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Vol.10,April2012
152
Design of a Qubit and a Decoder in Quantum Computing Based on a
Spin Field Effect
A. A. Suratgar1, S. Rafiei*2, A. A. Taherpour3, A. Babaei4
1 Assistant Professor, Electrical Engineering Department, Faculty of Engineering, Arak University, Arak, Iran.
1 Assistant Professor, Electrical Engineering Department, Amirkabir University of Technology, Tehran, Iran.
2 Young Researchers Club, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran.
*saeid.rafiei@iau-aligudarz.ac.ir
3 Professor, Chemistry Department, Faculty of Science, Islamic Azad University, Arak Branch, Arak, Iran.
4 faculty member of Islamic Azad University, Khomein Branch, Khomein,
ABSTRACT
In this paper we present a new method for designing a qubit and decoder in quantum computing based on the field
effect in nuclear spin. In this method, the position of hydrogen has been studied in different external fields. The more
we have different external field effects and electromagnetic radiation, the more we have different distribution ratios.
Consequently, the quality of different distribution ratios has been applied to the suggested qubit and decoder model.
We use the nuclear property of hydrogen in order to find a logical truth value. Computational results demonstrate the
accuracy and efficiency that can be obtained with the use of these models.
Keywords: quantum computing, qubit, decoder, gyromagnetic ratio, spin.
1. Introduction
Up to now many papers deal with the possibility to
realize a reversible computer based on the laws of
quantum mechanics [1].
Modern quantum chemical methods provide
powerful tools for theoretical modeling and
analysis of molecular electronic structures.
Implementation of quantum information process-
ing based on spatially nuclear spins in stable
molecules is one of the wide discussable applied
sciences areas [2-4].
For realizing quantum computing, some physical
systems, such as nuclear magnetic resonance,
trapped irons, cavity quantum electrodynamics,
and optical systems have been proposed. These
systems have the advantage of high quantum
coherence but cannot be integrated easily to form
large-scale circuits. Owing to large-scale integra-
tion and relatively high quantum coherence,
Josephson charge and phase qubits, based on the
macroscopic quantum effects in low-capacitance
Josephson junction circuits, have recently been
used in quantum information processing [7]. In this
paper different frequency, spin positions and
different hydrogen atoms in compound applied for
the qubit and decoder designing.
2. An overview on quantum concepts
In this chapter a short introduction is presented
into the interesting field of quantum in physics,
Moore´s law and a summary of the quantum
computer.
2.1 Quantum in physics
In classical physics, the physical states of an
object of interest can be defined exactly to a
degree, which is mainly limited by experimental
factors such as random and systematic errors. The
measurement of a physical state in quantum
mechanics is different as it includes intrinsic
uncertainty, which cannot be influenced by
improvements in experimental techniques. This
concept, originally proposed by Heisenberg, is
called the uncertainty principle, which states that
the uncertainties of measurement of energy ∆E
and interval of time ∆t, during which a microscopic
particle possesses that energy:
htE
. (1)
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
JournalofAppliedResearchandTechnology 153
Where h is Planck’s constant. Hence, only the
probabilities of getting particular results can be
obtained in quantum mechanical experiments,
fundamentally distinguishing them from the
classical ones. The uncertainties in quantum-
mechanical measurements stem from the
disturbance which measurement itself causes to
the measured state at a microscopic scale. In
NMR, the life times of spin states do not generally
exceed the spin-lattice relaxation time T1 , and
therefore the half-widths of NMR lines in spectra
must be at least of the order of 1/T1[2, 3, 8].
The uncertainties featured in quantum mechanical
measurements lead to a probability interpretation
of phenomena, where the quantum mechanical
states are described by the wave functions given in
particular representation. In Dirac formulism of
quantum mechanics used throughout this text, a
state of a quantum mechanical system is
described by the vector called ket and written as
|ψ>. The use of ket instead of the wave function
allows the form of analysis, which is independent
of the particular representation chosen. In this
formulism, different representations are regarded
as rotations in the vector space, hence the ket |ψ>
represents the quantum state no matter what
representation is chosen for the analysis [9].
The number of the ket components is 2(I) +1,
where I is spin. Thus, for spin ½ the ket has two
components, each of which is a complex number.
The number is represented by its real part only
when the imaginary part is zero [9].
In NMR the nuclear spin magnetization is
manipulated by applying a magnetic field which is
(a) transverse to the static magnetic field, i.e., in
the xy-plane, and (b) oscillating at close to the
Larmor frequency of the spins. Such a field is
created by passing the output of a radio-frequency
transmitter through a small coil which is located
close to the sample [2, 4].
If the field is applied along the x-direction and is
oscillating at ωRF, the Hamiltonian for one spin is
XRFz tIIH
cos2 10 (2)
The first term represents the interaction of the
spin with the static magnetic field and the second
one represents the interaction with the oscillating
field. The strength of the latter is given by ω1. It is
difficult to work with this Hamiltonian as it
depends on time. However, this time dependence
can be removed by changing to a rotating set of
axes or a rotating frame. These axes rotate about
the z-axis at frequency ωRF, and in the same
sense as the Larmor precession. In such a set of
axes the Larmor precession is no longer at ω0,
but at (ω0–ωRF); this quantity is called the offset,
Ω. The more important result of using the rotating
frame is that the time dependence of the
transverse field is removed. The details of how
this comes about are beyond the scope of this
paper but can be found in a number of standard
texts on NMR. In the rotating frame, the
Hamiltonian becomes time independent [2, 4].
XzRF IIH 10 )(
(3)
XZ II 1
Commonly, the strength of the radiofrequency field
is arranged to be much greater than typical offsets:
ω1»Ω. It is then permissible to ignore the offset
term and so write the pulse Hamiltonian as (for
pulses of either phase).
xxpulse IH 1,
or yypulse IH 1,
(4)
Such pulses are described as hard or non-
selective, in the sense that they affect spins over a
range of offsets. Pulses with lower field strengths,
ω1 are termed selective or soft [2, 4].
Single spin ½ in static magnetic field acting along
z-axis has two eigenkets: |α> (spin along the field)
and |β> (spin is opposite to the field) described by
columns:
1
0
and
0
1
(5)
In general, the state of spin ½ may be represented
by the combination of eigenkets written as the ket
|ψ> where:
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
Vol.10,April2012
154
1
22
10
0
0
12
1
0121
C
CC
C
cccc
(6)
C1 and C2 are complex numbers which relate to
probabilities of a spin to be in the particular state,
either in state |α> or in state |β>. The eigenkets are
special kets, which are normally orthogonal and
represent the states in which a quantum-
mechanical system can be found when its state is
measured. The particular eigenkets can be chosen
for description of a quantum mechanical state, like
a frame of reference. However, any chosen set of
eigenkets must be normalized and complete, in
order to be appropriate for a representation of a
quantum mechanical state [2, 10, 11].
In physics and mathematics, the Boltzmann
distribution is a certain distribution function or
probability measure for the distribution of the
states of a system; it underpins the concept of the
canonical ensemble, providing its underlying
distribution. A special case of the Boltzmann
distribution, used for describing the velocities of
particles of a gas is the Maxwell-Boltzmann
distribution. In more general mathematical settings,
the Boltzmann distribution is also known as the
Gibbs measure. The Boltzmann distribution for the
fractional number of particles X=Ni / N occupying a
set of states i possessing energy Ei is
TZ
Tk
E
g
N
N
X
B
i
i
i/exp.
(7)
where kB is the Boltzmann constant, T is
temperature (assumed to be a well- defined
quantity), gi is the degeneracy (meaning, the
number of states having energy Ei), N is the total
number of particles and Z(T) is the partition
function [2-6].
i
i
NN
iB
i
iTk
E
gTZ exp.
Alternatively, for a single system at a well-defined
temperature, it gives the probability that the system
is in the specified state. The Boltzmann distribution
applies only to particles at a high enough
temperature and low enough density that the
quantum effects can be ignored and the particles
obey Maxwell–Boltzmann statistics. The
Boltzmann distribution is often expressed in terms
of β = 1/kT where β is referred to as
thermodynamic beta. The term "exp (-βEi)" or "exp
(-Ei/(kBT))", which gives the (unnormalized)
relative probability of a state, is called the
Boltzmann factor and appears often in the study of
physics and chemistry [12, 13].
The gyromagnetic ratio (also sometimes known as
the magnetogyric ratio in other disciplines) of a
particle or system is the ratio of its magnetic dipole
moment to its angular momentum, and it is often
denoted by the symbol "γ", gamma. Its SI units are
radian per second per tesla (R/(S·T)) or,
equivalently, coulomb per kilogram (C/kg). The
term "gyromagnetic ratio" is sometimes used as a
synonym for a different but closely related quantity,
the g-factor. The g-factor, unlike the gyromagnetic
ratio, is dimensionless. For more on the g-factor,
see below, or see the article g-factor. Protons,
neutrons, and many nuclei carry nuclear spin,
which gives rise to a gyromagnetic ratio as above.
The ratio is conventionally written in terms of the
proton mass and charge, even for neutrons and for
other nuclei, for the sake of simplicity and
consistency. The relation is as follows:
N
p
gg
m
e
2 (9)
Where μN is the nuclear magneton, and g is the g-
factor of the nucleon or nucleus in question. The
gyromagnetic ratio of a nucleus is particularly
important because of the role it plays in nuclear
magnetic resonance (NMR) and magnetic
resonance imaging (MRI). These procedures rely
on the fact that nuclear spins press on a magnetic
field at a rate called the Larmor frequency (as
discussed previously), which is simply the product
of the gyromagnetic ratio with the magnetic field
strength. Approximate values for hydrogen atom
nuclei equals 42.5787 (γ / 2π (MHz/T)) [2-6].
(8)
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
JournalofAppliedResearchandTechnology 155
2.2 Moore´s Law
Electronic computer building is a fast improving
technology but its future is yet to be determined.
Gordon Moore, founder of Intel, observed an
interesting rule called Moore’s law in 1965. He
concluded that since the invention of transistors
the number of transistors per chip roughly doubled
every 18–24 months (see Figure 1) [14].
Figure 1. Representation of Moore´s law. The years
are given horizontally; the number of electrons
per device is represented vertically.
It means an exponential increase in the computing
power of computers. Although this was an
empirical observation in 1965 the law seems to be
valid nowadays. This law estimates serious
problem around 2015 [14].
The growth in processor’s performance is due to
the fact that we put more transistors on the same
size microchip.
This requires smaller and smaller transistors,
which can be achieved if we are able to draw
thinner and thinner lines onto the surface of a
semiconductor disk. Around nanometer thickness
we reach the nano world, where the new rules are
explained by the quantum mechanics [14].
2.3 Quantum Computer
General purpose quantum computers do not exist
yet nor are they likely to exist for 20–30 years,
although small-scale laboratory models and small
specialized commercial models have been
developed [16]. Owing to its property of large scale
integration, the superconducting qubits are the
promising candidates for scalable quantum
computing [17]. Nowadays the power and
capability of a quantum computer is primarily
theoretical speculation; the advent of the first fully
functional quantum computer will undoubtedly
bring many new and exciting applications [15].
Recently, much attention has been paid to the
physical realization of a quantum computer, which
works on the fundamental quantum mechanical
principle. The quantum computer can solve certain
hard problems exponentially faster than its
classical counterpart. By using unitary quantum
logic networks, a conventional quantum computer
may be implemented [17].
On the other hand, Raussendorf and Briegel
recently proposed an intriguing alternative
quantum computing strategy, i.e., the one-way
quantum computer, which constructs quantum
logic networks by using only single qubit projective
measurements on a generated cluster state. In the
quantum computer, quantum information is
encoded in the cluster state, processed, and read
out from the cluster state. The quantum computer
is universal in the sense that arbitrary unitary
quantum logic networks can be carried out based
on a suitable generated cluster state. Cluster
states thereby serve as a universal source for
quantum computers. Meanwhile, the cluster states
can also be used as entanglement resources,
which means that other entanglement states can
be constructed from the cluster states. As
mentioned above, the cluster states have special
characteristics and practical applications, hence
the preparations of the cluster states have been
implemented by many physical systems [17].
With the progress of high-precise fabricating
technique, superconducting qubits have shown their
competence in quantum computing. The Josephson
charge qubit and flux qubit are based on the
macroscopic quantum effects on superconducting
circuits. The decoherence time of superconducting
qubits is not very long, but the number of quantum
operations that can be completed during the
coherence time is also comparable with other
systems. Owing to its property of large-scale
integration, the superconducting qubits are the
promising candidates for scalable quantum
computing [17].
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
Vol.10,April2012
156
2.4 The Quantum Bit
In the classical information the smallest information
bearing unit is called a bit. In digital computers, the
voltage between the plates of a capacitor
represents a bit of information: a charged capacitor
denotes bit value 1 and an uncharged capacitor bit
value 0, but in advanced computers, one bit of
information can be encoded using two different
polarizations of light or two different electronic
states of an atom. However, if we choose an atom
as a physical bit then quantum mechanics tells us
that, apart from the two distinct electronic states,
the atom can be also prepared in a coherent
superposition of the two states. This means that
the atom is both in state 0 and state 1. Quantum
computers use quantum states which can be in a
superposition of many different numbers at once.
The simplest quantum system can be described by
means of a two-dimensional complex valued
vector in a two-dimensional Hilbert space. We call
it quantum bit, qubit or qbit (Figure 2). A quantum
computer manipulates qubits by executing a series
of quantum gates, each being unitary
transformation acting on a single qubit or pair of
qubits [14, 15].
Figure 2. The general representation of a qubit in
a two dimensional Hilbert-space.
In applying these gates in succession, quantum
computers can perform complicated unitary
transformations to a set of qubits in some initial
state. The qubits can then be measured with this
measurement serving as the final computational
result. This similarity in calculation between a
classical and quantum computer affords that in
theory, classical computers can accurately
simulate quantum computers. The simulation of
quantum computers on classical ones is a
computationally difficult problem because the
correlations among quantum bits are qualitatively
different from correlations among classical bits, as
first explained by John Bell. For example: take a
system of only a few hundred qubits, this exists in
a Hilbert space of dimension that in simulation
would require a classical computer to work with
exponentially large matrices (to perform
calculations on each individual state, which is also
represented as a matrix), meaning it would take an
exponentially longer time than even with a primitive
quantum computer [10, 11].
The simplest quantum system is a half-state of the
two-level spin. Its basic states, spin-down |↓〉 and
spinup|↑〉, may be relabelled to represent binary
zero and one, i.e., |0〉 and|1〉, respectively. The
state of such a single particle is described by the
following wave function:
10
(10)
The squares of the complex coefficients |α|2
and|β|2 represent the probabilities of finding the
particle in the corresponding states.
Generalizing this statement to a set of k spin ½
particles, we find that there are now 2k basis
states (quantum mechanical vectors that span a
Hilbert space) which is like saying that there are 2k
possible bit-strings of length k.
However, observing the system would cause it to
collapse into a single quantum state corresponding
to a single answer a single list of 500 1s and 0s, as
dictated by the measurement axiom of quantum
mechanics. The reason for this is an exciting result
derived from the massive quantum parallelism
achieved through superposition, which would be
the equivalent of performing the same operation on
a classical super-computer with 10150 separate
processors [10].
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JournalofAppliedResearchandTechnology
157
3.:An introduction to binary logics and
applications
Digital design is concerned with the design of
digital electronic circuits. The subject is also known
by other names such as logic design, switching
circuits, digital logic, and digital systems. Digital
circuits are employed in the design of systems
such as digital computers, electronic calculators,
digital control devices, digital communication
equipment, and many other applications that
require electronic digital hardware [14].
3.1 Decoder
Discrete quantities of information are represented
in digital system with binary codes. A binary code
of n bits is capable of representing up to distinct
elements of the coded information. A decoder is a
combinational circuit that converts binary
information from n input lines to a maximum of 2
n
unique output lines. If the n-bit decoded
information has unused or don’t-care
combinations, the decoder output will have less
then 2
n
outputs [18].
As an example, consider the 3-to-8 line decoder
circuit of Figure 3.
Figure 3. 3-to-8 line decoder.
The three minterms are decoded into eight
outputs, each output representing one of the
minterms of the 3-input variables. The three
inverters provide the complement of the inputs,
and each one of the eight AND gates generate one
of the minterms. A particular application of this
decoder would be a binary-to octal conversion.
The input variables may represent a binary
number, and the outputs will then represent the
eight digits in the octal number system. However,
the 3-to-8 line decoder can be used for decoding
any 3-bit code to provide eight outputs, one for
each element of the code [18].
Input Output
X
Y Z D
0
D
1
D
2
D
3
D
4
D
5
D
6
D
7
00 0 1 0 0 0 0 0 0 0
0 0 1 0 1 0 0 0 0 0 0
01 0 0 0 1 0 0 0 0 0
01 1 0 0 0 1 0 0 0 0
10 0 0 0 0 0 1 0 0 0
1 0 1 0 0 0 0 0 1 0 0
11 0 0 0 0 0 0 0 1 0
1 1 1 0 0 0 0 0 0 0 1
Table 1. Truth table of 3-to-8 line decoder.
The operation of the decoder may be further
clarified from its input-output relationships, listed in
Table 1. Observe that the output variables are
mutually exclusive because only one output can be
equal to 1 and represents the minterm equivalent
of the binary number presently available in the
input lines [18].
3.2 Encoder
An encoder is a digital function that produces a
reverse operation from that of a decoder. An
encoder has 2
n
(or less) input lines and n output
lines. The output lines generate the binary code for
2
n
input variables. An example of an encoder is
shown in Figure 4 [18].
Figure 4. Octal-to-binary encoder.
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
Vol.10,April2012
158
The octal-to-binary encoder consists of eight
inputs, one for each of the eight digits, and three
outputs that generate the corresponding binary
number. It is constructed with OR gates whose
inputs can be determined from the truth table given
in Table 2. The low-order output bit z is 1 if the
input octal digit is odd. Output y is 1 for octal digits
2, 3, 6, or 7. Output x is a 1 for octal digital 4, 5, 6,
or 7. Note that D0 is not connected to any OR gate;
the binary output must be all 0’s. This discrepancy
can be resolved by providing one more output to
indicate the fact that all inputs are not 0’s [18].
Input Output
D0 D1 D2 D3 D4 D5 D6 D7 X Y Z
1 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 1
0 0 1 0 0 0 0 0 0 1 0
0 0 0 1 0 0 0 0 0 1 1
0 0 0 0 1 0 0 0 1 0 0
0 0 0 0 0 1 0 0 1 0 1
0 0 0 0 0 0 1 0 1 1 0
0 0 0 0 0 0 0 1 1 1 1
Table 2. Truth table of octal-to-binary encoder.
The encoder in Figure 4 assumes that only one
input line can be equal to 1 at any time; otherwise
the circuit has no meaning. Note that the circuit
has eight inputs and could have 28 = 256 possible
input combinations. Only eight of these
combinations have any meaning. The other input
combinations are don’t-care conditions [14].
Encoders of this type (Figure 4) are not available in
IC packages, since they can be easily constructed
with OR. The type of encoder available in IC form
is called a priority encoder. These encoders
establish an input priority to ensure that only the
highest-priority input line is encoded. Thus, in
Table 2, if priority is given to an input with higher
subscript number over one with a lower subscript
number, then if both D2 and D5 are logic-1
simultaneously, the output will be 101 because D5
has a higher priority over D2. Of course, the truth
table of a priority encoder is different from the one
in Table 2 [14].
4. Qubit and quantum decoder design
In this section we propose a new method for qubit
and decoder implementation using the quantum
theory. We use the states of hydrogen nuclear spin.
4.1 Hydrogen Nuclear Spin
The reason statistics of the Maxwell-Boltzmann
probability distribution function is used in order to
do this is a direct result of the infinite small size of
atoms, molecules and spin populations. If a
computer were to keep track of a sample of the
nuclear spins at the selected temperature and
pressure, it would need to dynamically account for
the position and velocity vectors for the number of
nuclear spins (here, for hydrogen atoms). This is
too many operations for most modern computers
to handle adequately. Other problems occur of
course which stem from quantum mechanics and
our increasing inability to precisely know the exact
positions and velocities if nuclear spins were
chosen to examine [19].
The values of the magnetic field powerful (B0, in
Tesla), Frequency (υ in MHz), Boltzmann
distribution ratio (X = Ni /N) and τ = ln (1/(1–X)) of
hydrogen nuclear magnetic resonance are shown
in Table 3. The "τ" values which are shown in
Table 3 introduce the Napierian logarithmic of the
ratio of 1/ (1–X) as a digital index (constant
temperature).
In this study, the values that are introduced in
Table 3 were utilized as input for a decoder model.
The first value of the magnetic field was
approximated to zero. The Boltzmann distribution
ratio (X = Ni /N) and the "τ" values decreased by
increasing the magnetic field (B0, in Tesla) and the
induced frequency. By using these 3 values in the
decoder model of this study, different outputs can
be observed during the process.
Figure 7 shows the process of input of the different
3 values for H-atom (B0, υ and γ values) and
various matrices output as result of the process.
By changing one or more of the values, various
matrices result as output.
4.2 Qubit Design
The external field magnitudes on the nuclear spin
produce the spin moment in the Larmor frequency.
If this frequency overlaps by electromagnetic
radiation with the Larmor frequency, it gives the
energy and change of spin state (see Figure 5).
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
JournalofAppliedResearchandTechnology
159
The previously mentioned practice is the act of
writing. By removing the external field, the spin
returns to an earlier state which is called the act of
reading. Here the effect of reading is radiated in
the wave form.
Figure 5. Nuclear spin in external field.
Considering Table 1 and the above materials, B
0
is
drawn on as a logic zero:
0 (Low): B
0
=10
-5
T, f
1
=4.25787×10-4 MHZ,
τ
1
=23.409663.
And B
1
=2 T that makes X decrease, called the
binary one:
1 (High): B
1
=2T, f
2
=85.157444 MHZ,
τ2=11.203597.
In this design we can use some B for the zero and
one state that shows the relation between B and τ
in Figure 6.
Table 3. The spin status of hydrogen
in different magnetic fields.
Figure 6. The relation between B and τ.
By implementing the special frequency in the
external field effect use writes in the bit in order to
release the energy in atom for the read in the bit.
4.3 Quantum decoder design
In the excitation process of an organic compound,
if there is frequency sweeping in excitation, atoms
of hydrogen resonate in separated frequencies.
Different positions of hydrogen atoms is the reason
for this phenomenon. We can use this
phenomenon implementation as in Figure 7.
N
O
Magnet
ic Field
(B
0
, in
Tesla)
Frequency
(υ in MHz)
Boltzmann
Distribution Ratio
=
ln(1/1– X)
1 10
-5
≈ 0 4.25787
10
– 4
0.999999999931874 23.409663
2 0.5 21.289361 0.999996593708047 12.589886
3 1.0 42.578722 0.999993187427698 11.896741
4 1.5 63.868083 0.999989781158951 11.491277
5 2.0 85.157444 0.999986374901806 11.203597
6 2.5 106.446805 0.999982968656265 10.980455
7 3.0 127.736166 0.999979562422326 10.798135
8 3.5 149.025527 0.999976156199990 10.643986
9 4.0 170.314888 0.999972749989256 10.510457
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
Vol.10,April2012
160
Figure 7. Decoder implementation.
Where B is external field magnitude, ν is the
Larmor frequency of the field, T is temperature and
γ is magnetogyric of atoms. τ
i
is yield from Eq. (11).
)
1
1
(X
Ln
(11)
We will have a unique peak in one of the f
1
, f
2
… f
n
frequencies. If we have a peak in f
i
, then
associated output τ
i
is high. Thus, it can be used as
a decoder. In a similar manner. It can be used for
multi true value logic (as J. Lukasiewicz logic)
implementation.
5. Conclusion
This paper introduces the concept of a new
method for the design, analysis, modeling,
simulation of a qubit and decoder in a quantum
computer. Based on our proposal, we can
summarize our findings as follows:
1. We used the spin field effect for the qubit
design. The difference between the classical bit
and the qubit proposed is that a qubit can be in a
state other than 0 or 1. Additionally, the decoder
proposed has several lines for the selected in
output on a scale of the other one.
2. The suggested qubit and decoder needs to be
verified by more theoretical and experimental
research to determine its potential as an applicable
feature in the future.
3. The authors believe that the proposed
techniques can be applied to quantum computing.
Further research could be conducted to confirm
the effectiveness of the proposed techniques using
a variety of quantum computing techniques.
References
[1] V. G. Cattaneo, A. Leporati and R. Leporini, Quantum
Conservative Many-valued Computing, Fuzzy Sets and
Systems, Elsevier, no. 159, September. 2007, pp. 1001-
1030.
[2] J. Keeler, Understanding NMR spectroscopy, Wiley,
2006.
[3] W. H. Louisell, Quantum Statistical Properties of
Radiation, John Wiley & Sons, 1973.
[4] I. N. Levine, Quantum Chemistry, 4th edition,
Prentice-Hall Interna-tional Inc, New York, 1991.
[5] M. A. Bernstein, K. F. King and X. J. Zhou. Handbook
of MRI Pulse Sequences. San Diego: Elsevier Academic
Press, 2004.
[6] R. C. Weast, M. J. Astle. Handbook of chemistry and
physics. Boca Raton: CRC Press. p. E66. ISBN 0-8493-
0463-6, ed 1982.
[7] X. Zheng, P. Dong, Z. Xue, Z. Cao, Generation of
Cluster States with Josephson Charge Qubits, Physics
Letters A, Elsevier, no. 356, January. 2007, pp. 156-160.
[8] W. Heisenberg, Über den anschulichen Inhalt der
quantentheo-retischen kinematik und Mechanik, Z. Phys.
43, 172-198 (1927).
[9] E. D. Becker, High Resolution NMR, Academic Press,
23, 1969.
[10] M. H. Levitt. Spin Dynamics, Jon Wiley and Sons,
196, 2001.
[11] M. Munowitz, Coherence and NMR, John Wiley
&Sons, 18, 1988.
[12] Carter, Ashley H, Classical and Statistical
Thermodynamics, Prentice -Hall, Inc, New Jersey, 2001.
[13] Pathria, R. K, Statistical Mechanics, Butterworth-
Heinemann, 1996.
DesignofaQubitandaDecoderinQuantumComputingBasedonaSpinFieldEffect, S.Rafieietal./152‐161
JournalofAppliedResearchandTechnology 161
[14] L. Bacsardi, Satellite Communication Over Quantum
Channel, Acta Astronautica, PERGAMON, no. 61, March.
2007, pp. 144-149.
[15] S. Imre, B. Ferenc, Quantum Computing and
Communications: an engineering approach, Wiley, New
York, 2005.
[16] H. Guo, J. Zhang and G. J. Koehler, A survey of
quantum games, Decision Support Systems, Elsevier,
no. 46, April. 2008, pp. 318-332.
[17] X. H. Zheng, P. Dong, B. L. Yu and Z. L. Cao,
Preparation of Cluster States with Superconducting Qubit
Network, Solid State Communica-tions, Elsevier, no. 144,
September. 2007, pp. 206-209.
[18] M. M. Mano, Digital Design, Prentice Hall, 1984, pp.
167-175.
[19] http://user.mc.net/~buckeroo/MXDF.html
