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Title:

correlated systems

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Matrix-product states for strongly

Matrix-product states for strongly Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-06-25

Source:

http://edoc.ub.uni-muenchen.de/9755/1/Saberi_Hamed.pdf

http://edoc.ub.uni-muenchen.de/9755/1/Saberi_Hamed.pdf Minimize

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text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Ancilla-assisted sequential approximation of nonlocal unitary operations

Description:

We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing en...

We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the "no-go" theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary entanglers. Despite the negative response from the "no-go" theorem, we demonstrate explicitly how the matrix-product operator(MPO) formalism provides a flexible structure to develop protocols for sequential implementation of such entanglers with an optimal fidelity. The proposed numerical technique, that we call variational matrix-product operator (VMPO), offers a computationally efficient tool for characterizing the "globalness" and entangling capabilities of nonlocal unitary operations. ; Comment: Slightly improved version as published in Phys. Rev. A Minimize

Year of Publication:

2011-08-12

Document Type:

text

Subjects:

Quantum Physics ; Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Strongly Correlated Electrons

Quantum Physics ; Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Strongly Correlated Electrons Minimize

DDC:

518 Numerical analysis *(computed)*

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Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations

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We draw attention to the existence of "genuine" fidelity gaps in an ancilla-assisted sequential decomposition of genuinely entangling isometry and unitary operations of quantum computing. The gaps arise upon a bipartite decomposition of a multiqubit operation in a one-way sequential recipe in which an ancillary system interacts locally and only ...

We draw attention to the existence of "genuine" fidelity gaps in an ancilla-assisted sequential decomposition of genuinely entangling isometry and unitary operations of quantum computing. The gaps arise upon a bipartite decomposition of a multiqubit operation in a one-way sequential recipe in which an ancillary system interacts locally and only once with each qubit in a row. Given the known "no-go" associated with such a theoretically and experimentally desirable decomposition, various figures of merit are introduced to analyze the optimal "fidelity" with which an arbitrary genuinely entangling operation may admit such a sequential decomposition. An efficient variational matrix-product-operator (VMPO) protocol is invoked in order to obtain numerically the minimal values of the fidelity gaps incurred upon sequential decomposition of genuine entanglers. We term the values of the gaps so obtained genuine in the light of possible connections to the concept of the genuine multipartite entanglement and since they are independent of the ancilla dimension and the initial states the associated unitaries act upon. ; Comment: 7 pages, 4 figures Minimize

Year of Publication:

2013-06-03

Document Type:

text

Subjects:

Quantum Physics ; Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Strongly Correlated Electrons

Quantum Physics ; Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Strongly Correlated Electrons Minimize

DDC:

511 General principles of mathematics *(computed)*

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Title:

Matrix-product states for strongly correlated systems and quantum information processing

Publisher:

Ludwig-Maximilians-Universität München

Year of Publication:

2009-01-23

Document Type:

Dissertation ; NonPeerReviewed

Subjects:

Fakultät für Physik

Fakultät für Physik Minimize

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http://edoc.ub.uni-muenchen.de/9755/

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Title:

Ancilla-assisted sequential approximation of nonlocal unitary operations

Description:

We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing en...

We consider the recently proposed "no-go" theorem of Lamata et al [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the no-go theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary entanglers. Despite the negative response from the no-go theorem, we demonstrate explicitly how the matrix-product operator(MPO) formalism provides a flexible structure to develop protocols for sequential implementation of such entanglers with an optimal fidelity. The proposed numerical technique, that we call variational matrix-product operator (VMPO), offers a computationally efficient tool for characterizing the "globalness" and entangling capabilities of nonlocal unitary operations. Minimize

Publisher:

American Physical Society

Year of Publication:

2011-09-16

Document Type:

Artikel ; PeerReviewed

Language:

en ; en

Subjects:

530 Physik

530 Physik Minimize

DDC:

518 Numerical analysis *(computed)*

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http://epub.uni-regensburg.de/21833/1/1108.2647v1.pdf ; http://epub.uni-regensburg.de/21833/4/PhysRevA.84.032323.pdf ; Saberi, Hamed (2011) Ancilla-assisted sequential approximation of nonlocal unitary operations. Phys. Rev. A 84 (3), 032323 .

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Title:

Efficient classical simulation of the Gisin-Massar quantum cloning machine

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We provide here the technical details of the recently proposed tensor-network protocol for classical simulation of the Gisin-Massar quantum cloner by the authors [Phys. Rev. A, 85, 052323 (2012)]. The protocol essentially instructs how to efficiently simulate an optimal quantum cloning machine of Gisin-Massar on a classical computer. A viable co...

We provide here the technical details of the recently proposed tensor-network protocol for classical simulation of the Gisin-Massar quantum cloner by the authors [Phys. Rev. A, 85, 052323 (2012)]. The protocol essentially instructs how to efficiently simulate an optimal quantum cloning machine of Gisin-Massar on a classical computer. A viable computational platform for generation on demand of arbitrary number of optimal clones with controllable numerical resources is realized by rephrasing the Gisin-Massar output state in terms of the hierarchy of the so-called matrix-product states (MPS) and invoking parity features peculiar to such an output. Minimize

Year of Publication:

2013-05-09

Document Type:

text

Subjects:

Quantum Physics ; Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Strongly Correlated Electrons

Quantum Physics ; Condensed Matter - Mesoscale and Nanoscale Physics ; Condensed Matter - Strongly Correlated Electrons Minimize

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Title:

Sequential quantum cloning under real-life conditions

Description:

We consider a sequential implementation of the optimal quantum cloning machine of Gisin and Massar and propose optimization protocols for experimental realization of such a quantum cloner subject to the real-life restrictions. We demonstrate how exploiting the matrix-product state (MPS) formalism and the ensuing variational optimization techniqu...

We consider a sequential implementation of the optimal quantum cloning machine of Gisin and Massar and propose optimization protocols for experimental realization of such a quantum cloner subject to the real-life restrictions. We demonstrate how exploiting the matrix-product state (MPS) formalism and the ensuing variational optimization techniques reveals the intriguing algebraic structure of the Gisin-Massar output of the cloning procedure and brings about significant improvements to the optimality of the sequential cloning prescription of Delgado et al [Phys. Rev. Lett. 98, 150502 (2007)]. Our numerical results show that the orthodox paradigm of optimal quantum cloning can in practice be realized in a much more economical manner by utilizing a considerably lesser amount of informational and numerical resources than hitherto estimated. Instead of the previously predicted linear scaling of the required ancilla dimension D with the number of qubits n, our recipe allows a realization of such a sequential cloning setup with an experimentally manageable ancilla of dimension at most D=3 up to n=15 qubits. We also address satisfactorily the possibility of providing an optimal range of sequential ancilla-qubit interactions for optimal cloning of arbitrary states under realistic experimental circumstances when only a restricted class of such bipartite interactions can be engineered in practice. ; Comment: 8 pages, 4 figures Minimize

Year of Publication:

2012-04-11

Document Type:

text

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Title:

Sequential quantum cloning under real-life conditions

Publisher:

American Physical Society

Year of Publication:

2012-05-29

Document Type:

Artikel ; PeerReviewed

Language:

en

Subjects:

530 Physik

530 Physik Minimize

Relations:

http://epub.uni-regensburg.de/24693/1/4_PhysRevA.85.052323.pdf ; Saberi, Hamed und Mardoukhi, Yousof (2012) Sequential quantum cloning under real-life conditions. Phys. Rev. A 85, 052323-052330.

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Title:

Fractional Gaussian noise criterion for correlations characterization: a random-matrix-theory inspired perspective

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We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the straight analysis of the autocorrelation function. Exploiting the well-studied hierarchy of the fractional Gau...

We introduce a particular construction of an autocorrelation matrix of a time series and its analysis based on the random-matrix theory ideas that is capable of unveiling the type of correlations information which is inaccessible to the straight analysis of the autocorrelation function. Exploiting the well-studied hierarchy of the fractional Gaussian noise (fGn), an \emph{in situ} criterion for the sake of a quantitative comparison with the autocorrelation data is offered. We illustrate the applicability of our method by two paradigmatic examples from the orthodox context of the stock markets and the turbulence. Quite strikingly, a remarkable agreement with the fGn is achieved notwithstanding the non-Gaussianity in returns of the stock market. In the latter context, on the contrary, a significant deviation from an fGn is observed despite a Gaussian distribution of the velocity profile of the turbulence. ; Comment: 9 pages, 10 figures Minimize

Year of Publication:

2013-05-21

Document Type:

text

Subjects:

Physics - Data Analysis ; Statistics and Probability ; Condensed Matter - Statistical Mechanics ; Mathematical Physics

Physics - Data Analysis ; Statistics and Probability ; Condensed Matter - Statistical Mechanics ; Mathematical Physics Minimize

DDC:

519 Probabilities & applied mathematics *(computed)*

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Title:

Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group

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Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating quantum lattice problems can likewise be reformulated in terms of MPS. Thus, the latter constitute a commo...

Wilson's numerical renormalization group (NRG) method for solving quantum impurity models yields a set of energy eigenstates that have the form of matrix product states (MPS). White's density matrix renormalization group (DMRG) for treating quantum lattice problems can likewise be reformulated in terms of MPS. Thus, the latter constitute a common algebraic structure for both approaches. We exploit this fact to compare the NRG approach for the single-impurity Anderson model to a variational matrix product state approach (VMPS), equivalent to single-site DMRG. For the latter, we use an ``unfolded'' Wilson chain, which brings about a significant reduction in numerical costs compared to those of NRG. We show that all NRG eigenstates (kept and discarded) can be reproduced using VMPS, and compare the difference in truncation criteria, sharp vs. smooth in energy space, of the two approaches. Finally, we demonstrate that NRG results can be improved upon systematically by performing a variational optimization in the space of variational matrix product states, using the states produced by NRG as input. ; Comment: 19 pages, 14 figures Minimize

Year of Publication:

2008-04-01

Document Type:

text

Subjects:

Condensed Matter - Strongly Correlated Electrons ; Condensed Matter - Mesoscale and Nanoscale Physics

Condensed Matter - Strongly Correlated Electrons ; Condensed Matter - Mesoscale and Nanoscale Physics Minimize

DDC:

539 Modern physics *(computed)*

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