Page 195 - Principles and Applications of NanoMEMS Physics

4. NANOMEMS APPLICATIONS: CIRCUITS AND SYSTEMS 183

capacitance techniques and produces a signal that remains observable until
the spin relaxes; for Si:P this time may be of the order of hours [202].
Kane points out that a number of practical considerations must be
addressed to make this scheme workable [202]. For instance, before
beginning a computation, initialization will require the individual
determination of gate biases to account for fluctuations due to the variation
with position of both donors and gate sizes. These voltages, in turn, will
have to be stored to effect the calibration as needed. Also, gate voltage
fluctuations in essence couple the environment to the qubits, thus
contributing to spin decoherence. This decoherence is elicited by the
induction of difference spin precession frequencies in pertinent qubits, and
°
manifests in that two spins in phase at a given time, will be 180 out of
phase a time t later. It can be shown that [202],
φ
t = 1 , (41 )
φ
π 2 α 2 () ( )
S ν
V
V st
where α = d∆ dV is the tuning parameter of the A-gates, with ∆ the
fluctuating differential precession frequency of the spins, S is the spectral
V
density of the frequency fluctuations, and ν is the frequency difference
st
between the 10 − 01 and 10 + 01 states. Estimates, assuming the use of
low-temperature elctronics to bias the gates, suggest t ≈ 10 6 sec , which
φ
implies the ability of the nuclear spin QC to perform between 10 − 10 10
5
logical operations during t . Finally, measures have to be taken to render a
φ
predominance of certain polarization of electrons spins, e.g.,
(n ↑ n < 10 − 6 ), so that they can effectively mediate nuclear spin
↓
interactions. This, in turn, requires the electrons to occupy the lowest energy
levels, which occurs when 2µ B >> kT . With B ≈ 2 T , this sets the
B
operating temperature at 100mK.

4.3.1.4 Superconducting-Based Qubits

In the search for two-level quantum systems upon which qubits might be
based, Josephson junction-based superconducting qubits are currently the
most advanced. In contrast to the previously discussed qubits, which are
based on microscopic quantum effects of individual particles, such as ions,
electrons, or nuclei, superconducting-based qubits are based on macroscopic
quantum coherence effects [204], [205]. These are effects in which the qubit