Two-dimensional lattice gauge theories with superconducting quantum circuits

Marcos, D. Crespo; Widmer, Philippe; Rico, E.; Hafezi, Mohammad; Rabl, Peter; Wiese, U.‐J.; Zoller, P.

doi:10.1016/j.aop.2014.09.011

Cited by 121 publications

(118 citation statements)

References 55 publications

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“…During the last years, several proposal have been put forward dealing with the deliberate generation of dynamical gauge fields. Platforms based on ultracold atoms in optical lattices [37][38][39][40][41][42][43] or superconducting circuits [44,45] are discussed as promising systems which could serve as quantum simulators for dynamical gauge theories such as quantum electrodynamics and quantum chromodynamics [46,47]. In most cases these proposals require a great deal of engineering, meaning carefully choosing a setting which yields the desired interactions between for instance superconducting qubits.…”

Section: Introductionmentioning

confidence: 99%

Classical dynamical gauge fields in optomechanics

Walter

Marquardt

2016

New J. Phys.

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Artificial gauge fields for neutral particles such as photons, recently attracted a lot of attention in various fields ranging from photonic crystals to ultracold atoms in optical lattices to optomechanical arrays. Here we point out that, among all implementations of gauge fields, the optomechanical setting allows for the most natural extension where the gauge field becomes dynamical. The mechanical oscillation phases determine the effective artificial magnetic field for the photons, and once these phases are allowed to evolve, they respond to the flow of photons in the structure. We discuss a simple three-site model where we identify four different regimes of the gauge-field dynamics. Furthermore, we extend the discussion to a two-dimensional lattice. Our proposed scheme could for instance be implemented using optomechanical crystals. 4 1 and for convenience we introduce  J J 12,23,13 1,2,3 and similarly for B 12,23,13 . By introducing normal modes A J B A J B A J B A J B A J B A J

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Section: Introductionmentioning

confidence: 99%

Classical dynamical gauge fields in optomechanics

Walter

Marquardt

2016

New J. Phys.

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“…These use control atoms at lattice sites to ensure Gauss' law, and at plaquette centers to flip electric flux loops, while other Rydberg atoms act as qubits that represent the quantum link variables. Some analog quantum simulator constructions again use ultracold atoms in optical lattices [33,36,39], while others are based on superconducting circuits on a chip [46,47].…”

Section: Quantum Simulators For Abelian Gauge Theoriesmentioning

confidence: 99%

“…One can also imagine that a gauge theory quantum simulator can mimic qualitative features of heavy-ion collisions. Since we have no other way of reliably investigating QCD's real-time dynamics from first principles, the construction of quantum simulators for Abelian and non-Abelian gauge theories, with or without fermionic matter, is timely and most promising [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]. Once such systems are realized in the laboratory, they will also become interesting objects of study in their own right.…”

Section: Introductionmentioning

confidence: 99%

Towards quantum simulating QCD

Wiese

2014

Nuclear Physics A

104

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Quantum link models provide an alternative non-perturbative formulation of Abelian and non-Abelian lattice gauge theories. They are ideally suited for quantum simulation, for example, using ultracold atoms in an optical lattice. This holds the promise to address currently unsolvable problems, such as the real-time and high-density dynamics of strongly interacting matter, first in toy-model gauge theories, and ultimately in QCD.

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“…(b)The symmetry properties of C (49). sum is intended for repeated indices, and the last equality is obtained by equation(45) and links the physical indices j n j n symmetry relations(33) and(43)are now simply mapped to…”

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confidence: 99%

Building projected entangled pair states with a local gauge symmetry

Zohar

Burrello

2016

New J. Phys.

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Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and as a tool for the analysis of the recent proposals for quantum simulations of lattice gauge theories. In this paper we present a framework for describing locally gauge invariant states on lattices using PEPS. The PEPS constructed hereby shall include both bosonic and fermionic states, suitable for all combinations of matter and gauge fields in lattice gauge theories defined by either finite or compact Lie groups.This last step has been undertaken for two-dimensional tensor networks in the recent works [46,48,55]. In particular, Tagliacozzo et al [46] introduced a formalism for building bosonic PEPS describing pure lattice gauge theories with arbitrary groups and adopted a truncation scheme for the representations which we will extend in this work to include matter and fermionic PEPS (fPEPS) as well; Haegeman et al [48] developed, instead, a general, conceptual formalism to build PEPS which describe both gauge fields and bosonic matter through a gauging map of injective PEPS. Finally, in [55], the authors presented an explicit analytical and numerical construction for the specific case of a truncated U(1) gauge-invariant state including both fermionic matter and bosonic gauge fields.In this work, we develop a more general framework for the construction of PEPS with local gauge invariance for lattice gauge theories whose gauge group G is either a compact Lie, or a finite group. We aim at unifying all the elements required for complete descriptions of lattice gauge theories: in particular we focus on gauge invariant states which include both matter and gauge fields and we propose a constructive approach to define tensor network states where the matter can be either bosonic or fermionic and is associated to an arbitrary representation of the gauge group. A special attention will indeed be devoted to the construction of fPEPS because of their more immediate relevance in the study of models which are closer to the usual particle physics theories.Throughout this paper we adopt the mathematical stucture discussed in [57] to describe the physical components of the PEPS and, in particular, the Hilbert spaces used to describe the matter and the gauge field degrees of freedom. We will show that such description, based on the representations of the gauge group, can be naturally extended to the virtual states constituting the links of the tensor network. Furthermore, to make this work self-contained, we will summarize the main elements of the construction presented in [57] without assuming that the reader is acquainted with PEPS or lattice gauge theories; the required PEPS details are reviewed and constructed along the paper, as well as their relations with lattice gauge theory.

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Two-dimensional lattice gauge theories with superconducting quantum circuits

Cited by 121 publications

References 55 publications

Classical dynamical gauge fields in optomechanics

Classical dynamical gauge fields in optomechanics

Towards quantum simulating QCD

Building projected entangled pair states with a local gauge symmetry

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