories are fundamental to such distinct fields as particle
physics, condensed matter or quantum information theory. The recent progress in
the control of artificial quantum systems already allows for studying Abelian
lattice gauge theories in table-top experiments. However, the realization of
non-Abelian models remains challenging. Here, we employ a coherent quantum
control scheme to enforce non-Abelian gauge invariance, and discuss this idea
in detail for a one dimensional SU(2) lattice gauge system. Finally, we comment
on how to extend our scheme to other non-Abelian gauge symmetries and higher
spatial dimensions, which summarized, provides a promising route for the
quantum simulation of non-Abelian lattice gauge theories.
Related papers
- A Floquet-Rydberg quantum simulator for confinement in $\mathbb{Z}_2$
gauge theories [44.99833362998488]
Recent advances in the field of quantum technologies have opened up the road for the realization of small-scale quantum simulators.
We present a scalable Floquet scheme for the quantum simulation of the real-time dynamics in a $mathbbZ$ LGT.
We show that an observation of gauge-invariant confinement dynamics in the Floquet-Rydberg setup is at reach of current experimental techniques.
arXiv Detail & Related papers (2023-11-28T13:01:24Z) - Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain [46.99825956909532]
Local quantum measurements do not simply disentangle degrees of freedom, but may actually strengthen the entanglement in the system.
This paper explores how a finite density of local measurement modifies a given state's entanglement structure.
arXiv Detail & Related papers (2023-10-04T09:51:00Z) - Spin exchange-enabled quantum simulator for large-scale non-Abelian gauge theories [0.0]
A central requirement for the faithful implementation of large-scale lattice gauge theories (LGTs) on quantum simulators is the protection of the underlying gauge symmetry.
We propose an experimentally feasible approach to implement large-scale non-Abelian $mathrmSU(N)$ and $mathrmU(N)$ LGTs with dynamical matter in $d+1$D.
Our approach paves the way towards near-term realizations of large-scale non-Abelian quantum link models in analog quantum simulators.
arXiv Detail & Related papers (2023-05-10T18:00:02Z) - Quantum and classical spin network algorithms for $q$-deformed
Kogut-Susskind gauge theories [0.0]
We introduce $q$-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group.
Our proposal simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties.
Our work gives a new perspective for the application of tensor network methods to high-energy physics.
arXiv Detail & Related papers (2023-04-05T15:49:20Z) - General quantum algorithms for Hamiltonian simulation with applications
to a non-Abelian lattice gauge theory [44.99833362998488]
We introduce quantum algorithms that can efficiently simulate certain classes of interactions consisting of correlated changes in multiple quantum numbers.
The lattice gauge theory studied is the SU(2) gauge theory in 1+1 dimensions coupled to one flavor of staggered fermions.
The algorithms are shown to be applicable to higher-dimensional theories as well as to other Abelian and non-Abelian gauge theories.
arXiv Detail & Related papers (2022-12-28T18:56:25Z) - Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
Indistinguishability of particles is a fundamental principle of quantum mechanics.
braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions.
We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
arXiv Detail & Related papers (2022-10-19T02:28:44Z) - Gradient expansion of the non-Abelian gauge-covariant Moyal star-product [0.0]
Motivated by the recent developments of gauge-covariant methods in the phase-space, a systematic method is presented aiming at the generalisation of the Moyal star-product to a non-Abelian gauge covariant one at any order.
It might be of fundamental importance for the mathematical elaborations of gauge theory using the strict or deformation quantisation principles.
A gauge-covariant formulation taking into account possible geometrical connections in both the position and momentum spaces is also constructed at leading orders.
arXiv Detail & Related papers (2021-11-02T10:53:28Z) - Photon-mediated Stroboscopic Quantum Simulation of a $\mathbb{Z}_{2}$
Lattice Gauge Theory [58.720142291102135]
Quantum simulation of lattice gauge theories (LGTs) aims at tackling non-perturbative particle and condensed matter physics.
One of the current challenges is to go beyond 1+1 dimensions, where four-body (plaquette) interactions, not contained naturally in quantum simulating devices, appear.
We show how to prepare the ground state and measure Wilson loops using state-of-the-art techniques in atomic physics.
arXiv Detail & Related papers (2021-07-27T18:10:08Z) - Shearing approach to gauge invariant Trotterization [0.0]
We show how time evolution can be compiled in an Abelian gauge theory.
We show that cyclically shearing the spatial network converts simultaneous updates to many quantum numbers into conditional updates of a single quantum number.
The features that make shearing successful at preserving Abelian gauge symmetry may also be found in non-Abelian theories.
arXiv Detail & Related papers (2021-05-24T21:35:03Z) - Quantum simulation of gauge theory via orbifold lattice [47.28069960496992]
We propose a new framework for simulating $textU(k)$ Yang-Mills theory on a universal quantum computer.
We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories.
arXiv Detail & Related papers (2020-11-12T18:49:11Z) - From the Jaynes-Cummings model to non-Abelian gauge theories: a guided
tour for the quantum engineer [0.0]
Non-Abelian lattice gauge theories play a central role in high energy physics, condensed matter and quantum information.
We introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model.
We show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems.
arXiv Detail & Related papers (2020-06-01T20:53:36Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.