Page 190 - Principles and Applications of NanoMEMS Physics

178 Chapter 4

molecules per state because the net polarization of spins is only about one
part in one million. Herein lies one of the main limitations of NMR-based
QC [193], [200]: The fact that the pseudo-pure state signal decreases
exponentially with the number of qubits prepared, while the noise level
remains constant, precludes the methods for extracting pseudo-pure states
from working for more than about 10 nuclear spins.
Thus, the use of pseudo-pure states enables one to obtain a result despite
the highly random nature of the initial state. The question then becomes,
how does one transform an initial random state into a pseudo-pure state with
deviation 000 ... 000 000 ... 000 ? A technique, among various, that is
employed applies magnetic field gradient to the sample in order to make the
frequency of the precessing spins position-dependent and, thus, make it
possible to distinguish different parts of the sample. In particular, the
gradient field induces a position-dependent phase change along the sample.
This is the basis of NMR imaging [193].
Another issue that derives from the ensemble nature of the sample, is that
care must be taken to reduce unintended coupling between qubits [193]. The
established technique to accomplish this is called “refocusing” [193], [194].
The fundamental idea is to apply a pulse at the midpoint of the evolution
°
period to a given spin, of such a phase (typically 180 ) as to undue the
evolution it has experienced over the time period due to the influence of the
undesired coupling [193].
One common issue with QC is the effect of decoherence. In the case of
NMR-based QC decoherence is characterized in terms of two parameters,
namely, the energy relaxation rate, T 1, and the phase randomization rate, T 2
[194]. T 1 captures the energy lost by precessing spins to various mechanisms
such as couplings to other spins, and to phonons and paramagnetic ions, and
chemical reactions such as ions exchanges with the solvent. This source of
decoherence may, by properly choosing the molecules and liquid samples,
be extended to tens of seconds. T 2 captures energy losses due to short- and
long-range spin-spin couplings, the effects of fluctuating magnetic fields due
to the spatial anisotropy of the chemical shifts, local paramagnetic ions, or
unstable laboratory fields. These factors, by properly choosing the quality of
the samples and laboratory equipment allow a decoherence time of one
second or more for molecules in solution [194].

4.3.1.3 The Semiconductor Solid-State Qubit

Given the predominance of solid state silicon electronics technology,
there is a strong motivation to discover and develop paradigms for quantum
computing that exploit qubits embedded in silicon wafers. An early example
of this is the scheme for a silicon-based nuclear spin quantum computer