Topological fault-tolerance in cluster state quantum computation

By Robert Raussendorf, J. Harrington, Kovid Goyal. 2007

568 citations recorded by the source corpus.

We describe a fault-tolerant version of the one-way quantum computer using a cluster state in three spatial dimensions. Topologically protected quantum gates are realized by choosing appropriate boundary conditions on the cluster. We provide equivalence transformations for these boundary conditions that can be used to simplify fault-tolerant circuits and to derive circuit identities in a topological manner. The spatial dimensionality of the scheme can be reduced to two by converting one spatial axis of the cluster into time. The error threshold is 0.75% for each source in an error model with preparation, gate, storage and measurement errors. The operational overhead is poly-logarithmic in the circuit size.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0306a493722600711de4b7bb8b0c4e17a9fb83f3

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Surface code quantum computing by lattice surgery (2011, methodology): “For both code types, d rounds of error correction are needed fully to correct the lattice, in order to produce a spatio-temporal cell of depth d to perform minimum weight matching of the ends of error chains [25].”
Quantum computational advantage with a programmable photonic processor (2022, background): “This is particularly notable because three-dimensional cluster states are sufficient for measurement-based fault-tolerant quantum computing 28,29 ; although the states we synthesize are themselves not cluster states, the device can be readily programmed to generate cluster states by selecting…”
Macroscopic quantum states: Measures, fragility, and implementations (2017, methodology): “We remark that 3D cluster states have been show to be universal for fault-tolerant (encoded) quantum computation using a 2D surface code, with an error threshold for single qubit depolarizing noise of about 0.75% (Briegel et al., 2009; Raussendorf et al., 2007).”
Experimental demonstration of a hyper-entangled ten-qubit Schr\ (2008, methodology): “Indeed, by taking advantage of the hyper-entanglement, it is now possible to reach some experimental regimes that are hardly accessible before, for instance, demonstrations of the robustness of anyonic braiding (7), topological or decoherence-free cluster-state encoding (8,9,42) that require manipul”
Micro-combs: A novel generation of optical sources (2017, background): “quantum computation [316,317] and topological quantum error correction [318].”
Halving the cost of quantum addition (2017, background): “The surface code [5, 8, 21, 22, 11] is a quantum error correcting code that works on a 2D nearest-neighbour array of qubits and achieves a threshold error rate of approximately 1%.”
The XZZX surface code (2020, methodology): “Decoders based on the minimum-weight perfectmatching algorithm [37, 38] are ubiquitous in the quantum error-correction literature [5, 14, 32, 39, 76].”
Optimal resources for topological two-dimensional stabilizer codes : Comparative study (2007, background): “Thus, a topological code amounts to a quantum memory with topological protection and it can be endowed with extra computational capabilities under certain circumstances [8], [10], [9].”
Observation of eight-photon entanglement (2011, background): “One immediate application is to demonstrate the topological error correction schem”
Why I am optimistic about the silicon-photonic route to quantum computing (2016, methodology): “The red/black coloring of qubits is primarily to aid the eye, though for this lattice correspond to primal/dual qubits of the scheme in [19, 21].”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, methodology): “A full fault-tolerant computation can be performed on the RHG lattice with the help of the RHG scheme [40–42, 84].”