We propose a scheme for electron spin quantum computing based on
electron spin in semiconductors. This scheme shares many similarities
with the existing Kane nuclear spin proposal. We show how quantum
computation may be carried out in this proposal, including single
qubit rotations and CNOT gate. We show how this control can
potentially lead to gate speeds 100-1000 times faster than the
existing nuclear spin proposal, and up to 10<sup>6</sup> times faster than a typical electron spin dephasing time, <i>T<sub>2</sub>(<sub>e</sub>)</i>.
The publication in 1994 of Shor's algorithm, which allows factorization of composite number <i>N</i> in a time polynomial in its binary length <i>L</i> has been the primary catalyst for the race to construct a functional quantum computer. However, it seems clear that any practical system that may be developed will not be able to perform completely error free quantum gate operations or shield even idle qubits from inevitable error effects. Hence, the practicality of quantum algorithms needs to be investigated to estimate what demands must be made of quantum error correction (QEC). Several different quantum circuits implementing the quantum period finding (QPF) subroutine, which lies at the heart of Shor's algorithm have been designed, but each tacitly assumes that arbitrary pairs of qubits can be interacted. While some architectures posses this property, many promising proposals are best suited to realizing a single line of qubits with nearest neighbor interactions only. This paper will present a circuit suitable for implementing the QPF subroutine for such linear nearest neighbor (LNN) designs. We will then present direct simulation results showing for both the LNN circuit and for a circuit utilizing arbitrary interactions, that the QPF subroutine is very sensitive to a small number of errors in the entire circuit. These results can then be used to briefly examine some of the practical issues to implementing such large scale quantum algorithms.
We construct fault-tolerant approximations of rotation gates
required by Shor's algorithm using only fault-tolerant gates that
can be applied to the 7-qubit Steane code. A general scaling law
of how rapidly these fault-tolerant approximations converge to
arbitrary single-qubit gates is also determined.