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Cited by 1,090Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Measurement-based quantum computation

Open access
Briegel, H. J., Browne, D. E., Dür, W., Raussendorf, R., Van den Nest, M.·2009·Nature Physics
DOI 10.1038/nphys1157
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Abstract

Quantum computation offers a promising new kind of information processing, where the non-classical features of quantum mechanics are harnessed and exploited. A number of models of quantum computation exist. These models have been shown to be formally equivalent, but their underlying elementary concepts and the requirements for their practical realization can differ significantly. A particularly exciting paradigm is that of measurement-based quantum computation, where the processing of quantum information takes place by rounds of simple measurements on qubits prepared in a highly entangled state. We review recent developments in measurement-based quantum computation with a view to both fundamental and practical issues, in particular the power of quantum computation, the protection against noise (fault tolerance) and steps towards experimental realization. Finally, we highlight a number of connections between this field and other branches of physics and mathematics. So-called one-way schemes have emerged as a powerful model to describe and implement quantum computation. This article reviews recent progress, highlights connections to other areas of physics and discusses future directions.

AI snapshot

Written from the paper’s full text.

TL;DR

This review surveys measurement-based quantum computation (MQC), focusing on the one-way quantum computer, where a universal 2D cluster state is consumed by adaptive single-qubit measurements. It covers experimental proposals, fault-tolerance thresholds, entanglement-based universality and classical simulatability, and connections to classical statistical mechanics.

Key findings

  • In the one-way model, universal quantum computation is achieved by sequences of adaptive single-qubit measurements on a 2D cluster state prepared independently of the algorithm; the entire computational power is traced to the entangled resource state.
  • Fault-tolerance results include a threshold of \(6.7 \times 10^{-3}\) for a 3D cluster state with probabilistic gate errors including imperfect preparation, and \(7.5 \times 10^{-3}\) for a 2D variant, described as the highest known threshold for a two-dimensional local architecture. Optical schemes show a trade-off allowing e.g. gate error rate \(10^{-4}\) and photon loss rate \(3 \times 10^{-3}\), and with only non-unit source/detection efficiencies a threshold of \(\eta_S \eta_D > 2/3\).
  • Universal state-preparator resources must be maximally entangled with respect to all types of entanglement; 1D cluster states, GHZ states, W-states, Dicke states, and certain ground states of strongly correlated 1D spin systems are not universal, while graph states on regular 2D lattices (triangular, hexagonal, Kagome) and lattices with up to about 40% defects are universal.
  • A mapping identifies the Ising partition function \(Z_L\) with an overlap between a graph state \(|\psi_L\rangle\) and a product state; solvability of the 2D Ising model without magnetic fields implies efficient classical simulation of MQC on the toric code state, and the 2D Ising model with magnetic fields is “complete” for partition functions of any \(q\)-state spin model on an arbitrary lattice.

Methods

  • Review article; no primary data, sample, or new experiments are reported.
  • Main analysis is a conceptual synthesis of theoretical and experimental developments in MQC, fault tolerance, entanglement resource theory, classical simulation, and mappings to classical spin models.

Limitations

  • Stated in the paper: single-site addressing in optical lattices remains unsolved; scalable photonic one-way computation needs higher-efficiency single photon sources; it is not known whether a universal quantum computer disallows efficient classical simulation; and understanding of universality in MQC remains incomplete.
  • Evident from the text: as a review, it presents no new experimental data or systematic meta-analysis, and its coverage is explicitly a “selection of recent results” focused on the one-way quantum computer rather than all measurement-based approaches.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/nphys1157

Cites

113 of 113 references verified0 citation errors · 0 not checkable

Statistics

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Claims the paper makes

0 of 107 cited sources checked · 0 supported · 0 flagged

  • Interpretationreasoning
    § 1 Introduction · p. 2

    The entire computational power of the one-way quantum computer can be traced back to the properties of its entangled resource state.

    “the computational power of such a quantum computer can be traced back entirely to the properties of its entangled resource state”
    • Also stated in: § 4 Entanglement as a resource for computational power · p. 9 · plain
      “the entire computational power of the one-way quantum computer is carried by the entanglement structure of its resource state.”
    Quote in the paperSubstantial claim
  • Interpretationreasoning
    § 1 Introduction · p. 2

    The problem of experimental realization of a quantum computer in MQC is reduced to preparing a specific multi-particle state and performing single-qubit measurements.

    “the problem of an experimental realization of a quantum computer is now reduced to the preparation of a specific multi-particle state, and the ability to perform single-qubit measurements”
    Quote in the paperSubstantial claim
  • Premisereasoning
    § 1 Introduction · p. 2

    In one-way quantum computation, the algorithm is specified by the pattern of single-qubit measurements (order and basis).

    “In a second step, the qubits in the system are measured individually , in a certain order and basis-and it is this measurement pattern which specifies the entire algorithm”
    Quote in the paperSubstantial claim
  • Premisecitation
    § 1 Introduction · p. 2

    In one-way quantum computation, the resource state (2D-cluster state) is prepared independently of the quantum algorithm to be implemented.

    “the system is first prepared in a highly entangled quantum state, the 2D-cluster state 20 (see Fig. 1), independently of the quantum algorithm which is to be implemented”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [20] Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001). source

      Not checked in the free run.

  • Premisecitation
    § 1 Introduction · p. 2

    The one-way quantum computer achieves universal quantum computation using only single-qubit measurements.

    “in the one-way quantum computer-which will be the focus of this article-universal quantum computation can be achieved with single-qubit measurements only”
    • Also stated in: § 2 Experimental proposals and achievements · p. 4 · plain
      “The oneway quantum computer is universal : even though the results of the measurements in every step of the computation are random, any quantum computation can deterministically be realized.”
    • Also stated in: § 4 Entanglement as a resource for computational power · p. 9 · plain
      “In MQC, universal quantum computation is realized by performing sequences of single-qubit measurements on a system which has initially been prepared in a 2D-cluster state.”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [10] Raussendorf, R. & Briegel, H. J. A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001). source

      Not checked in the free run.

    • cites [11] Raussendorf, R. & Briegel, H. J. Computational model underlying the one-way quantum computer. Quantum Inform. Comput. 2, 443–486 (2002). source

      Not checked in the free run.

    • cites [12] Raussendorf, R., Browne, D. E. & Briegel, H. J. Measurement-based quantum computation using cluster states. Phys. Rev. A 68, 022312 (2003). source

      Not checked in the free run.

  • May combine two claims. 15
  • Classified as probably not a substantial claim. 8

  • May combine two claims.

    Premisecitation
    § 2 Experimental proposals and achievements · p. 3

    In optical lattices, tuning the polarization of trapping lasers can induce entangling interactions between neighboring atoms and create a cluster state across the whole lattice.

    “Tuning the polarization of the trapping lasers can induce entangling interactions 22,23 between neighboring atoms across the array and create a cluster state across the whole lattice 20,24,25 .”
    Quote in the paperNot a substantial claim0 of 5 sources checked
    • cites [22] Jaksch, D., Briegel, H. J., Cirac, J. I., Gardiner, C. W. & Zoller, P. Entanglement of atoms via cold controlled collisions. Phys. Rev. Lett. 82, 1975–1978 (1999). source

      Not checked in the free run.

    • cites [23] Jaksch, D. & Zoller, P. The cold atom Hubbard toolbox. Ann. Phys. 315, 52–79 (2005). source

      Not checked in the free run.

    • cites [20] Briegel, H. J. & Raussendorf, R. Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001). source

      Not checked in the free run.

    • cites [24] Briegel, H. J., Raussendorf, R. & Schenzle, A. in Laser Physics at the Limits (eds Figger, H. et al.) 236–261 (Springer, 2002).

      Not checked in the free run.

    • cites [25] Mandel, O. et al. Controlled collisions for multi-particle entanglement of optically trapped atoms. Nature 425, 937–940 (2003). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § 2 Experimental proposals and achievements · p. 4

    Proof-of-principle experiments of a one-way quantum computer with few qubits have already been performed using photons.

    “Proof-of-principle experiments of a one-way quantum computer with few qubits have already been performed in which qubits are represented by photons.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 2 Experimental proposals and achievements · p. 5

    In hybrid optical-matter schemes, entangling operations can be achieved non-deterministically via emission of photons entangled with qubits and non-deterministic linear optical entangling gates.

    “Entangling operations can be achieved non-deterministically, via the emission of photons, entangled with the qubits, and then adopting non-deterministic linear optical entangling gates 50,51 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [50] Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007). source

      Not checked in the free run.

    • cites [51] Laurat, J. et al. Towards experimental entanglement connection with atomic ensembles in the single excitation regime. New J. Phys. 9, 207 (2007). source

      Not checked in the free run.

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    Premisecitation
    § 2 Experimental proposals and achievements · p. 5

    Demonstration experiments of key components of one-way quantum computation have been achieved using post-selection, demonstrating basic principles including simple algorithms and active feed forward.

    “However, demonstration experiments of the key components have been achieved, using post-selection 43-49 .”
    • Also stated in: § 2 Experimental proposals and achievements · p. 5 · boosted
      “These achievements have demonstrated the basic principles of one-way quantum computation, with recent experiments including simple algorithms and active feed forward of measurement results 46,49 .”
    Quote in the paperNot a substantial claim0 of 7 sources checked
    • cites [43] Walther, P. et al. Experimental one-way quantum computing. Nature 434, 169–176 (2005). source

      Not checked in the free run.

    • cites [44] Kiesel, N. et al. Experimental analysis of a four-qubit photon cluster state. Phys. Rev. Lett. 95, 210502 (2005). source

      Not checked in the free run.

    • cites [45] Lu., C. Y. et al. Experimental entanglement of six photons in graph states. Nature Phys. 3, 91–95 (2007). source

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    • cites [46] Prevedel, R. et al. High-speed linear optics quantum computing using active feed-forward. Nature 445, 65–69 (2007). source

      Not checked in the free run.

    • cites [47] Vallone, G., Pomarico, E., De Martini, F., Mataloni, P. & Berardi, V. Realization and characterization of a 2-photon 4-qubit linear cluster state. Phys. Rev. Lett. 98, 180502 (2007). source

      Not checked in the free run.

    • cites [48] Chen, K. et al. Experimental realization of one-way quantum computing with two-photon four-qubit cluster states. Phys. Rev. Lett. 99, 120503 (2007). source

      Not checked in the free run.

    • cites [49] Vallone, G., Pomarico, E., De Martini, F. & Mataloni, P. Active one-way quantum computation with 2-photon 4-qubit cluster states. Phys. Rev. Lett. 100, 160502 (2008). source

      Not checked in the free run.

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    Premisecitation
    § 2 Experimental proposals and achievements · p. 3

    Recent experiments use exchange interactions in double-well potentials to create arrays of robust Bell pairs, which could be used as an alternative way to create cluster states in the lattice.

    “Recent experiments use exchange interactions in double-well potentials to create arrays of robust Bell pairs, which could be used as an alternative way to create cluster states in the lattice 29,30”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [29] Anderlini, M. et al. Controlled exchange interaction between pairs of neutral atoms in an optical lattice. Nature 448, 452–455 (2007). source

      Not checked in the free run.

    • cites [30] Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295–299 (2008). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 2 Experimental proposals and achievements · p. 5

    There have been proposals to implement one-way quantum computation or create cluster states in solid state systems using superconducting circuits and quantum dots.

    “In addition to these works, there have been a series of proposals how to implement one-way quantum computation (or to create cluster states) in solid state systems, using superconducting circuits 55 and quantum dots 56,57 .”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [55] Tanamoto, T., Liu, Y. X., Fujita, S., Hu, X. & Nori, F. Producing cluster states in charge qubits and flux qubits. Phys. Rev. Lett. 97, 230501 (2006). source

      Not checked in the free run.

    • cites [56] Borhani, M. & Loss, D. Cluster states from Heisenberg interaction. Phys. Rev. A 71, 034308 (2005). source

      Not checked in the free run.

    • cites [57] Weinstein, Y. S., Hellberg, C. S. & Levy, J. Quantum-dot cluster-state computing with encoded qubits. Phys. Rev. A 72, 020304(R) (2005). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S4 (based).

    Interpretationreasoning
    § 2 Experimental proposals and achievements · p. 4

    Combining single-site addressing and lattice-wide entangling operations would allow large-scale one-way quantum computation to be realized in an optical lattice system.

    “Combining single-site addressing and lattice-wide entangling operations would allow large-scale one-way quantum computation to be realized in an optical lattice system.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisenone given
    § 2 Experimental proposals and achievements · p. 6

    One-way computation can be implemented in a variety of systems, offering massively parallel operations (e.g., atoms in optical lattices) or non-deterministic operations (e.g., photons).

    “One-way computation can be implemented in a variety of systems, offering e.g. massively parallel operations, such as with atoms in optical lattices, or even non-deterministic operations, such as with photons.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 3 Topological protection of information and fault-tolerant computation · p. 7

    The one-way quantum computer may be advantageously combined with the KLM scheme of optical quantum computation, and fault-tolerant schemes using photons have been developed.

    “First, after it was realized 37,42,68 that the one-way quantum computer may be advantageously combined with the KLM scheme of optical quantum computation 7 and fault-tolerant schemes using photons were developed 69-71 .”
    Quote in the paperNot a substantial claim0 of 7 sources checked
    • cites [37] Nielsen, M. A. Optical quantum computation using cluster states. Phys. Rev. Lett. 93, 040503 (2004). source

      Not checked in the free run.

    • cites [42] Browne, D. E. & Rudolph, T. Resource-efficient linear optical quantum computation. Phys. Rev. Lett. 95, 010501 (2005). source

      Not checked in the free run.

    • cites [68] Mor, T. & Yoran, N. Methods for scalable optical quantum computation. Phys. Rev. Lett. 97, 090501 (2006). source

      Not checked in the free run.

    • cites [7] Knill, E., Laflamme, R. & Milburn, G. J. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001). source

      Not checked in the free run.

    • cites [69] Dawson, C. M., Haselgrove, H. L. & Nielsen, M. A. Noise thresholds for optical quantum computers. Phys. Rev. Lett. 96, 020501 (2006). source

      Not checked in the free run.

    • cites [70] Dawson, C. M., Haselgrove, H. L. & Nielsen, M. A. Noise thresholds for optical cluster-state quantum computation. Phys. Rev. A 73, 052306 (2006). source

      Not checked in the free run.

    • cites [71] Varnava, M., Browne, D. E. & Rudolph, T. Loss tolerance in one-way quantum computation via counterfactual error correction. Phys. Rev. Lett. 97, 120501 (2006). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § 3 Topological protection of information and fault-tolerant computation · p. 8

    A 3D cluster state combines the universality already found in the 2D counterpart with the topological error-correction capabilities of the toric code.

    “A 3D cluster state combines the universality already found in the 2D counterpart with the topological error-correction capabilities of the toric code 74 .”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [74] Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003). source

      Not checked in the free run.

  • May combine two claims.

    Premisecitation
    § 3 Topological protection of information and fault-tolerant computation · p. 9

    The 2D variant yields a threshold value of 7.5 × 10^-3, which is the highest known threshold for a two-dimensional local architecture.

    “It yields a threshold value of 7 . 5 × 10 -3 77 which is the highest known threshold for a two-dimensional local architecture (see also 78 ).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [77] Raussendorf, R. & Harrington, J. Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007). source

      Not checked in the free run.

    • cites [78] Svore, K. M., DiVincenzo, D. P. & Terhal, B. M. Noise threshold for a fault-tolerant two-dimensional lattice architecture. Quant. Inf. Comp. 7, 297–318 (2007).

      Not checked in the free run.

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    Premisecitation
    § 3 Topological protection of information and fault-tolerant computation · p. 8

    Error-correction is directly built into the 3D cluster lattice and yields a threshold of 6.7 × 10^-3 for a model with probabilistic gate errors, including imperfect preparation of the cluster state.

    “Error-correction is directly built into the cluster lattice and yields a threshold of 6 . 7 × 10 -3 75 , for a model with probabilistic gate errors, including imperfect preparation of the cluster state.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [75] Raussendorf, R., Harrington, J. & Goyal, K. Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9, 199 (2007). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § 3 Topological protection of information and fault-tolerant computation · p. 9

    This scenario is suited for realization in optical lattices, arrays of superconducting qubits, and ion traps.

    “This scenario is suited for realization in e.g. optical lattices, but also arrays of superconducting qubits, and ion traps.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Premisecitation
    § 4 Entanglement as a resource for computational power · p. 10

    Toric code states and ground states of several 1D spin systems are examples of simulatable states.

    “Further interesting examples of simulatable states include the toric code states 92 and the ground states of several 1D spin systems 93 .”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [92] Bravyi, S. & Raussendorf, R. Measurement-based quantum computation with the toric code states. Phys. Rev. A 76, 022304 (2007). source

      Not checked in the free run.

    • cites [93] Verstraete, F. & Cirac, J. I. Matrix product states represent ground states faithfully. Phys. Rev. B 73, 094423 (2006). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § 4 Entanglement as a resource for computational power · p. 9

    In each of these non-universal cases, there is at least one type of entanglement which is nonmaximal, implying they cannot be universal state preparator resources.

    “However, in each case there is at least one type of entanglement which is nonmaximal, implying that these states cannot be universal state preparator resources.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 4 Entanglement as a resource for computational power · p. 9

    There exist several natural notions of 'universality'.

    “Afirst feature which is to be emphasized, is that there exist several natural notions of 'universality' 79 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [79] Van den Nest, M., Dür, W., Miyake, A. & Briegel, H. J. Fundamentals of universality in one-way quantum computation. New J. Phys. 9, 204 (2007). source

      Not checked in the free run.

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    Premisecitation
    § 4 Entanglement as a resource for computational power · p. 10

    For the majority of states identified as not universal, efficient classical simulation is possible; specifically, the outcome probabilities of any sequence of single-qubit measurements can be efficiently and exactly computed.

    “For example, for the majority of states which have been identified above as not being universal, one has shown that efficient classical simulation is possible. More precisely, for such states it is possible to efficiently and exactly compute the outcome probabilities of any sequence of single-qubit measurements.”
    Quote in the paperNot a substantial claim0 of 4 sources checked
    • cites [88] Markov, I. & Shi, Y. Simulating quantum computation by contracting tensor networks. SIAM J. Comput. 38, 963–981 (2008). source

      Not checked in the free run.

    • cites [89] Jozsa, R. On the simulation of quantum circuits. Preprint at < http://arxiv.org/abs/quant-ph/0603163 > (2006).

      Not checked in the free run.

    • cites [90] Yoran, N. & Short, A. J. Classical simulation of limited-width cluster-state quantum computation. Phys. Rev. Lett. 96, 170503 (2006). source

      Not checked in the free run.

    • cites [91] Shi, Y.-Y., Duan, L.-M. & Vidal, G. Classical simulation of quantum many-body systems with a tree tensor network. Phys. Rev. A 74, 022320 (2006). source

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  • Classified as probably not a substantial claim.

    Premisecitation
    § 4 Entanglement as a resource for computational power · p. 9

    A universal measurement-based quantum computer is identified as a device which allows for universal state preparation by local operations only.

    “Thus, a universal measurement-based quantum computer is then identified as a device which allows for universal state preparation by local operations only 79,80 .”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [79] Van den Nest, M., Dür, W., Miyake, A. & Briegel, H. J. Fundamentals of universality in one-way quantum computation. New J. Phys. 9, 204 (2007). source

      Not checked in the free run.

    • cites [80] Van den Nest, M., Miyake, A., Dür, W. & Briegel, H. J. Universal resources for measurement-based quantum computation. Phys. Rev. Lett. 97, 150504 (2006). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation
    § 5 MQCand classical statistical mechanics · p. 12

    Additional connections between MQC and other fields have been established, for example to decidability of formal languages in mathematical logic.

    “Finally, we mention that additional connections between MQC and other fields have been established, e.g. to decidability of formal languages in mathematical logic 103 .”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [103] Van den Nest, M. & Briegel, H. J. Measurement-based quantum computation and undecidable logic. Foundations Phys. 38, 448–457 (2008). source

      Not checked in the free run.

  • May combine two claims.

    Interpretationreasoning
    § 5 MQCand classical statistical mechanics · p. 12

    Any model whose partition function can efficiently be computed leads to a corresponding MQC that offers no computational advantage over classical devices, and vice versa.

    “Eq. (2) now implies that any model where the partition function can efficiently be computed, leads to a corresponding MQC which offers no computational advantage over classical devices, and vice versa.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Premisecitation
    § 5 MQCand classical statistical mechanics · p. 11

    The multiparticle entangled state |ψ_L> encodes the interaction pattern and is a graph state.

    “The multiparticle entangled state | ψ L 〉 95 encodes the interaction pattern and is a graph state 21 (see Fig. 1).”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [95] Van den Nest, M., Dür, W. & Briegel, H. J. Completeness of the classical 2D Ising model and universal quantum computation. Phys. Rev. Lett. 100, 110501 (2008). source

      Not checked in the free run.

    • cites [21] Hein, M. et al. in Quantum Computers, Algorithms and Chaos Vol. 162 Int. School of Physics Enrico Fermi (eds Casati, G et al.) 115–218 (IOS Press, 2006).

      Not checked in the free run.

  • May combine two claims.

    Premisenone given
    § 5 MQCand classical statistical mechanics · p. 11

    The product state ⊗_i |α_i> contains no entanglement and specifies interaction strengths, local magnetic fields, and the temperature of the model.

    “The product state ⊗ i | α i 〉 contains no entanglement and specifies interaction strengths and local magnetic fields as well as the temperature of the model.”
    Quote in the paperSubstantial claim
22 of 22

  • The paper relies on this without support.

    In realistic physical systems, decoherence tends to make quantum systems behave more classically.

    “In realistic physical systems, decoherence tends to make quantum systems behave more classically.”

  • The paper relies on this without support.

    Different quantum computational models can simulate one another efficiently and are equivalent in the complexity-theoretic sense.

    “since the different quantum computational models can simulate one another efficiently and are thus, in this complexity theoretic sense, equivalent.”
2 of 2

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • Another significant step is the discovery of cluster-state quantum computing (Raussendorf and Briegel, 2001; Raussendorf et al., 2003; Briegel et al., 2009), which is based on the preparation of highly entangled multi-qubit states, the so-called cluster states (Briegel and Raussendorf, 2001) and adaptive one-qubit measurements.

    “Another significant step is the discovery of”

    From Multiphoton entanglement and interferometry (2012) · cites this paper as Briegel et al., 2009

  • BQC uses the concept of one-way quantum computing, a measurement-based model of computation.

    “BQC uses the concept of one-way quantum computing [33-37], a measurement-based model of computation [38, 39] which represents a paradigm shift in the understanding of complex data processing by clearly separating the classical and quantum parts of a computation.”

    From Demonstration of Blind Quantum Computing (2012) · cites this paper as [37]

Cites

Flagged first, then by citations

Research works printed but not linked: 5

  1. Bernstein, E. & Vazirani, U. Proc. 25th Annual ACM Symp. on the Theory of Computing 11–20 (ACM, 1993).
  2. Shor, P. W. Proc. 37th Annual Symp. Foundations of Computer Science 56–65 (IEEE Computer Society Press, 1996).
  3. Raussendorf, R. Measurement-Based Quantum Computation with Cluster States. Thesis, Ludwig-Maximilians-Univ. Munich (2003). · DOI · Paper page
  4. Aliferis, P. & Leung, D. W. Computation by measurements: A unifying picture. Phys. Rev. A 70, 062314 (2004). · DOI · Paper page
  5. Aharonov, D., Arad, I., Eban, E. & Landau, Z. Polynomial quantum algorithms for additive approximations of the Potts model and other points of the Tutte plane. Preprint at < http://arxiv.org/abs/quant-ph/0702008 > (2007). · arXiv

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Authors
Briegel, H. J., Browne, D. E., Dür, W., Raussendorf, R., & Van den Nest, M.
Affiliations
  • Austrian Academy of Sciences (AT)
  • University College London (GB)
  • University of British Columbia (CA)
Corresponding author
Briegel, H. J.
ORCID
Venue
Nature Physics
Publisher
Springer Science and Business Media LLC
Published
2009-01
Volume
5
Issue
1
Pages
19-26
ISSN
  • 1745-2473 (ISSN-L)
  • 1745-2481
DOI
10.1038/nphys1157
OpenAlex
W2045702468
Semantic Scholar
7389fe01fdee8536402c08294cf789855a15c810
Cited by
1,090
References
113
Citations by year
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FWCI
39.35
Type
journal article
Language
en
Open access
Licence
www.springer.com/tdm (tdm)
Locations
  • Nature Physics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Max Planck Institute for Plasma Physics (submittedVersion)
  • UCL Discovery (University College London) (submittedVersion)
  • MPG.PuRe (Max Planck Society) (submittedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
measurement-based quantum computation, one-way quantum computation, fault tolerance, noise protection, quantum information processing

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-09.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-09.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

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