Topologically Decoherence-Protected Qubits with Trapped Ions

Milman, P.; Maineult, W.; Guibal, S.; Guidoni, Luca; Douçot, Benoît; Ioffe, L. B.; Coudreau, Thomas

doi:10.1103/physrevlett.99.020503

Cited by 42 publications

(49 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…5 Extensions of (1) to global interactions possess even better fault tolerant properties. 6 Originally introduced as an orbital model for Mott insulators, 7 research into the actual CM has been pushed by several groups, which established degenerate ground-state properties, 8 first-order quantum phase transitions, 9 relation to p + ip superconductivity, 10 and the existence of directional order. 11,12,13 Reference 12 argues that quantum spins support a resistivity of the ordered phase towards quenched disorder, which is in sharp contrast to classical degrees of freedom for which the ordered phase vanishes rapidly with increasing disorder.…”

Section: Introductionmentioning

confidence: 99%

Finite-temperature Néel ordering of fluctuations in a plaquette orbital model

Wenzel

Janke

2009

Phys. Rev. B

View full text Add to dashboard Cite

We present a pseudo-spin model which should be experimentally accessible using solid-state devices and, being a variation on the compass model, adds to the toolbox for the protection of qubits in the area of quantum information. Using Monte Carlo methods, we find for both classical and quantum spins in two and three dimensions Ising type Néel ordering of energy fluctuations at finite temperatures without magnetic order. We also readdress the controversy concerning the stability of the ordered state in the presence of quenched impurities and present numerical results which are at clear variance with earlier claims in the literature.

show abstract

Section: Introductionmentioning

confidence: 99%

Finite-temperature Néel ordering of fluctuations in a plaquette orbital model

Wenzel

Janke

2009

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…These systems are also candidates to exhibit topological quantum order [8]. Furthermore, it was recently shown how to simulate these models using polar molecules in optical lattices and systems of trapped ions with state-of-the-art technology [9,10].Generally speaking, the symmetries in these systems involve large degeneracies in their energy spectra, which make their numerical simulation difficult [11]. This fact, together with the lack of exact solutions, makes it hard to elucidate their phase diagrams.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

First Order Phase Transition in the Anisotropic Quantum Orbital Compass Model

2009

View full text Add to dashboard Cite

We investigate the anisotropic quantum orbital compass model on an infinite square lattice by means of the infinite projected entangled-pair state algorithm. For varying values of the Jx and Jz coupling constants of the model, we approximate the ground state and evaluate quantities such as its expected energy and local order parameters. We also compute adiabatic time evolutions of the ground state, and show that several ground states with different local properties coexist at Jx = Jz. All our calculations are fully consistent with a first order quantum phase transition at this point, thus corroborating previous numerical evidence. Our results also suggest that tensor network algorithms are particularly fitted to characterize first order quantum phase transitions. Introduction.-When quantum many-body systems are cooled down close to zero temperature, important collective phenomena may occur [1]. A good example is provided by transition-metal oxides, whose physical properties have become of increasing interest in the last few years [2]. In these compounds the orbital degrees of freedom of the atomic electrons play a key role in determining properties such as metal-insulator transitions, high-temperature superconductivity and colossal magnetoresistance.The paradigmatic approach to these systems is based on the so-called orbital compass models [3,4], which have been the subject of many studies in the past both in the classical and quantum regimes. For these systems, JahnTeller effects produce an anisotropy of the pseudospin couplings which is intertwined with the orientation of the interaction bonds. The properties of these systems have attracted considerable attention since they are endowed with symmetries that effectively reduce the dimensionality of the system (the so-called dimensional reduction) [5,6]. Despite of their apparent simplicity, orbital compass models are relevant in a variety of contexts, such as in determining the physics of Mott insulators with orbital degrees of freedom [3] and the implementation of protected qubits for quantum computation in Josephson junction arrays [7]. These systems are also candidates to exhibit topological quantum order [8]. Furthermore, it was recently shown how to simulate these models using polar molecules in optical lattices and systems of trapped ions with state-of-the-art technology [9,10].Generally speaking, the symmetries in these systems involve large degeneracies in their energy spectra, which make their numerical simulation difficult [11]. This fact, together with the lack of exact solutions, makes it hard to elucidate their phase diagrams. In this paper we use a tensor product state (TPS) [12,13] or projected entangled-pair state (PEPS) [14] to study the twodimensional anisotropic quantum orbital compass model (AQOCM) and, in particular, to investigate whether its phase transition is of first order [15,16] or second order [17]. More specifically, we use the infinite PEPS (iPEPS)

show abstract

“…Controlled-string operations can be applied to other lattice Hamiltonians as well [43,44], which may provide robust quantum memory with their degenerate ground states. For example subsystem codes [43] can be constructed out of 2D and 3D nearest neighbor spin-1/2 interactions that are realizable with atomic systems [6,7].…”

Section: Discussionmentioning

confidence: 99%

Anyonic interferometry and protected memories in atomic spin lattices

et al. 2008

View full text Add to dashboard Cite

Strongly correlated quantum systems can exhibit exotic behavior called topological order which is characterized by non-local correlations that depend on the system topology. Such systems can exhibit remarkable phenomena such as quasi-particles with anyonic statistics and have been proposed as candidates for naturally fault-tolerant quantum computation. Despite these remarkable properties, anyons have never been observed in nature directly. Here we describe how to unambiguously detect and characterize such states in recently proposed spin lattice realizations using ultra-cold atoms or molecules trapped in an optical lattice. We propose an experimentally feasible technique to access non-local degrees of freedom by performing global operations on trapped spins mediated by an optical cavity mode. We show how to reliably read and write topologically protected quantum memory using an atomic or photonic qubit. Furthermore, our technique can be used to probe statistics and dynamics of anyonic excitations.By definition, topologically ordered states [1] cannot be distinguished by local observables, i.e. there is no local order parameter. They can arise as ground states of certain Hamiltonians which have topological degeneracy and which provide robustness against noise and quasi-local perturbations. These properties of such systems are attractive for quantum memories. However, the local indistinguishability makes measuring and manipulating the topological states difficult because they are only coupled by global operations. One way to access this information is to measure properties of the low lying particlelike excitations. In two dimensions, the quasi-particles act like punctures in a surface which can have anyonic statistics and the topological properties are probed by braiding different particle types around each other. The existence of anyons also implies a topological degeneracy [2]. Quantum Hall fluids at certain filling fractions are believed to be topologically protected and there is a vigorous experimental effort to verify anyonic statistics in these systems [3]. A standard approach is to perform some kind of interferometry where one looks for non-trivial action on the fusion state space upon braiding. This is manifested as the evolution of a non-trivial statistical phase in the abelian case, or a change in the amplitude of the participating states in the non-abelian case. Some experimental evidence consistent with observation of abelian anyonic statistics in a ν = 2/5 filled Quantum Hall state has been reported [4] but an unambiguous detection of anyons is still considered an open issue [5].Spin lattice Hamiltonians can also exhibit topological order and such Hamiltonians can be built with atoms [6] or molecules [7] trapped in an optical lattice. A significant advantage of using atomic systems is that the microscopic physics is well known and there are established techniques for coherent control and measurement. Suggestions have been made for how one would design anyonic interferometers in these systems by using ...

show abstract

Topologically Decoherence-Protected Qubits with Trapped Ions

Cited by 42 publications

References 31 publications

Finite-temperature Néel ordering of fluctuations in a plaquette orbital model

Finite-temperature Néel ordering of fluctuations in a plaquette orbital model

First Order Phase Transition in the Anisotropic Quantum Orbital Compass Model

Anyonic interferometry and protected memories in atomic spin lattices

Contact Info

Product

Resources

About