Page 179 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 167
G
G
H = − µ⋅ B = − Ȗ= B I , (10)
I 0 z
will split into two energy levels, see Fig. 4-13 at the top of next page.
These two energy levels in a non-zero field embody a two-state quantum
system that can be used as a qubit. The controlled manipulation of these
qubits to effect quantum computations is the goal of NMR-based quantum
computing (QC). The origins, development, progress and status of NMR-
based QC has been addressed recently in extensive review articles by
Laflamme, Knill, Cory et al. [193], and by Vandersypen and Chuang [194].
Our presentation, therefore, will follow these closely.

B= B
B= B 0 0
2 2 1 1
m I = −= −
m I
2 2
B= 0 0
B=
= = Ȧ Ȧ = 2µ= 2µ ω ω = Ȗ= Ȗ= = B B
0 0 0 0 0 0
1 1 1 1
m I = =
m I
2 2
Figure 4-13. Energy level splitting when a nucleus of intrinsic angular momentum I = 1 2
is exposed to a constant magnetic field B .
0
In practice, limits germane to currently available techniques preclude
detecting the energy absorbed by a single nucleus. Therefore, a substance
containing a multitude of nuclei, whose contributions add, must be employed
[193]. The system of choice for NMR-based QC consists of the very large
number of nuclei belonging to atoms forming a molecule in a liquid, so-
called liquid-state NMR. Fig. 4-14 depicts a typical molecule used to form

Cl
Cl Cl
Cl
13
13 C C 13 C C
13

H H Cl
Cl

Figure 4-14. Trichloroethylene molecule for liquid-state NMR-based QC. The proton (H),
13
13
and the two carbons ( C) are employed to realize qubits. The C nucleus has spin ½. [193].
qubits is the trichloroethylene (TCE) molecule, which contains a hydrogen
nucleus possessing a strong magnetic moment. As a result, when the
molecule is exposed to a constant strong magnetic field, B, each hydrogen’s