Topological fault-tolerance in cluster state quantum computation

Raussendorf, Robert; Harrington, Jim; Goyal, Kovid

doi:10.1088/1367-2630/9/6/199

Cited by 586 publications

(1,000 citation statements)

References 31 publications

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“…This paper is a simplified review of the quantum computing scheme of [1,2]. The scheme requires a 2-D square lattice of nearest neighbor coupled qubits with initialization, readout, memory and quantum gates all operating with error rates less than approximately 1% -the least challenging set of physical requirements devised to date.…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

High-threshold universal quantum computation on the surface code

2009

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“…In the surface code, measurements of nontrivial commuting operators (stabilizers) are used to project onto a "code state," and logical qubits are effectively encoded in the anyon charge of a region by ceasing certain stabilizer measurements [26][27][28][29]. The logical gates necessary for universal quantum computation are realized through sequences of measurements used to move and braid the logical qubits.…”

Section: Introductionmentioning

confidence: 99%

Majorana Fermion Surface Code for Universal Quantum Computation

2015

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We introduce an exactly solvable model of interacting Majorana fermions realizing Z 2 topological order with a Z 2 fermion parity grading and lattice symmetries permuting the three fundamental anyon types. We propose a concrete physical realization by utilizing quantum phase slips in an array of Josephson-coupled mesoscopic topological superconductors, which can be implemented in a wide range of solid-state systems, including topological insulators, nanowires, or two-dimensional electron gases, proximitized by s-wave superconductors. Our model finds a natural application as a Majorana fermion surface code for universal quantum computation, with a single-step stabilizer measurement requiring no physical ancilla qubits, increased error tolerance, and simpler logical gates than a surface code with bosonic physical qubits. We thoroughly discuss protocols for stabilizer measurements, encoding and manipulating logical qubits, and gate implementations.

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“…1 contains an example of a (primal) nest generated by Autotune. This nest is associated with the surface code [15][16][17]. Only a basic understanding of the definitions of detection events and nests contained in this paragraph is required to read this work.…”

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confidence: 99%

Analytic asymptotic performance of topological codes

Fowler

2013

Phys. Rev. A

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Topological quantum error correction codes are extremely practical, typically requiring only a 2-D lattice of qubits with tunable nearest neighbor interactions yet tolerating high physical error rates p. It is computationally expensive to simulate the performance of such codes at low p, yet this is a regime we wish to study as low physical error rates lead to low qubit overhead. We present a very general method of analytically estimating the low p performance of the most promising class of topological codes. Our method can handle arbitrary periodic quantum circuits implementing the error detection associated with this class of codes, and arbitrary Pauli error models for each type of quantum gate. Our analytic expressions take only seconds to obtain, versus hundreds of hours to perform equivalent low p simulations.

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Topological fault-tolerance in cluster state quantum computation

Cited by 586 publications

References 31 publications

High-threshold universal quantum computation on the surface code

High-threshold universal quantum computation on the surface code

Majorana Fermion Surface Code for Universal Quantum Computation

Analytic asymptotic performance of topological codes

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