  Quantum computers promise vastly enhanced computational power and an uncanny
ability to solve classically intractable problems. However, few proposals exist
for robust, solid state implementation of such computers where the quantum
gates are sufficiently miniaturized to have nanometer-scale dimensions. Here I
present a new approach whereby a complete computer with nanoscale gates might
be self-assembled using chemical synthesis. Specifically, I demonstrate how to
self-assemble the fundamental unit of this quantum computer - a 2-qubit
universal quantum controlled-NOT gate - based on two exchange coupled
multilayered quantum dots. Then I show how these gates can be wired using
thiolated conjugated molecules as electrical connectors. A qubit is encoded in
the ground state of a quantum dot spin-split by the Rashba interaction.
Arbitrary qubit rotations are effected by bringing the spin splitting energy in
a target quantum dot in resonance with a global ac magnetic field by applying a
potential pulse of appropriate amplitude and duration to the dot. The
controlled dynamics of the 2-qubit controlled-NOT operation (XOR) can be
realized by exploiting the exchange coupling with the nearest neighboring dot.
A complete prescription for initialization of the computer and data
input/output operations is presented.
