## Resilient quantum computation (1998)

Venue: | Science |

Citations: | 64 - 3 self |

### BibTeX

@ARTICLE{Nielsen98resilientquantum,

author = {Michael A. Nielsen},

title = {Resilient quantum computation},

journal = {Science},

year = {1998},

pages = {342--345}

}

### Years of Citing Articles

### OpenURL

### Abstract

This article is a short introduction to and review of the cluster-state model of quantum computation, in which coherent quantum information processing is accomplished via a sequence of single-qubit measurements applied to a fixed quantum state known as a cluster state. We also discuss a few novel properties of the model, including a proof that the cluster state cannot occur as the exact ground state of any naturally occurring physical system, and a proof that measurements on any quantum state which is linearly prepared in one dimension can be efficiently simulated on a classical computer, and thus are not candidates for use as a substrate for quantum computation. Key words: quantum computation, cluster states, one-way quantum computer 1.

### Citations

1506 |
Quantum Computation and Quantum Information
- Nielson, Chuang
- 2000
(Show Context)
Citation Context ...nswered about simulation is: “when can one physical system be used to efficiently simulate another?” Recent work on this question has been motivated by the blossoming of interest in quantum computers =-=[20]-=-, as-yet hypothetical devices which, it is hoped, can be used to efficiently simulate any other physical system. Thus, by asking what physical resources are universal for quantum computation, i.e., ca... |

668 |
Can quantum-mechanical description of physical reality be considered complete? Phys
- Einstein, Podolsky, et al.
- 1935
(Show Context)
Citation Context ...asured, i.e., by varying θ, we can vary the unitary transformation effected on the second qubit, without destroying any quantum information. This may be regarded as a generalization of the EPR effect =-=[8]-=-, and may also be viewed as an instance of a quantum error-correcting code (see, e.g., Chapter 11 of [20], and compare with the two-qubit error-detection code in [14].) We can use (12) to explain how ... |

252 |
Quantum computational networks
- Deutsch
- 1989
(Show Context)
Citation Context ...e another, and thus do not differ in the class of computational problems they can efficiently solve. The most widely used model of quantum computation at the present time is the quantum circuit model =-=[7]-=-, which is a generalization of the well-known classical circuit model based on Boolean logical operations such as and and not. We provide a brief review of the quantum circuit model in this section, r... |

151 |
Stabilizer codes and quantum error-correction
- Gottesman
(Show Context)
Citation Context ... the conditions under which quantum error-correcting code states can arise as ground states of Hamiltonian systems. Our results are framed in terms of the stabilizer formalism introduced by Gottesman =-=[9]-=- (see Chapter 10 of [20] for a review). Using the two-stage preparation procedure for the cluster state associated to a graph G it is easy to verify that a set of generators for the stabilizer group o... |

100 | A one-way quantum computer
- Raussendorf, Briegel
(Show Context)
Citation Context ...nderstanding of quantum measurement as a process that inherently destroys quantum coherence. We focus on a class of measurement-based models of quantum computation proposed by Raussendorf and Briegel =-=[24]-=-, the so-called cluster-state model, or one-way quantum computer. The cluster-state model has a remarkably rich structure that is not fully understood, but which differs substantially from the convent... |

45 | The complexity of the local Hamiltonian problem
- Kempe, Kitaev, et al.
(Show Context)
Citation Context ...o develop a general understanding of which clusters can and cannot arise as ground states of physically reasonable Hamiltonians. Note that when the use of ancilla qubits is allowed, the techniques of =-=[12]-=- may be used to obtain any cluster state as an approximate non-degenerate ground state of a reasonable Hamiltonian. However, these techniques have the disadvantage that the resulting gap to the first ... |

29 | Approximation by quantum circuits
- Knill
- 1995
(Show Context)
Citation Context ...l quantum circuits synthesizing desirable unitary operations. For a generic unitary U on n qubits, the number of gates required to synthesize (or even just to approximate) U scales exponentially in n =-=[13]-=-. Such exponential scaling is prohibitively expensive, and it is usually considered far more desirable to find families of unitary operations which can be synthesized using a number of gates that scal... |

29 |
Persistent entanglement in arrays of interacting particles
- Briegel, Raussendorf
(Show Context)
Citation Context ...del of quantum computation. Note that the states we have called cluster states are sometimes also known as graph states. Originally, the term “cluster state” was introduced by Raussendorf and Briegel =-=[28]-=- to refer to the case where the graph G is a two-dimensional square lattice. This was the class of states which they showed in [27] could be used as a substrate for quantum computation. The term “grap... |

27 | Computational model underlying the one-way quantum computer
- Raussendorf, Briegel
- 2002
(Show Context)
Citation Context ...been developed in [1, 6, 11]. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, =-=[28, 2, 17, 22, 23, 29, 26, 25, 27]-=- and references therein for more information. The structure of the paper is as follows. Section 2 presents a short review of the standard unitary quantum circuits model of quantum computation. Section... |

23 |
Unified derivations of measurement-based schemes for quantum computation
- Childs, Leung, et al.
(Show Context)
Citation Context ...sed quantum computation has been proposed in [19], and developed in [15, 16]. We will not explore this other approach here, but note that connections between the two approaches have been developed in =-=[1, 6, 11]-=-. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, [28, 2, 17, 22, 23, 29, 26, ... |

23 | Optical quantum computation using cluster states - Nielsen - 2004 |

20 |
Fault-tolerant quantum computation with cluster states
- Nielsen, Dawson
- 2005
(Show Context)
Citation Context ...been developed in [1, 6, 11]. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, =-=[28, 2, 17, 22, 23, 29, 26, 25, 27]-=- and references therein for more information. The structure of the paper is as follows. Section 2 presents a short review of the standard unitary quantum circuits model of quantum computation. Section... |

17 |
Resource-efficient linear optical quantum computation,” Phys
- Browne, Rudolph
- 2005
(Show Context)
Citation Context ...ry model of quantum computing. These differences have led to new insights into quantum computational complexity [25], and to dramatic simplifications in experimental proposals for quantum computation =-=[21, 3, 30]-=-. An alternate approach to measurement-based quantum computation has been proposed in [19], and developed in [15, 16]. We will not explore this other approach here, but note that connections between t... |

16 |
Unifying quantum computation with projective measurements only and one way quantum computation
- Jorrand, Perdrix
(Show Context)
Citation Context ...sed quantum computation has been proposed in [19], and developed in [15, 16]. We will not explore this other approach here, but note that connections between the two approaches have been developed in =-=[1, 6, 11]-=-. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, [28, 2, 17, 22, 23, 29, 26, ... |

16 | Two-qubit projective measurements are universal for quantum computation
- Leung
- 2001
(Show Context)
Citation Context ...d to dramatic simplifications in experimental proposals for quantum computation [21, 3, 30]. An alternate approach to measurement-based quantum computation has been proposed in [19], and developed in =-=[15, 16]-=-. We will not explore this other approach here, but note that connections between the two approaches have been developed in [1, 6, 11]. More generally, the literature on measurement-based quantum comp... |

15 |
Efficient high-fidelity quantum computation using matter qubits and linear optics. Phys
- Barrett, Kok
- 2005
(Show Context)
Citation Context ...been developed in [1, 7, 14]. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, =-=[32, 2, 8, 20, 25, 26, 33, 3, 13, 30, 29, 31]-=- and references therein for more information. The structure of the paper is as follows. Section 2 presents a short review of the standard unitary quantum circuits model of quantum computation. Section... |

14 |
Experimental one-way quantum computing
- Walther, Resch, et al.
(Show Context)
Citation Context ...ry model of quantum computing. These differences have led to new insights into quantum computational complexity [25], and to dramatic simplifications in experimental proposals for quantum computation =-=[21, 3, 30]-=-. An alternate approach to measurement-based quantum computation has been proposed in [19], and developed in [15, 16]. We will not explore this other approach here, but note that connections between t... |

13 |
Methodology for quantum logic gate construction
- Zhou, Leung, et al.
(Show Context)
Citation Context ...l We now explain how quantum circuits can be simulated using a cluster-state computation. The key idea underlying the simulation is a simple circuit identity, sometimes known as one-bit teleportation =-=[31]-=-: |ψ〉 • H ��� �� (11) |+〉 • X m H|ψ〉[Author and title] 7 Here m is the outome (zero or one) of the computational basis measurement on the first qubit. This identity is easily verified by expanding |ψ... |

12 |
The one-way quantum computer - a non-network model of quantum computation
- Raussendorf, Browne, et al.
(Show Context)
Citation Context ...hat is not fully understood, but which differs substantially from the conventional unitary model of quantum computing. These differences have led to new insights into quantum computational complexity =-=[25]-=-, and to dramatic simplifications in experimental proposals for quantum computation [21, 3, 30]. An alternate approach to measurement-based quantum computation has been proposed in [19], and developed... |

9 | 2004c) Measurement-based quantum Turing machines and their universality
- Perdrix, Jorrand
(Show Context)
Citation Context ...been developed in [1, 6, 11]. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, =-=[28, 2, 17, 22, 23, 29, 26, 25, 27]-=- and references therein for more information. The structure of the paper is as follows. Section 2 presents a short review of the standard unitary quantum circuits model of quantum computation. Section... |

8 |
Thresholds for linear optics quantum computation
- Knill, Laflamme, et al.
- 2000
(Show Context)
Citation Context ...a generalization of the EPR effect [8], and may also be viewed as an instance of a quantum error-correcting code (see, e.g., Chapter 11 of [20], and compare with the two-qubit error-detection code in =-=[14]-=-.) We can use (12) to explain how cluster-state computation can simulate quantum circuits. We begin by explaining how to simulate a single-qubit circuit of the form: |+〉 HZα1 HZα2 (13) This apparently... |

8 |
Valence bond solids for quantum computation
- Verstraete, Cirac
- 2004
(Show Context)
Citation Context |

8 |
The measurement calculus. arXiv:quant-ph/0412135
- Danos, Kashefi, et al.
- 2004
(Show Context)
Citation Context ...been developed in [1, 7, 14]. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, =-=[32, 2, 8, 20, 25, 26, 33, 3, 13, 30, 29, 31]-=- and references therein for more information. The structure of the paper is as follows. Section 2 presents a short review of the standard unitary quantum circuits model of quantum computation. Section... |

4 |
Fault-tolerant quantum computation with graph states
- Aliferis, Leung
- 2005
(Show Context)
Citation Context |

3 |
Computation by measurements: a unifying picture. arXiv:quant-ph/0404082
- Aliferis, Leung
- 2004
(Show Context)
Citation Context ...ng the remarkable property that all the basic dynamical operations are non-unitary quantum measurements, yet they can still be used to simulate arbitrary quantum dynamics, including unitary dynamics. =-=[1]-=-[Author and title] 2 Such models of quantum computation thus challenge the conventional understanding of quantum measurement as a process that inherently destroys quantum coherence. We focus on a cla... |

3 |
Quantum computation by measurement and quantum
- Nielsen
(Show Context)
Citation Context ...nal complexity [25], and to dramatic simplifications in experimental proposals for quantum computation [21, 3, 30]. An alternate approach to measurement-based quantum computation has been proposed in =-=[19]-=-, and developed in [15, 16]. We will not explore this other approach here, but note that connections between the two approaches have been developed in [1, 6, 11]. More generally, the literature on mea... |

3 |
A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single qubit states
- Rudolph, Virmani
- 2005
(Show Context)
Citation Context |

2 |
Universal quantum gates, chapter
- Brylinski, Brylinski
- 2002
(Show Context)
Citation Context ...ling two-qubit gate, such as the controllednot or controlled-phase, it turns out that the gate set is universal, meaning that it can be used to synthesize an arbitrary unitary operation on the qubits =-=[4]-=-. The challenge of quantum computation is to find small quantum circuits synthesizing desirable unitary operations. For a generic unitary U on n qubits, the number of gates required to synthesize (or ... |

2 |
Journal club notes on cluster-state quantum computation. http://qinfo.org/qc-by-measurement
- Nielsen
- 2003
(Show Context)
Citation Context ...ster state model In this section we explain the cluster-state model of quantum computation, and explain how cluster states can be used to efficiently simulate quantum circuits. Our discussion follows =-=[22, 18]-=-, which are based in turn on the original paper [24].[Author and title] 5 3.1. How a cluster-state computation works A cluster-state computation begins with the preparation of a special entangled man... |

1 |
Quantum states far from the energy eigenstates of any local
- Haselgrove, Nielsen, et al.
- 2003
(Show Context)
Citation Context ...ion that this is typically not possible, provided we make a restriction that is usually physically reasonable, namely, that the system has only two-body interactions. The argument we give is based on =-=[10]-=-, which studied the conditions under which quantum error-correcting code states can arise as ground states of Hamiltonian systems. Our results are framed in terms of the stabilizer formalism introduce... |

1 |
Quantum computation by measurements. arXiv:quant-ph/0310189
- Leung
- 2003
(Show Context)
Citation Context ...d to dramatic simplifications in experimental proposals for quantum computation [21, 3, 30]. An alternate approach to measurement-based quantum computation has been proposed in [19], and developed in =-=[15, 16]-=-. We will not explore this other approach here, but note that connections between the two approaches have been developed in [1, 6, 11]. More generally, the literature on measurement-based quantum comp... |

1 |
Complexity of graph state preparation. arXiv:quant-ph/0412071
- Mhalla, Perdrix
- 2004
(Show Context)
Citation Context |

1 |
Nonlinear quantum optical computing via measurement
- Hutchinson, Milburn
(Show Context)
Citation Context ...been developed in [1, 7, 14]. More generally, the literature on measurement-based quantum computation has grown rapidly, and we cannot do a thorough survey of all developments here; see, for example, =-=[32, 2, 8, 20, 25, 26, 33, 3, 13, 30, 29, 31]-=- and references therein for more information. The structure of the paper is as follows. Section 2 presents a short review of the standard unitary quantum circuits model of quantum computation. Section... |