A fault-tolerant one-way quantum computer

Raussendorf, Robert; Harrington, Jim; Goyal, Kovid

doi:10.1016/j.aop.2006.01.012

Cited by 374 publications

(573 citation statements)

References 20 publications

(52 reference statements)

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“…Note that we combine any single-qubit gates with neighboring two-qubit gates and thus do not have a separate single-qubit error rate. All four of these error rates are set to the same value p and all operations are assumed to take the same amount of time to permit our threshold error rate to be compared with others in the literature [2,21,22].…”

Section: Threshold Error Ratementioning

confidence: 99%

High-threshold universal quantum computation on the surface code

2009

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We present a comprehensive and self-contained simplified review of the quantum computing scheme of [1,2], which features a 2-D nearest neighbor coupled lattice of qubits, a threshold error rate approaching 1%, natural asymmetric and adjustable strength error correction and low overhead, arbitrarily long-range logical gates. These features make it by far the best and most practical quantum computing scheme devised to date. We restrict the discussion to direct manipulation of the surface code using the stabilizer formalism, both of which we also briefly review, to make the scheme accessible to a broad audience.

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Section: Threshold Error Ratementioning

confidence: 99%

High-threshold universal quantum computation on the surface code

2009

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“…The sufficient connectivity implies that measurement-based quantum computation can be realized. The main advantage of using such a 3D resource state is that the quantum computation can be implemented in a topologically protected manner and can tolerate high error rates [33]. We remark that there exist z = 3 regular structures in 3D with higher percolation thresholds than 1/3 [45].…”

Section: Aklt State On the Diamond Latticementioning

confidence: 99%

“…For the latter lattice one can generalize the consideration to three-dimensional percolation and consider conversion of a 3D random graph state (in the supercritical phase) to a 3D cluster state, which can then be useful for providing a fault-tolerant implementation of MBQC [33]. Even though we do not pursue technical demonstration in the present paper, we believe that the AKLT state on the diamond lattice is universal for MBQC.…”

Section: Aklt State On the Diamond Latticementioning

confidence: 99%

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Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states

Wei

Raussendorf

2015

Phys. Rev. A

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We demonstrate that the spin-2 Affleck-Kennedy-Lieb-Tasaki (AKLT) state on the square lattice is a universal resource for the measurement-based quantum computation. Our proof is done by locally converting the AKLT to two-dimensional random planar graph states and by certifying that with high probability the resulting random graphs are in the supercritical phase of percolation using Monte Carlo simulations. One key enabling point is the exact weight formula that we derive for arbitrary measurement outcomes according to a spin-2 POVM on all spins. We also argue that the spin-2 AKLT state on the three-dimensional diamond lattice is a universal resource, the advantage of which would be the possibility of implementing fault-tolerant quantum computation with topological protection. In addition, as we deform the AKLT Hamiltonian, there is a finite region that the ground state can still support a universal resource before making a transition in its quantum computational power.

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“…In particular, in measurementbased quantum computation (MBQC) [1,2], the role of quantum many-body states played in quantum computation is very clear: once the special resource state, which is called the cluster state, is prepared, universal quantum computation is possible with adaptive local measurements on each qubit. This clear separation between the resource preparation and the execution of computation itself has also relaxed the requirements for experimental realization of quantum computation [3][4][5][6][7][8][9][10][11]. Recently, the concept of quantum computational tensor network (QCTN), which is a novel framework of MBQC on general many-body states, has been proposed [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Computational power and correlation in a quantum computational tensor network

Fujii

Morimae

2012

Phys. Rev. A

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We investigate relationships between computational power and correlation in resource states for quantum computational tensor network, which is a general framework for measurement-based quantum computation. We find that if the size of resource states is finite, not all resource states allow correct projective measurements in the correlation space, which is related to non-vanishing two-point correlations in the resource states. On the other hand, for infinite-size resource states, we can always implement correct projective measurements if the resource state can simulate arbitrary single-qubit rotations, since such a resource state exhibits exponentially decaying two-point correlations. This implies that a many-body state whose two-point correlation cannot be upperbounded by an exponentially decaying function cannot simulate arbitrary single-qubit rotations.

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A fault-tolerant one-way quantum computer

Cited by 374 publications

References 20 publications

High-threshold universal quantum computation on the surface code

High-threshold universal quantum computation on the surface code

Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states

Computational power and correlation in a quantum computational tensor network

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