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Efficient fault-tolerant quantum computing

Nature volume 399, pages 124–126 (1999)Cite this article

Abstract

Quantum computing1—the processing of information according to the fundamental laws of physics—offers a means to solve efficiently a small but significant set of classically intractable problems. Quantum computers are based on the controlled manipulation of entangled quantum states, which are extremely sensitive to noise and imprecision; active correction of errors must therefore be implemented without causing loss of coherence. Quantum error-correction theory2,3,4,5,6,7,8,9 has made great progress in this regard, by predicting error-correcting ‘codeword’ quantum states. But the coding is inefficient and requires many quantum bits10,11,12, which results in physically unwieldy fault-tolerant quantum circuits10,11,12,13,14,15,16,17,18. Here I report a general technique for circumventing the trade-off between the achieved noise tolerance and the scale-up in computer size that is required to realize the error correction. I adapt the recovery operation (the process by which noise is suppressed through error detection and correction) to simultaneously correct errors and perform a useful measurement that drives the computation. The result is that a quantum computer need be only an order of magnitude larger than the logic device contained within it. For example, the physical scale-up factor10,11 required to factorize a thousand-digit number is reduced from 1,500 to 22, while preserving the original tolerated gate error rate (10−5) and memory noise per bit (10−7). The difficulty of realizing a useful quantum computer is therefore significantly reduced.

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Figure 1: Method to measure X̄ 010 while simultaneously extracting the syndrome for Z errors.
Figure 2: Fault-tolerant Toffoli gate on three qubits in the same block.

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Acknowledgements

The author is supported by The Royal Society and St Edmund Hall, Oxford.

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  1. Department of Atomic and Laser Physics, Clarendon Laboratory, Parks Road, OX1 3PU, Oxford, UK

    Andrew M. Steane

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Steane, A. Efficient fault-tolerant quantum computing. Nature 399, 124–126 (1999). https://doi.org/10.1038/20127

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