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Sep 23, 2013
09/13

by
E. Rico; H. J. Briegel

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A quantum anti-ferromagnetic spin-1 model is characterised on a 2D lattice with the following requirements: i) The Hamiltonian is made out of nearest neighbour interactions. ii) It is homogeneous, translational and rotational invariant. iii) The ground state is a real singlet state of SU(2) (non-chiral). iv) It has a local spin-1 representation. Along the way to characterise the system, connections with classical statistical mechanics and integrable models are explored. Finally, the relevance...

Source: http://arxiv.org/abs/0710.2349v2

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Sep 17, 2013
09/13

by
R. Raussendorf; H. J. Briegel

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The one-way quantum computer (QCc) is a universal scheme of quantum computation consisting only of one-qubit measurements on a particular entangled multi-qubit state, the cluster state. The computational model underlying the QCc is different from the quantum logic network model and it is based on different constituents. It has no quantum register and does not consist of quantum gates. The QCc is nevertheless quantum mechanical since it uses a highly entangled cluster state as the central...

Source: http://arxiv.org/abs/quant-ph/0207183v1

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Sep 24, 2013
09/13

by
C. Mora; H. J. Briegel

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In this paper we give a definition for the Kolmogorov complexity of a pure quantum state. In classical information theory the algorithmic complexity of a string is a measure of the information needed by a universal machine to reproduce the string itself. We define the complexity of a quantum state by means of the classical description complexity of an (abstract) experimental procedure that allows us to prepare the state with a given fidelity. We argue that our definition satisfies the intuitive...

Source: http://arxiv.org/abs/quant-ph/0412172v1

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Sep 18, 2013
09/13

by
W. Dür; H. J. Briegel

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We give a review on entanglement purification for bipartite and multipartite quantum states, with the main focus on theoretical work carried out by our group in the last couple of years. We discuss entanglement purification in the context of quantum communication, where we emphasize its close relation to quantum error correction. Various bipartite and multipartite entanglement purification protocols are discussed, and their performance under idealized and realistic conditions is studied....

Source: http://arxiv.org/abs/0705.4165v2

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Sep 17, 2013
09/13

by
J. Eisert; H. -J. Briegel

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We present a measure of quantum entanglement which is capable of quantifying the degree of entanglement of a multi-partite quantum system. This measure, which is based on a generalization of the Schmidt rank of a pure state, is defined on the full state space and is shown to be an entanglement monotone, that is, it cannot increase under local quantum operations with classical communication and under mixing. For a large class of mixed states this measure of entanglement can be calculated...

Source: http://arxiv.org/abs/quant-ph/0007081v3

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Sep 22, 2013
09/13

by
W. Dür; H. -J. Briegel

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We investigate the lifetime of macroscopic entanglement under the influence of decoherence. For GHZ-type superposition states we find that the lifetime decreases with the size of the system (i.e. the number of independent degrees of freedom) and the effective number of subsystems that remain entangled decreases with time. For a class of other states (e.g. cluster states), however, we show that the lifetime of entanglement is independent of the size of the system.

Source: http://arxiv.org/abs/quant-ph/0307180v1

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Sep 18, 2013
09/13

by
W. Dür; H. -J. Briegel

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We show that thresholds for fault-tolerant quantum computation are solely determined by the quality of single-system operations if one allows for d-dimensional systems with $8 \leq d \leq 32$. Each system serves to store one logical qubit and additional auxiliary dimensions are used to create and purify entanglement between systems. Physical, possibly probabilistic two-system operations with error rates up to 2/3 are still tolerable to realize deterministic high quality two-qubit gates on the...

Source: http://arxiv.org/abs/quant-ph/0210069v2

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Sep 19, 2013
09/13

by
M. Van den Nest; H. J. Briegel

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We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for measurement-based quantum computation, is reflected in the expressive power of (classical) formal logic languages defined on the underlying mathematical graphs. In particular, we show that for all graph state resources which can yield a computational speed-up with...

Source: http://arxiv.org/abs/quant-ph/0610040v2

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Sep 23, 2013
09/13

by
W. Dür; J. Calsamiglia; H. -J. Briegel

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We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations) any state chosen from the set of two-colorable graph states (CSS codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement...

Source: http://arxiv.org/abs/quant-ph/0411209v2

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Sep 19, 2013
09/13

by
W. Dür; H. Aschauer; H. -J. Briegel

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We introduce a class of multiparticle entanglement purification protocols that allow us to distill a large class of entangled states. These include cluster states, GHZ states and various error correction codes all of which belong to the class of two-colorable graph states. We analyze these schemes under realistic conditions and observe that they are scalable, i.e. the threshold value for imperfect local operations does not depend on the number of parties for many of these states. When compared...

Source: http://arxiv.org/abs/quant-ph/0303087v3

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Jun 30, 2018
06/18

by
M. Zwerger; H. J. Briegel; W. Dür

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We investigate entanglement purification protocols based on hashing, where a large number of noisy entangled pairs is jointly processed to obtain a reduced number of perfect, noiseless copies. While hashing and breeding protocols are the only purification protocols that asymptotically obtain a nonzero yield, they are not applicable in a realistic scenario if local gates and measurements are imperfect. We show that such problems can be overcome by a compact measurement-based implementation,...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1405.4207

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Sep 22, 2013
09/13

by
M. Hein; J. Eisert; H. J. Briegel

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Graph states are multi-particle entangled states that correspond to mathematical graphs, where the vertices of the graph take the role of quantum spin systems and edges represent Ising interactions. They are many-body spin states of distributed quantum systems that play a significant role in quantum error correction, multi-party quantum communication, and quantum computation within the framework of the one-way quantum computer. We characterize and quantify the genuine multi-particle...

Source: http://arxiv.org/abs/quant-ph/0307130v7

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Jul 20, 2013
07/13

by
T. Carle; H. J. Briegel; B. Kraus

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We study a spin-gas model, where N_S system qubits are interacting with N_B bath qubits via many-body interactions. We consider multipartite Ising interactions and show how the effect of decoherence depends on the specific coupling between the system and its environment. For instance, we analyze the influence of decohenerce induced by k-body interactions for different values of k. Moreover, we study how the effect of decoherence depends on the correlation between baths that are coupled to...

Source: http://arxiv.org/abs/1007.5422v1

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Sep 23, 2013
09/13

by
M. Zwerger; H. J. Briegel; W. Dür

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We investigate measurement-based entanglement purification protocols (EPP) in the presence of local noise and imperfections. We derive a universal, protocol-independent threshold for the required quality of the local resource states, where we show that local noise per particle of up to 24% is tolerable. This corresponds to an increase of the noise threshold by almost an order of magnitude, based on the joint measurement-based implementation of sequential rounds of few-particle EPP. We...

Source: http://arxiv.org/abs/1303.2852v1

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Sep 19, 2013
09/13

by
L. Hartmann; W. Dür; H. -J. Briegel

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Quantum mechanical entanglement can exist in noisy open quantum systems at high temperature. A simple mechanism, where system particles are randomly reset to some standard initial state, can counteract the deteriorating effect of decoherence, resulting in an entangled steady state far from thermodynamical equilibrium. We present models for both gas-type systems and for strongly coupled systems. We point out in which way the entanglement resulting from such a reset mechanism is different from...

Source: http://arxiv.org/abs/quant-ph/0703138v1

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Sep 20, 2013
09/13

by
H. Aschauer; W. Dür; H. -J. Briegel

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We investigate multiparticle entanglement purification schemes which allow one to purify all two colorable graph states, a class of states which includes e.g. cluster states, GHZ states and codewords of various error correction codes. The schemes include both recurrence protocols and hashing protocols. We analyze these schemes under realistic conditions and observe for a generic error model that the threshold value for imperfect local operations depends on the structure of the corresponding...

Source: http://arxiv.org/abs/quant-ph/0405045v2

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Jun 27, 2018
06/18

by
M. Zwerger; H. J. Briegel; W. Dür

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We review and discuss the potential of using measurement-based elements in quantum communication schemes, where certain tasks are realized with the help of entangled resource states that are processed by measurements. We consider long-range quantum communication based on the transmission of encoded quantum states, where encoding, decoding and syndrome read-out are implemented using small-scale resource states. We also discuss entanglement-based schemes and consider measurement-based quantum...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1506.00985

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Sep 21, 2013
09/13

by
M. Zwerger; W. Dür; H. J. Briegel

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We introduce measurement-based quantum repeaters, where small-scale measurement-based quantum processors are used to perform entanglement purification and entanglement swapping in a long-range quantum communication protocol. In the scheme, pre-prepared entangled states stored at intermediate repeater stations are coupled with incoming photons by simple Bell-measurements, without the need of performing additional quantum gates or measurements. We show how to construct the required resource...

Source: http://arxiv.org/abs/1204.2178v1

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Sep 23, 2013
09/13

by
M. Hein; W. Dür; H. -J. Briegel

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We investigate entanglement properties of multipartite states under the influence of decoherence. We show that the lifetime of (distillable) entanglement for GHZ-type superposition states decreases with the size of the system, while for a class of other states -namely all graph states with constant degree- the lifetime is independent of the system size. We show that these results are largely independent of the specific decoherence model and are in particular valid for all models which deal with...

Source: http://arxiv.org/abs/quant-ph/0408165v1

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Sep 20, 2013
09/13

by
R. Raussendorf; D. E. Browne; H. J. Briegel

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We give a detailed account of the one-way quantum computer, a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. We prove its universality, describe why its underlying computational model is different from the network model of quantum computation and relate quantum algorithms to mathematical graphs. Further we investigate the scaling of required resources and give a number of examples for circuits of...

Source: http://arxiv.org/abs/quant-ph/0301052v2

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0.0

Jun 30, 2018
06/18

by
M. Tiersch; E. J. Ganahl; H. J. Briegel

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Quantum information processing devices need to be robust and stable against external noise and internal imperfections to ensure correct operation. In a setting of measurement-based quantum computation, we explore how an intelligent agent endowed with a projective simulator can act as controller to adapt measurement directions to an external stray field of unknown magnitude in a fixed direction. We assess the agent's learning behavior in static and time-varying fields and explore composition...

Topic: Quantum Physics

Source: http://arxiv.org/abs/1407.1535

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Sep 19, 2013
09/13

by
M. Van den Nest; W. Dür; H. J. Briegel

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We relate a large class of classical spin models, including the inhomogeneous Ising, Potts, and clock models of q-state spins on arbitrary graphs, to problems in quantum physics. More precisely, we show how to express partition functions as inner products between certain quantum stabilizer states and product states. This connection allows us to use powerful techniques developed in quantum information theory, such as the stabilizer formalism and classical simulation techniques, to gain general...

Source: http://arxiv.org/abs/quant-ph/0610157v1

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Sep 19, 2013
09/13

by
L. Hartmann; B. Kraus; H. -J. Briegel; W. Dür

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We investigate the influence of memory errors in the quantum repeater scheme for long-range quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable waiting times for classical signals. We show how to overcome these limitations by (i) improving local memory, and (ii) introducing two new operational modes of the quantum repeater. In both operational modes, the repeater is run blindly, i.e. without waiting...

Source: http://arxiv.org/abs/quant-ph/0610113v2

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Sep 19, 2013
09/13

by
M. Van den Nest; W. Dür; H. J. Briegel

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We prove that the 2D Ising model is complete in the sense that the partition function of any classical q-state spin model (on an arbitrary graph) can be expressed as a special instance of the partition function of a 2D Ising model with complex inhomogeneous couplings and external fields. In the case where the original model is an Ising or Potts-type model, we find that the corresponding 2D square lattice requires only polynomially more spins w.r.t the original one, and we give a constructive...

Source: http://arxiv.org/abs/0708.2275v2

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Sep 22, 2013
09/13

by
O. Gittsovich; R. Hübener; E. Rico; H. J. Briegel

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In this paper, we introduce a real-space renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization techniques, namely the strong disorder renormalization technique (SDRT) and the contractor renormalization (CORE). We analyze the performance of the method on the 2D random transverse field Ising model (RTFIM).

Source: http://arxiv.org/abs/0908.1312v1

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Sep 18, 2013
09/13

by
J. Calsamiglia; L. Hartmann; W. Dür; H. -J. Briegel

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We study the dynamics of entanglement in spin gases. A spin gas consists of a (large) number of interacting particles whose random motion is described classically while their internal degrees of freedom are described quantum-mechanically. We determine the entanglement that occurs naturally in such systems for specific types of quantum interactions. At the same time, these systems provide microscopic models for non--Markovian decoherence: the interaction of a group of particles with other...

Source: http://arxiv.org/abs/quant-ph/0502017v1

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25

Sep 20, 2013
09/13

by
L. Hartmann; J. Calsamiglia; W. Dür; H. J. Briegel

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We analyze a microscopic decoherence model in which the total system is described as a spin gas. A spin gas consists of N classically moving particles with additional, interacting quantum degrees of freedom (e.g. spins). For various multipartite entangled probe states, we analyze the decoherence induced by interactions between the probe- and environmental spins in such spin gases. We can treat mesoscopic environments (10^5 particles). We present results for a lattice gas, which could be...

Source: http://arxiv.org/abs/quant-ph/0506208v1

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Sep 21, 2013
09/13

by
A. Asadian; D. Manzano; M. Tiersch; H. J. Briegel

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In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperature, which are coupled to opposite ends of the lattice, with focus on the validity of Fourier's law of heat conduction. We provide analytical solutions of the heat current through the quantum system in the non-equilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The...

Source: http://arxiv.org/abs/1204.0904v1

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Sep 21, 2013
09/13

by
M. Tiersch; U. E. Steiner; S. Popescu; H. J. Briegel

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In theories of spin-dependent radical pair reactions, the time evolution of the radical pair, including the effect of the chemical kinetics, is described by a master equation in the Liouville formalism. For the description of the chemical kinetics, a number of possible reaction operators have been formulated in the literature. In this work, we present a framework that allows for a unified description of the various proposed mechanisms and the forms of reaction operators for the spin-selective...

Source: http://arxiv.org/abs/1204.4634v1

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Sep 18, 2013
09/13

by
H. -J. Briegel; W. Dür; J. I. Cirac; P. Zoller

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In quantum communication via noisy channels, the error probability scales exponentially with the length of the channel. We present a scheme of a quantum repeater that overcomes this limitation. The central idea is to connect a string of (imperfect) entangled pairs of particles by using a novel nested purification protocol, thereby creating a single distant pair of high fidelity. The scheme tolerates general errors on the percent level.

Source: http://arxiv.org/abs/quant-ph/9803056v1

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Sep 19, 2013
09/13

by
W. Dür; M. Hein; J. I. Cirac; H. -J. Briegel

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We consider noisy, non-local unitary operations or interactions, i.e. the corresponding evolutions are described by completely positive maps or master equations of Lindblad form. We show that by random local operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a...

Source: http://arxiv.org/abs/quant-ph/0507134v1

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Sep 17, 2013
09/13

by
W. Dür; R. Raussendorf; V. M. Kendon; H. -J. Briegel

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We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even using existing set-ups-- seems feasible. We analyze the influence of possible imperfections in the experiment and investigate the transition from a quantum random walk to the classical random walk for increasing errors and decoherence.

Source: http://arxiv.org/abs/quant-ph/0207137v1

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Sep 22, 2013
09/13

by
M. Van den Nest; W. Dür; A. Miyake; H. J. Briegel

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We build a framework allowing for a systematic investigation of the issue: "Which quantum states are universal resources for one-way quantum computation?" We start by re-examining what is exactly meant by "universality" in quantum computation, and what the implications are for universal one-way quantum computation. Given the framework of a measurement-based quantum computer, where quantum information is processed by local operations only, the most general universal one-way...

Source: http://arxiv.org/abs/quant-ph/0702116v2

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Sep 20, 2013
09/13

by
M. Van den Nest; W. Dür; G. Vidal; H. J. Briegel

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We investigate for which resource states an efficient classical simulation of measurement based quantum computation is possible. We show that the Schmidt--rank width, a measure recently introduced to assess universality of resource states, plays a crucial role in also this context. We relate Schmidt--rank width to the optimal description of states in terms of tree tensor networks and show that an efficient classical simulation of measurement based quantum computation is possible for all states...

Source: http://arxiv.org/abs/quant-ph/0608060v1

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Sep 22, 2013
09/13

by
R. Hübener; M. Van den Nest; W. Dür; H. J. Briegel

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We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum stabilizer states and product states, thereby generalizing mappings for some specific models established in [Phys. Rev. Lett. 98, 117207 (2007)]. For Ising- and Potts-type models with and without external magnetic field, we show how the entanglement features of the...

Source: http://arxiv.org/abs/0812.2127v2

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Sep 22, 2013
09/13

by
M. Van den Nest; W. Dür; R. Raussendorf; H. J. Briegel

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We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we recover and generalize the simulability of Valiant's match-gates by invoking the solvability of the free-fermion eight-vertex model. Our mappings furthermore provide a systematic formalism to obtain simple quantum algorithms to approximate partition functions of...

Source: http://arxiv.org/abs/0805.1214v1

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Sep 20, 2013
09/13

by
M. Van den Nest; K. Luttmer; W. Dür; H. J. Briegel

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We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact, non-degenerate ground state. We determine for any graph state the minimal d such that it is the non-degenerate ground state of a d-body interaction Hamiltonian, while we show for d'-body Hamiltonians H with d'n spins.

Source: http://arxiv.org/abs/quant-ph/0612186v1

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Sep 21, 2013
09/13

by
S. Anders; M. B. Plenio; W. Dür; F. Verstraete; H. -J. Briegel

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We introduce a variational method for the approximation of ground states of strongly interacting spin systems in arbitrary geometries and spatial dimensions. The approach is based on weighted graph states and superpositions thereof. These states allow for the efficient computation of all local observables (e.g. energy) and include states with diverging correlation length and unbounded multi-particle entanglement. As a demonstration we apply our approach to the Ising model on 1D, 2D and 3D...

Source: http://arxiv.org/abs/quant-ph/0602230v1

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Sep 23, 2013
09/13

by
H. -J. Briegel; T. Calarco; D. Jaksch; J. I. Cirac; P. Zoller

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We develop a method to entangle neutral atoms using cold controlled collisions. We analyze this method in two particular set-ups: optical lattices and magnetic micro-traps. Both offer the possibility of performing certain multi-particle operations in parallel. Using this fact, we show how to implement efficient quantum error correction and schemes for fault-tolerant computing.

Source: http://arxiv.org/abs/quant-ph/9904010v1

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Sep 21, 2013
09/13

by
W. D{ü}r; L. Hartmann; M. Hein; M. Lewenstein; H. J. Briegel

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We consider N initially disentangled spins, embedded in a ring or d-dimensional lattice of arbitrary geometry, which interact via some long--range Ising--type interaction. We investigate relations between entanglement properties of the resulting states and the distance dependence of the interaction in the limit N to infinity. We provide a sufficient condition when bipartite entanglement between blocks of L neighboring spins and the remaining system saturates, and determine S_L analytically for...

Source: http://arxiv.org/abs/quant-ph/0407075v2

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Sep 22, 2013
09/13

by
G. De las Cuevas; W. Dür; H. J. Briegel; M. A. Martin-Delgado

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We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_2 LGT. In this way, all classical spin models with apparently very different features are unified in a single complete model, and a physical relation between all models is established. As applications of this result, we present a new method to do...

Source: http://arxiv.org/abs/0812.3583v2

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Sep 20, 2013
09/13

by
D. Jaksch; H. -J. Briegel; J. I. Cirac; C. W. Gardiner; P. Zoller

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We show that by using cold controlled collisions between two atoms one can achieve conditional dynamics in moving trap potentials. We discuss implementing two qubit quantum--gates and efficient creation of highly entangled states of many atoms in optical lattices.

Source: http://arxiv.org/abs/quant-ph/9810087v1

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Sep 21, 2013
09/13

by
J. -M. Cai; W. Dür; M. Van den Nest; A. Miyake; H. J. Briegel

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Recently, a framework was established to systematically construct novel universal resource states for measurement-based quantum computation using techniques involving finitely correlated states. With these methods, universal states were found which are in certain ways much less entangled than the original cluster state model, and it was hence believed that with this approach many of the extremal entanglement features of the cluster states could be relaxed. The new resources were constructed as...

Source: http://arxiv.org/abs/0902.1097v2

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Jul 20, 2013
07/13

by
H. -J. Briegel; W. Dür; S. J. van Enk; J. I. Cirac; P. Zoller

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We show how to create maximally entangled EPR pairs between spatially distant atoms, each of them inside a high-Q optical cavity, by sending photons through a general, noisy channel, such as a standard optical fiber. An error correction scheme that uses few auxiliary atoms in each cavity effectively eliminates photoabsorption and other transmission errors. This realizes the `absorption free channel.' A concatenation protocol using the absorption free channel allows for quantum communication...

Source: http://arxiv.org/abs/quant-ph/9712027v1

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Sep 19, 2013
09/13

by
H. J. Briegel; D. E. Browne; W. Dür; R. Raussendorf; M. Van den Nest

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Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics can be harnessed and exploited. A number of models of quantum computation exist, including the now well-studied quantum circuit model. Although these models have been shown to be formally equivalent, their underlying elementary concepts and the requirements for their practical realization can differ significantly. The new paradigm of measurement-based quantum...

Source: http://arxiv.org/abs/0910.1116v2

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Sep 21, 2013
09/13

by
M. Hein; W. Dür; J. Eisert; R. Raussendorf; M. Van den Nest; H. -J. Briegel

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Graph states form a rich class of entangled states that exhibit important aspects of multi-partite entanglement. At the same time, they can be described by a number of parameters that grows only moderately with the system size. They have a variety of applications in quantum information theory, most prominently as algorithmic resources in the context of the one-way quantum computer, but also in other fields such as quantum error correction and multi-partite quantum communication, as well as in...

Source: http://arxiv.org/abs/quant-ph/0602096v1

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34

Sep 22, 2013
09/13

by
E. Rico; R. Hübener; S. Montangero; N. Moran; B. Pirvu; J. Vala; H. J. Briegel

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An isotropic anti-ferromagnetic quantum state on a square lattice is characterized by symmetry arguments only. By construction, this quantum state is the result of an underlying valence bond structure without breaking any symmetry in the lattice or spin spaces. A detailed analysis of the correlations of the quantum state is given (using a mapping to a 2D classical statistical model and methods in field theory like mapping to the non-linear sigma model or bosonization techniques) as well as the...

Source: http://arxiv.org/abs/0811.1049v2

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59

Sep 23, 2013
09/13

by
C. E. Mora; M. Piani; A. Miyake; M. Van den Nest; W. Dür; H. J. Briegel

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We investigate which quantum states can serve as universal resources for approximate and stochastic measurement-based quantum computation, in the sense that any quantum state can be generated from a given resource by means of single-qubit (local) operations assisted by classical communication. More precisely, we consider the approximate and stochastic generation of states, resulting e.g. from a restriction to finite measurement settings or from possible imperfections in the resources or local...

Source: http://arxiv.org/abs/0904.3641v2