Fault-tolerant quantum computation with constant error

D. Aharonov*, M. Ben-Or

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

375 Scopus citations

Abstract

In the past year many developments have taken place in the area of quantum error corrections. Recently Shor showed how to perform fault tolerant quantum computation when, η, the probability for a fault in one time step per qubit or per gate, is polylogarithmically small. This paper closes the gap and shows how to perform fault tolerant quantum computation when the error probability, η, is smaller than some constant threshold, η0. The cost is polylogarithmic in time and space, and no measurements are used during the quantum computation. The same result is shown also for quantum circuits which operate on nearest neighbors only. To achieve this noise resistance, we use concatenated quantum error correcting codes. The scheme presented is general, and works with any quantum code, that satisfies certain restrictions, namely that it is a `proper quantum code'. The constant threshold η0 is a function of the parameters of the specific proper code used. We present two explicit classes of proper quantum codes. The first class generalizes classical secret sharing with polynomials. The codes are defined over a field with p elements, which means that the elementary quantum particle is not a qubit but a `qupit'. The second class uses a known class of quantum codes and converts it to a proper code. We estimate the threshold η0 to be≈10-6. Hopefully, this paper motivates a search for proper quantum codes with higher thresholds, at which point quantum computation becomes practical.

Original languageAmerican English
Pages (from-to)176-188
Number of pages13
JournalConference Proceedings of the Annual ACM Symposium on Theory of Computing
DOIs
StatePublished - 1997
EventProceedings of the 1997 29th Annual ACM Symposium on Theory of Computing - El Paso, TX, USA
Duration: 4 May 19976 May 1997

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