Quantum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions

Hauke, Philipp; Marcos, D. Crespo; Dalmonte, Marcello; Zoller, P.

doi:10.1103/physrevx.3.041018

Cited by 190 publications

(196 citation statements)

References 94 publications

(192 reference statements)

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“…For gauge-variant perturbations that do not couple distant sites, the noise protection can be realized by global beams in a superlattice configuration. The mechanism is universal, as it can be extended to any symmetry and dimensionality, and can be applied to different microscopic systems beyond cold atom gases, such as superconducting qubits and trapped ions [28,29]. …”

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confidence: 99%

Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms

et al. 2014

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We show how engineered classical noise can be used to generate constrained Hamiltonian dynamics in atomic quantum simulators of many-body systems, taking advantage of the continuous Zeno effect. After discussing the general theoretical framework, we focus on applications in the context of lattice gauge theories, where imposing exotic, quasi-local constraints is usually challenging. We demonstrate the effectiveness of the scheme for both Abelian and non-Abelian gauge theories, and discuss how engineering dissipative constraints substitutes complicated, non-local interaction patterns by global coupling to laser fields.PACS numbers: 03.65. Xp,37.10.Jk,11.15.Ha Laboratory experiments with atomic quantumdegenerate gases have established a synergetic link between atomic physics and condensed matter [1][2][3], and hold prospects for a similar connection to high-energy physics [4][5][6][7][8][9][10][11][12]. Loaded into optical lattices, cold atoms realize Hubbard models, which can be designed and controlled via external fields to mimic the dynamics of quantum many-body systems in equilibrium and nonequilibrium situations [3, 13]. While a focus of research during the last decade has been the development of a toolbox for designing specific lattice Hamiltonians [1-3], we address below the problem of implementing desired Hubbard dynamics in the presence of constraints, i.e., we wish to keep the system dynamics within a certain subspace of the total Hilbert space. A familiar way of imposing such constraints is to add an energy penalty to the Hamiltonian [14]. Below, we describe an alternative scenario that is based on driving the system with engineered classical noise, exploiting the Zeno effect [15][16][17][18][19][20]. As we will see, 'adding noise' provides a general tool to implement -in an experimentally efficient and accessible way -highly nontrivial constraints in quantum many-body systems.The present work is motivated by the ongoing quest to build a quantum simulator for Abelian and non-Abelian lattice gauge theories (LGTs) with cold atoms in optical lattices [5][6][7][8][9][10][11][12].LGTs play a prominent role in both particle and condensed matter physics: in the standard model, the interaction between constituents of matter are mediated by gauge bosons [21][22][23][24], and in frustrated magnetism, quantum spin liquids are suitably described in the language of gauge theories [14,25,26]. The key feature of a LGT is the presence of local (gauge) symmetries. The generators G a x of these local gauge transformations, with x denoting lattice sites and a a color index, commute with the lattice Hamiltonian, [H 0 , G a x ] = 0 for all x, a, and thus provide local conservation laws. They can be interpreted in analogy to Gauss's law from electrodynamics, as they constrain the dynamics of the system to a physical LGTs consist of fermions ψx living on sites, coupled to gauge fields Ux,x+1 living on links. The dynamics can be constrained to the physical subspace by coupling independent noise sources linearly to each gener...

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Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms

et al. 2014

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“…Realization.-There have been numerous proposals for the realization of QLM models [11][12][13][14][15][16][17]53]. Here we introduce a simple scheme (Fig.…”

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“…Various ideas for creating dynamical gauge fields have been proposed [5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently the Schwinger model has been simulated in ion chains [18].…”

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Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

2017

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We show that whereas spin-1/2 one-dimensional U(1) quantum-link models (QLMs) are topologically trivial, when implemented in ladder-like lattices these models may present an intriguing ground-state phase diagram, which includes a symmetry protected topological (SPT) phase that may be readily revealed by analyzing long-range string spin correlations along the ladder legs. We propose a simple scheme for the realization of spin-1/2 U(1) QLMs based on single-component fermions loaded in an optical lattice with s-and p-bands, showing that the SPT phase may be experimentally realized by adiabatic preparation.The realization of lattice gauge models using ultra cold gases has attracted a major theoretical attention in recent years [1][2][3][4]. Various ideas for creating dynamical gauge fields have been proposed [5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently the Schwinger model has been simulated in ion chains [18]. Particular interest has been devoted to quantum-link models (QLMs) [19], which generalize lattice gauge theory [20] by realizing continuous gauge symmetries with discrete gauge variables (quantum links). QLMs are relevant in particle physics, and in particular QCD [21], and in condensed matter physics [22,23]. In U(1) QLMs, links are represented by quantum spins and fermions provide the matter field, making these QLMs particularly suitable for simulation with cold lattice gases.In this Letter we study the topological properties of spin-1/2 U(1) QLMs. Topological quantum systems have become one of the most active research areas during the past decades [24,25]. In particular the understanding of topological phases in strongly correlated quantum systems remains challenging. The study of symmetry protected topological (SPT) states has triggered a large progress in this field [26]. SPT phases have been classified by means of entanglement properties and group theoretical considerations [27][28][29][30][31][32]. Indeed in onedimensional (1D) systems, SPT phases are the only realizable class of topological quantum states, a prominent example being the so-called Haldane phase of odd-integer spin chains [33,34]. Generalizations of the Haldane phase have been theoretically studied in the context of ultracold gases [35][36][37][38][39][40].Real or synthetic ladder-like lattices have recently constituted the focus of major efforts [41][42][43] in the context of the realization of static gauge fields in ultra-cold atomic systems. We show below that although in 1D spin-1/2 U(1) QLMs are topologically trivial, when implemented in ladder-like lattices these models present an intriguing ground-state phase diagram, which interestingly includes an SPT phase that we characterize using a generalized topological order parameter and the entanglement spectrum. We show that the SPT phase may be revealed by analyzing string spin correlations along the ladder legs. Moreover, we propose a simple scheme for the realization of the QLM based on s-p lattices [44], showing that the SPT phase may be experimentally realized by adiab...

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“…. N. The tunability of the latter, to our knowledge so far only considered in Hauke et al [47], is a crucial ingredient for some of the NP-complete models discussed in Table 1. The coupling to the vibrational modes appears through the positions x i , which can be expanded as kx i = N q=1 η iq a † q + h.c., where η iq = M iq k/ 2Mω q /h is the Lamb-Dicke parameter with M the ion mass.…”

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confidence: 99%

“…For the same reason, few theoretical works have considered a site-dependent tunability of couplings [38,[45][46][47] or fields [48]. In contrast, our purpose of engineering NP-complete problems in Hamiltonian Equation (1) requires a certain degree of programmability of the interaction matrix elements J ij and fields h z i (see e.g., Lucas [16]).…”

Section: Np-complete Models Realizable With Available Trapped-ion Tecmentioning

confidence: 99%

Probing entanglement in adiabatic quantum optimization with trapped ions

et al. 2015

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Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.

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Quantum Simulation of a Lattice Schwinger Model in a Chain of Trapped Ions

Cited by 190 publications

References 94 publications

Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms

Constrained Dynamics via the Zeno Effect in Quantum Simulation: Implementing Non-Abelian Lattice Gauge Theories with Cold Atoms

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

Probing entanglement in adiabatic quantum optimization with trapped ions

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