1
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Boyajian WL, Clausen J, Trenkwalder LM, Dunjko V, Briegel HJ. On the convergence of projective-simulation-based reinforcement learning in Markov decision processes. Quantum Mach Intell 2020; 2:13. [PMID: 33184611 PMCID: PMC7644479 DOI: 10.1007/s42484-020-00023-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2019] [Accepted: 07/02/2020] [Indexed: 06/11/2023]
Abstract
In recent years, the interest in leveraging quantum effects for enhancing machine learning tasks has significantly increased. Many algorithms speeding up supervised and unsupervised learning were established. The first framework in which ways to exploit quantum resources specifically for the broader context of reinforcement learning were found is projective simulation. Projective simulation presents an agent-based reinforcement learning approach designed in a manner which may support quantum walk-based speedups. Although classical variants of projective simulation have been benchmarked against common reinforcement learning algorithms, very few formal theoretical analyses have been provided for its performance in standard learning scenarios. In this paper, we provide a detailed formal discussion of the properties of this model. Specifically, we prove that one version of the projective simulation model, understood as a reinforcement learning approach, converges to optimal behavior in a large class of Markov decision processes. This proof shows that a physically inspired approach to reinforcement learning can guarantee to converge.
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Affiliation(s)
- W. L. Boyajian
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - J. Clausen
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - L. M. Trenkwalder
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
| | - V. Dunjko
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
| | - H. J. Briegel
- Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria
- Department of Philosophy, University of Konstanz, 78457 Konstanz, Germany
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2
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Abstract
We introduce an alternative type of quantum repeater for long-range quantum communication with improved scaling with the distance. We show that by employing hashing, a deterministic entanglement distillation protocol with one-way communication, one obtains a scalable scheme that allows one to reach arbitrary distances, with constant overhead in resources per repeater station, and ultrahigh rates. In practical terms, we show that, also with moderate resources of a few hundred qubits at each repeater station, one can reach intercontinental distances. At the same time, a measurement-based implementation allows one to tolerate high loss but also operational and memory errors of the order of several percent per qubit. This opens the way for long-distance communication of big quantum data.
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Affiliation(s)
- M Zwerger
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
- Departement Physik, Universität Basel, Klingelbergstraße 82, 4056 Basel, Switzerland
| | - A Pirker
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
| | - V Dunjko
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
| | - H J Briegel
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
- Fachbereich Philosophie, Universität Konstanz, Universitätsstraße 10, 78464 Konstanz, Germany
| | - W Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 21a, 6020 Innsbruck, Austria
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3
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Tiersch M, Ganahl EJ, Briegel HJ. Adaptive quantum computation in changing environments using projective simulation. Sci Rep 2015; 5:12874. [PMID: 26260263 PMCID: PMC4531334 DOI: 10.1038/srep12874] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2015] [Accepted: 07/10/2015] [Indexed: 12/02/2022] Open
Abstract
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 strategies in the projective simulator to improve the agent's performance. We demonstrate the applicability by correcting for stray fields in a measurement-based algorithm for Grover's search. Thereby, we lay out a path for adaptive controllers based on intelligent agents for quantum information tasks.
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Affiliation(s)
- M. Tiersch
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21A, A-6020, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21A, A-6020, Innsbruck, Austria
| | - E. J. Ganahl
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21A, A-6020, Innsbruck, Austria
| | - H. J. Briegel
- Institute for Theoretical Physics, University of Innsbruck, Technikerstraße 21A, A-6020, Innsbruck, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Technikerstraße 21A, A-6020, Innsbruck, Austria
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4
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Abstract
We present a hybrid scheme for quantum computation that combines the modular structure of elementary building blocks used in the circuit model with the advantages of a measurement-based approach to quantum computation. We show how to construct optimal resource states of minimal size to implement elementary building blocks for encoded quantum computation in a measurement-based way, including states for error correction and encoded gates. The performance of the scheme is determined by the quality of the resource states, where within the considered error model a threshold of the order of 10% local noise per particle for fault-tolerant quantum computation and quantum communication.
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Affiliation(s)
- M Zwerger
- 1] Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria [2] Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, Innsbruck, Austria
| | - H J Briegel
- 1] Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria [2] Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, Innsbruck, Austria
| | - W Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstr. 25, A-6020 Innsbruck, Austria
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5
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Lanyon BP, Zwerger M, Jurcevic P, Hempel C, Dür W, Briegel HJ, Blatt R, Roos CF. Experimental violation of multipartite Bell inequalities with trapped ions. Phys Rev Lett 2014; 112:100403. [PMID: 24679272 DOI: 10.1103/physrevlett.112.100403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/19/2013] [Indexed: 06/03/2023]
Abstract
We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First, we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second, we analyze Greenberger-Horne-Zeilinger states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Bell-type inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.
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Affiliation(s)
- B P Lanyon
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - M Zwerger
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - P Jurcevic
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - C Hempel
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - W Dür
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - H J Briegel
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - R Blatt
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
| | - C F Roos
- Institut für Quantenoptik und Quanteninformation der Österreichischen Akademie der Wissenschaften, A-6020 Innsbruck, Austria and Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
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6
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Abstract
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Chemical magnetometers are radical
pair systems such as solutions of pyrene and N,N-dimethylaniline (Py–DMA) that show magnetic field
effects in their spin dynamics and their fluorescence. We investigate
the existence and decay of quantum entanglement in free geminate Py–DMA
radical pairs and discuss how entanglement can be assessed in these
systems. We provide an entanglement witness and propose possible observables
for experimentally estimating entanglement in radical pair systems
with isotropic hyperfine couplings. As an application, we analyze
how the field dependence of the entanglement lifetime in Py–DMA
could in principle be used for magnetometry and illustrate the propagation
of measurement errors in this approach.
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Affiliation(s)
- M Tiersch
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences , Technikerstrasse 21A, A-6020 Innsbruck, Austria
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7
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Lanyon BP, Jurcevic P, Zwerger M, Hempel C, Martinez EA, Dür W, Briegel HJ, Blatt R, Roos CF. Measurement-based quantum computation with trapped ions. Phys Rev Lett 2013; 111:210501. [PMID: 24313469 DOI: 10.1103/physrevlett.111.210501] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/03/2013] [Revised: 10/21/2013] [Indexed: 06/02/2023]
Abstract
Measurement-based quantum computation represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the one-way quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurement-based quantum computation using deterministically generated cluster states, in a system of trapped calcium ions. First we implement a universal set of operations for quantum computing. Second we demonstrate a family of measurement-based quantum error correction codes and show their improved performance as the code length is increased. The methods presented can be directly scaled up to generate graph states of several tens of qubits.
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Affiliation(s)
- B P Lanyon
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21A, 6020 Innsbruck, Austria and Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25, 6020 Innsbruck, Austria
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8
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Zwerger M, Briegel HJ, Dür W. Universal and optimal error thresholds for measurement-based entanglement purification. Phys Rev Lett 2013; 110:260503. [PMID: 23848858 DOI: 10.1103/physrevlett.110.260503] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/21/2013] [Indexed: 06/02/2023]
Abstract
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 generalize our results to multipartite EPP, where we encounter similarly high error thresholds.
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Affiliation(s)
- M Zwerger
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria
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9
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Asadian A, Manzano D, Tiersch M, Briegel HJ. Heat transport through lattices of quantum harmonic oscillators in arbitrary dimensions. Phys Rev E Stat Nonlin Soft Matter Phys 2013; 87:012109. [PMID: 23410285 DOI: 10.1103/physreve.87.012109] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2012] [Indexed: 06/01/2023]
Abstract
In d-dimensional lattices of coupled quantum harmonic oscillators, we analyze the heat current caused by two thermal baths of different temperatures, which are coupled to opposite ends of the lattice, with a 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 nonequilibrium steady state using the rotating-wave approximation and bath interactions described by a master equation of Lindblad form. The influence of local dephasing in the transition of ballistic to diffusive transport is investigated.
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Affiliation(s)
- A Asadian
- Institute for Theoretical Physics, University of Innsbruck, Technikerstrasse 25, Innsbruck A-6020, Austria
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10
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Tiersch M, Steiner UE, Popescu S, Briegel HJ. Open Quantum System Approach to the Modeling of Spin Recombination Reactions. J Phys Chem A 2012; 116:4020-8. [DOI: 10.1021/jp209196a] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Tiersch
- Institute for Quantum Optics
and Quantum Information, Austrian Academy of Sciences, Technikerstrasse 21A, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, Technikerstrasse 25, A-6020
Innsbruck, Austria
| | - U. E. Steiner
- Fachbereich
Chemie, Universität Konstanz, D-78457
Konstanz, Germany
| | - S. Popescu
- H. H.
Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8
1TL, United Kingdom
| | - H. J. Briegel
- Institute for Quantum Optics
and Quantum Information, Austrian Academy of Sciences, Technikerstrasse 21A, A-6020 Innsbruck, Austria
- Institute for Theoretical Physics, University of Innsbruck, Technikerstrasse 25, A-6020
Innsbruck, Austria
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11
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Cai JM, Dür W, Van den Nest M, Miyake A, Briegel HJ. Quantum computation in correlation space and extremal entanglement. Phys Rev Lett 2009; 103:050503. [PMID: 19792472 DOI: 10.1103/physrevlett.103.050503] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2009] [Indexed: 05/28/2023]
Abstract
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 "computationally universal" states-i.e., they allow one to efficiently reproduce the classical output of each quantum computation-whereas the cluster states are universal in a stronger sense since they are "universal state preparators." Here, we show that the new resources are universal state preparators after all, and must therefore exhibit a whole class of extremal entanglement features, similar to the cluster states.
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Affiliation(s)
- J-M Cai
- Institut für Quantenoptik und Quanteninformation der Osterreichischen, Akademie der Wissenschaften, Innsbruck, Austria
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12
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De las Cuevas G, Dür W, Briegel HJ, Martin-Delgado MA. Unifying all classical spin models in a lattice gauge theory. Phys Rev Lett 2009; 102:230502. [PMID: 19658914 DOI: 10.1103/physrevlett.102.230502] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/16/2009] [Indexed: 05/28/2023]
Abstract
The partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), is expressed as a special instance of the partition function of the 4D Z2 LGT. This unifies all classical spin models with apparently very different features in a single complete model. This result is applied to establish a new method to compute the mean-field theory of Abelian discrete LGTs with d > or = 4, and to show that computing the partition function of the 4D Z2 LGT is computationally hard (#P hard). The 4D Z2 LGT is also proved to be approximately complete for Abelian continuous models. The proof uses techniques from quantum information.
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Affiliation(s)
- G De las Cuevas
- Institut für Theoretische Physik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
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13
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Van den Nest M, Dür W, Briegel HJ. Completeness of the classical 2D Ising model and universal quantum computation. Phys Rev Lett 2008; 100:110501. [PMID: 18517767 DOI: 10.1103/physrevlett.100.110501] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2007] [Indexed: 05/26/2023]
Abstract
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 with respect to the original one, and we give a constructive method to map such models to the 2D Ising model. For more general models the overhead in system size may be exponential. The results are established by connecting classical spin models with measurement-based quantum computation and invoking the universality of the 2D cluster states.
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Affiliation(s)
- M Van den Nest
- Institut für Quantenoptik und Quanteninformation der Osterreichischen Akademie der Wissenschaften, Innsbruck, Austria
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14
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Abstract
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 insights into these models in a unified way. We recover and generalize several symmetries and high-low temperature dualities, and we provide an efficient classical evaluation of partition functions for all interaction graphs with a bounded tree-width.
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Affiliation(s)
- M Van den Nest
- Institut für Quantenoptik und Quanteninformation der Osterreichischen Akademie der Wissenschaften, Innsbruck, Austria
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15
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Abstract
We present a scheme of quantum computation that consists entirely of one-qubit measurements on a particular class of entangled states, the cluster states. The measurements are used to imprint a quantum logic circuit on the state, thereby destroying its entanglement at the same time. Cluster states are thus one-way quantum computers and the measurements form the program.
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Affiliation(s)
- R Raussendorf
- Theoretische Physik, Ludwig-Maximilians-Universität München, Germany
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16
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Briegel HJ, Raussendorf R. Persistent entanglement in arrays of interacting particles. Phys Rev Lett 2001; 86:910-913. [PMID: 11177971 DOI: 10.1103/physrevlett.86.910] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/11/2000] [Revised: 08/28/2000] [Indexed: 05/23/2023]
Abstract
We study the entanglement properties of a class of N-qubit quantum states that are generated in arrays of qubits with an Ising-type interaction. These states contain a large amount of entanglement as given by their Schmidt measure. They also have a high persistency of entanglement which means that approximately N/2 qubits have to be measured to disentangle the state. These states can be regarded as an entanglement resource since one can generate a family of other multiparticle entangled states such as the generalized Greenberger-Horne-Zeilinger states of <N/2 qubits by simple measurements and classical communication.
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Affiliation(s)
- H J Briegel
- Sektion Physik, Ludwig-Maximilians-Universität, Theresienstrasse 37, D-80333 München, Germany
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17
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Briegel HJ, Englert BG, Scully MO. Spectral properties of a micromaser: Atomic-beam statistics and the field correlation function. Phys Rev A 1996; 54:3603-3613. [PMID: 9913888 DOI: 10.1103/physreva.54.3603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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18
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Briegel HJ, Meyer GM, Englert BG. Dynamic noise reduction in multilevel lasers: Nonlinear theory and the pump-operator approach. Phys Rev A 1996; 53:1143-1159. [PMID: 9912994 DOI: 10.1103/physreva.53.1143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Briegel HJ, Englert BG, Ginzel C, Schenzle A. One-atom maser with a periodic and noisy pump: An application of damping bases. Phys Rev A 1994; 49:5019-5041. [PMID: 9910823 DOI: 10.1103/physreva.49.5019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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21
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22
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Ginzel C, Briegel HJ, Martini U, Englert BG, Schenzle A. Quantum optical master equations: The one-atom laser. Phys Rev A 1993; 48:732-738. [PMID: 9909648 DOI: 10.1103/physreva.48.732] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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23
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