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Roads towards fault-tolerant universal quantum computation

A Correction to this article was published on 16 May 2018

This article has been updated


A practical quantum computer must not merely store information, but also process it. To prevent errors introduced by noise from multiplying and spreading, a fault-tolerant computational architecture is required. Current experiments are taking the first steps toward noise-resilient logical qubits. But to convert these quantum devices from memories to processors, it is necessary to specify how a universal set of gates is performed on them. The leading proposals for doing so, such as magic-state distillation and colour-code techniques, have high resource demands. Alternative schemes, such as those that use high-dimensional quantum codes in a modular architecture, have potential benefits, but need to be explored further.

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Figure 1: Transversal and non-transversal gates for the Steane code.
Figure 2: Lattice code surgery in the surface code.
Figure 3: Several circuit gadgets.
Figure 4: Magic-state distillation.
Figure 5: Colour codes.

Change history

  • 16 May 2018

    In Fig. 2b of this Review, gates 'Xa+c' and 'Zb' were swapped. This error has been corrected online.


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E.T.C. is supported by the EPSRC (EP/M024261/1). B.M.T. and C.V. acknowledge support from the EU through the ERC GRANT EQEC. This research was also supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development and Innovation.

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E.T.C., B.M.T. and C.V. contributed equally to the planning, writing, researching and graphical work in this Review. C.V. made the movie on the 3D colour code.

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Correspondence to Barbara M. Terhal.

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The authors declare no competing financial interests.

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Reviewer Information Nature thanks H. Bombín and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Construction of a 3D colour code

A short video explaining what makes a tetrahedral colour code. (MP4 44487 kb)

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Campbell, E., Terhal, B. & Vuillot, C. Roads towards fault-tolerant universal quantum computation. Nature 549, 172–179 (2017).

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