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Summary: Fault-Tolerant Quantum Computation With
Constant Error
D. Aharonov M. Ben-Or y
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, , 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 quan-
tum computation when the error probability, , is smaller than some
constant threshold, 0 . 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 satis es certain restrictions, namely that it is a
\proper quantum code". The constant threshold 0 is a function of
the parameters of the speci c proper code used.
We present two explicit classes of proper quantum codes. The rst
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