Physics – Quantum Physics
Scientific paper
2004-11-30
Quantum Information and Computation 11, 867-873 (2011)
Physics
Quantum Physics
8 pages, 2 figures. Much shorter version containing only the results still relevant to the field
Scientific paper
We present a simple method for constructing optimal fault-tolerant approximations of arbitrary unitary gates using an arbitrary discrete universal gate set. The method presented is numerical and scales exponentially with the number of gates used in the approximation. However, for the specific case of arbitrary single-qubit gates and the fault-tolerant gates permitted by the concatenated 7-qubit Steane code, we find gate sequences sufficiently long and accurate to permit the fault-tolerant factoring of numbers thousands of bits long. A general scaling law of how rapidly these fault-tolerant approximations converge to arbitrary single-qubit gates is also determined.
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