Quantum magnetism of spin-ladder compounds with trapped-ion crystals

Bermúdez, A.; Almeida, J. R. L. de; Ott, Konstantin; Kaufmann, Henning; Ulm, Stefan; Poschinger, Ulrich; Schmidt‐Kaler, F.; Retzker, Alex; Plenio, Martin B.

doi:10.1088/1367-2630/14/9/093042

Cited by 34 publications

(49 citation statements)

References 158 publications

(246 reference statements)

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“…As pictured in Fig. 5, it would also be possible to shelve specific ions in electronic states outside of the qubit subspace, allowing for multiple types of effective lattice configurations [67]. The residual effects of micromotion in 2D traps can be well-characterized, leading to a slightly longer spin-spin interaction range and a reduced (but still easily achievable) 2D trap stability region.…”

Section: Discussionmentioning

confidence: 99%

Two-dimensional ion crystals in radio-frequency traps for quantum simulation

Richerme

2016

Phys. Rev. A

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The computational difficulty of solving fully quantum many-body spin problems is a significant obstacle to understanding the behavior of strongly correlated quantum matter. Experimental iontrap quantum simulation is a promising approach for studying these lattice spin models, but has so far been limited to one-dimensional systems. This work argues that such quantum simulation techniques are extendable to a 2D ion crystal confined in a radiofrequency (rf) trap. Using appropriately chosen parameters, driven ion motion due to the rf fields can be made small and will not limit the types of quantum spin models that can be experimentally encoded. The rf-driven motion is calculated to modestly reduce the stability region of a 2D crystal and must be considered when designing the 2D trap. The system will be scalable to 100+ quantum particles, far beyond the realm of classical intractability, while maintaining the traditional ion-trap strengths of individual-ion control, long quantum coherence times, and site-resolved projective spin measurements.

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Section: Discussionmentioning

confidence: 99%

Two-dimensional ion crystals in radio-frequency traps for quantum simulation

Richerme

2016

Phys. Rev. A

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“…Due to the large stability of this phase against external perturbations, a quantum simulator that could reproduce this kind of couplings would be able to prepare a large number of fully entangled pairs in a robust way. In the last years several proposals for the experimental simulations of spin systems in ion trap experiments [40][41][42][43] suggest that this kind of setup could be readily in a near future.…”

Section: Discussion and Perspectivesmentioning

confidence: 99%

Dimerized ground states inspin−Sfrustrated systems

Lamas

Matera

2015

Phys. Rev. B

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We study a family of frustrated anti-ferromagnetic spin-S systems with a fully dimerized ground state. Starting from the simplest case of the frustrated zig-zag spin ladder, we generalize the family to more complex geometries like tetrahedral ladders and spin tubes. After present some numerical results about the phase diagram of these systems, we show that the ground state is robust against the inclusion of weak disorder in the couplings as well as several kinds of perturbations, allowing to study some other interesting models as a perturbative expansion of the exact one. A discussion on how to determine the dimerization region in terms of quantum information estimators is also presented. Finally, we explore the relation of these results with a the case of the a 4-leg spin tube which recently was proposed as a model for the description of the compound Cu2Cl4D8C4SO2, delimiting the region of the parameter space where this model presents dimerization in its ground state.

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“…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 magnetism of spin-ladder compounds with trapped-ion crystals

Cited by 34 publications

References 158 publications

Two-dimensional ion crystals in radio-frequency traps for quantum simulation

Two-dimensional ion crystals in radio-frequency traps for quantum simulation

Dimerized ground states inspin−Sfrustrated systems

Probing entanglement in adiabatic quantum optimization with trapped ions

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