Indonesian J
ournal of Ele
c
trical Engin
eering and
Computer Sci
e
nce
Vol. 2, No. 3,
Jun
e
201
6, pp. 675 ~ 68
3
DOI: 10.115
9
1
/ijeecs.v2.i3.pp67
5-6
8
3
675
Re
cei
v
ed Ma
rch 4, 2
016;
Re
vised Ap
ril
29, 2016; Accepte
d
May 1
2
, 2016
A Quantum Pointer Signal Processing
Resear
ch
Shu
y
ue Wu,
Jingfan
g Wa
ng
Schoo
l of Elect
r
ical & Informat
i
on En
gin
eer
in
g
Hun
an Intern
ation
a
l Econ
omic
s Universit
y
Cha
ngsh
a
, Po
stcode: 41
020
5, Chin
a
A
b
st
r
a
ct
In qu
antu
m
gr
ay-scal
e
i
m
a
g
e
process
i
n
g
, th
e stor
ag
e i
n
q
uantu
m
st
ates
is the c
o
lor
inf
o
rmatio
n
and
the
pos
itio
n i
n
for
m
atio
n
Accordi
ng to
t
he
adv
antag
e
of smal
l ra
ng
e
of the
gr
ay sc
ale
in
a
gray-s
cal
e
imag
e, a nov
el
storage
expre
ssion
of q
u
a
n
tum
gray-sca
le
image
is
pro
p
o
sed and de
monstrated in
th
i
s
study. Besides
, a new
concept of
"quantu
m
pointer" is p
u
t forw
ard
base
d
on the expr
essio
n
. Quan
t
u
m
poi
nter is th
e v
i
ncul
u
m
b
e
tw
een the
infor
m
ation
of gr
ay-sc
a
le a
nd
positi
o
n
of each
pix
e
l i
n
qu
antu
m
gra
y
-
scale
i
m
a
ges.
The feas
ib
ility
i
s
verifi
ed f
o
r th
e pr
op
osed
q
u
antu
m
po
inter,
and
the
pr
opert
i
es
of b
i
-dir
ecti
on
and s
ub-b
l
ock
are us
ed, the
storing
and
ot
her o
perati
ons
of qua
ntu
m
gr
ay-scal
e
i
m
a
g
e
are s
i
mpl
e
r
an
d
mor
e
conv
eni
e
n
t.
Ke
y
w
ords
: Quantu
m
i
m
a
ge p
r
ocessi
ng, qu
a
n
tum
gray-sca
l
e
imag
e, qua
ntum p
o
i
n
ter, qu
antu
m
gray-sc
a
le
imag
e storing
Copy
right
©
2016 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
Combi
n
ing
q
uantum
me
chani
cs an
d
compute
r
o
r
igi
nated th
at B
enioff u
s
ed
quantum
mech
ani
cs to de
scrib
e
compute
r
[1]. Feynma
n p
r
opo
se
d q
u
a
n
tum comp
uter in
19
82 [
2
],
quantum m
e
chani
cs di
scipl
i
nes
with the
depth an
d
b
r
eadth
both
wa
s fully integrated
with th
e
comp
uter,
an
d then
there
are
a
funda
mental
b
r
e
a
kthroug
h in
th
e devel
opme
n
t of qu
antu
m
comp
uting. S
i
milar to the
cla
ssi
c
com
p
uter, qu
antu
m
com
pute
r
system i
s
m
ade to b
e
m
o
re
perfe
ct, there
mu
st be
the
inde
pen
dent
algo
rithm
s
which
ad
apted
to the
chara
c
teri
stics
of the
system to co
mplete a vari
ety of complex arithm
etic operatio
ns. In order to e
ffectively utilize
quantum
pa
rallelism
an
d
qua
ntum
st
ates'
supe
rp
os
ition,
enta
ngled
natu
r
e
,
colla
pse, e
t
c.,
Deut
sch p
r
o
posed
Deut
sch q
uantu
m
algorith
m
[3], the algo
rith
m not only d
e
mon
s
trate
d
the
cha
r
a
c
teri
stics of qu
antu
m
paralleli
sm, and it
al
so
refle
c
ted
the sp
eed
a
nd efficie
n
cy
of a
quantum
co
mputer if it
wa
s comp
ared to a
cl
a
s
sical comp
uter. Sho
r
p
r
e
s
ente
d
a
qu
antum
quality factori
ng algo
rithm i
n
1994 [4]. Tarsus fa
ct
ori
z
ation pro
b
lem
belong
s to a
class of typical
NP
(non
-det
ermini
stic pol
ynomial) co
mplete
p
r
obl
em, but thi
s
probl
em
whi
c
h Sho
r
alg
o
ri
thm
solved
i
s
u
n
s
olvabl
e in
th
e cl
assi
cal
al
gorithm
.
Gro
v
er q
uantum
sea
r
ch al
go
rithm a
ppea
re
d
in
1995 [5], the algorith
m
' largest contrib
u
tion wa
s that
the com
p
lexity of the search will redu
ce to
√
from the
cla
ssi
c
cal
c
ulati
on N. Th
e im
proved
al
gorithm of Grover als
o
followed [6,7,8]. The
emergen
ce
o
f
quantu
m
al
gorithm
can
solve th
e
pr
o
b
lem
whi
c
h
a
lot of
cla
s
sic co
mputin
g
can
not solve, be
cau
s
e of the
s
e advant
ag
es pre
c
isely, there a
r
e m
o
re
comp
re
hen
si
ve
research a
r
ea
with qua
ntum
combin
ation
[7], the quantum image p
r
o
c
e
ssi
ng is o
n
e
of them.
Quantum i
m
a
ge processin
g
develop
me
nt so far,
its
d
i
rectio
n can b
e
bro
adly divi
ded into
three categories
. The firs
t
c
a
tegory is
that the
im
age
informatio
n i
s
sto
r
ed
in th
e
qua
ntum
sta
t
e
stora
ge exp
r
ession of the
quantum
sta
t
es; the se
co
nd is that the
variou
s digit
a
l conve
r
sion
of
the cla
s
sic im
age i
s
extend
ing the q
uant
um re
al
m; the
third catego
ry focuses
on
quantum i
m
a
ge
geomet
ric tra
n
sformation.
Qubit L
a
ttice
[8, 9], R
eal
Ket [10] a
n
d
Flexible
Repre
s
e
n
tation
of
Quantum Ima
ge (F
RQI) [11
]
expression
belon
gs to
th
e first categ
o
ry. Qubit Lattice and Real Ket
method
s a
r
e
based o
n
qu
a
n
tum entan
gl
ement sy
ste
m
,
the differe
nce i
s
that th
e forme
r
i
s
ai
med
at all aspe
cts of imag
e
pro
c
e
ssi
ng, the latte
r m
a
j
o
r role i
s
in
image
com
p
re
ssi
on. F
R
QI
prop
osed m
e
thod is unive
rsal
signifi
can
c
e; it is
able t
o
have a
go
o
d
play in th
e
image
storag
e
,
comp
re
ssion
and geo
met
r
ic tra
n
sfo
r
m
a
tions [12, 1
3
]. Quantum
gray image
based on im
age
expre
ssi
on in
this
study al
so b
e
lon
g
to
the firs
t cate
gory.
The m
a
in
directio
n of
extensio
n
in
Cla
ssi
cal Q
u
antum Di
gita
l image con
v
erter a
r
e q
uantum
wav
e
let tran
sform [14], quantum
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IJEECS
Vol.
2, No. 3, Jun
e
2016 : 675
– 683
676
Fouri
e
r tran
sform [15] a
n
d
quantu
m
di
screte
co
si
ne
transfo
rm [1
6
,
17]. These
transfo
rmatio
ns
have full use
of the parall
e
l, supe
rimp
ose
d
qua
ntu
m
entangl
em
ent and ot
h
e
r
ch
aracte
rist
ics,
variou
s fo
rm
s of
quantu
m
tran
sform
a
t
improve
mo
re obviou
s
ly i
n
the
role
an
d efficie
n
cy
and
other
aspe
cts than the
cl
assic form. M
a
n
y
types of
u
n
i
t
ary tran
sformation o
perator
with qu
ant
um
geomet
ric tra
n
sformation
were give
n [1
8, 19], an
d
q
uantum
ci
rcui
t wa
s d
e
si
gn
ed th
roug
h th
ese
transfo
rmatio
ns [20, 2
1
], the ap
plica
b
ili
ty of
geometric tran
sfo
r
ma
tions a
r
e the
o
retically pro
v
ed
and can be i
m
pleme
n
ted.
2. Materials
and Method
s
2.1. Quantu
m Expressio
n
of Gra
y
scale Image
TIn classi
c gray image,
the image is
wi
thout colo
r in
formation, col
o
r satu
ratio
n
is ze
ro,
each pixel i
s
con
s
tituted
with its
gray
scale in
fo
rma
t
ion and
lo
ca
tion inform
ation, and
its g
r
ay
scale is divid
ed into 256 l
e
vels of gray
, it is
from 0-255. Similarl
y, in the quantum gray
scale
image, the i
m
age
pixels
are
rep
r
e
s
ent
ed by the
gr
a
y
scal
e
an
d p
o
sition, they
are
expre
s
se
d a
s
follows
:
1
2
0
2
|
|
2
1
|
n
j
n
j
M
Q
(1)
Whe
r
e in:
Q
|
is the qua
ntu
m
state rep
r
ese
n
tati
on of
storin
g the
entire g
r
ay
scale
image;
M
|
is g
r
ay inform
atio
n for en
co
din
g
ima
ge,
M
u
s
ed
exp
r
e
ssi
on i
s
quantu
m
-bit bi
na
ry
string. Be
cau
s
e the im
age
to be re
pre
s
e
n
ted is a
gray
scale ima
ge, its gray value
s
ra
nge from
0
to 255, the
r
e
is a l
e
sse
r
extent, and t
here
is
no
re
pre
s
entatio
n
that the imag
e be
com
e
s v
e
ry
compli
cate
d. But note that, M is a gray value bi
na
ry st
ring represen
tation,
gray may be the sa
me
in different l
o
cation
s, but t
he g
r
ay scal
e inform
ation
must b
e
uni
que o
n
the
same lo
cation.
In
other
wo
rd
s, M expre
s
sion
of
a positio
n
must be
only
one, but M
it
self can vary
betwe
en 0
-
25
5
gray scale va
lues, it is a string of variab
le expre
ssi
on
;
| j
>
coding
is the positio
n of the image
information; representation
j is
still bi
na
ry stri
ngs.
j
= 0,
1, …, 2
2n
– 1; n i
s
t
he q
uantum
bit
numbe
r
whi
c
h is
req
u
ire
d
to encode,
while |
j
>=|
0
>
1,
…,
|
2
2n
–1> i
s
2n
qua
ntu
m
gro
und
st
ates
whi
c
h
the
in
volved g
r
ayscale
im
a
ge rquantum
stat
e represents;
i
s
a
q
uantu
m
computatio
n
operator, it is calle
d the te
nso
r
p
r
od
uct.
In cl
a
ssi
cal d
i
gital
image repre
s
e
n
tation
,
each pixel
can
be rep
r
e
s
ent
ed
by
th
e co
ordin
a
tes, according
to
th
e
ho
rizontal ordin
a
te rep
r
ese
n
tation an
d
the
pixel expression, location
s
t
ate of quantum gr
ayscale image may r
e
pr
es
ent
a fur
t
her
s
p
lit,
namely:
v
h
j
|
|
|
(2)
Whe
r
e:
h
|
re
pre
s
ent
s the
x-dire
ction
a
l
informatio
n;
v
|
is the
co
ded ima
ge
informatio
n in
the y directio
n.
Thus,
ba
sed
on the
above
expre
s
sion,
Figure 1
is th
e 2
×
2 ima
g
e
, its exp
a
n
s
i
on of th
e
expre
ssi
on is
as follo
w:
)
11
|
|
10
|
|
01
|
|
00
|
(|
2
1
|
3
2
1
0
M
M
M
M
Q
(3)
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IJEECS
ISSN:
2502-4
752
A Quantum
Pointer Sign
al Processin
g
Rese
arch (Sh
u
y
ue
Wu
)
677
Figure 1. 2×2
gray image
It should b
e
noted that th
e expre
s
sion
of M
0
, M
1
, M
2
, M
3
are repre
s
e
n
ted b
y
a binary
string, and si
nce ea
ch pixel
gray
are
di
fferent,
M
0
, M
1
, M
2
, M
3
is not eq
ual to
each oth
e
r,
and
each po
sition
has a uni
que
gray scale value.
Proof :
Fro
m
a qu
antu
m
algo
rithm,
the esta
blis
h
m
ent of the
expre
ssi
on i
s
pre
pared
from the
initia
l quant
um
sta
t
e, an exp
r
e
s
sion
of
the
st
orag
e
state i
s
co
nverted
by
qua
ntum g
a
te
cha
nge.
Step 1
: P
r
e
paratio
n of
th
e initial
qua
n
t
um state
is
1
2
0
|
|
n
S
, and the initi
a
l state
1
2
0
|
n
is divided int
o
0
|
0
|
|
2
n
S
.
Step 2
:
Ha
d
a
mard T
r
an
sf
orm
n
H
2
|
is
u
s
ed, The 2n H
do
o
r
s a
c
t on the 2n initial qubit
of the
quantu
m
state
at th
e
sa
me tim
e
. After t
he effect of
Ha
dam
ard
door,
interme
d
iate
q
uantu
m
state ca
n be
obtaine
d:
1
2
0
2
2
2
|
0
|
2
1
)
0
|
0
(|
|
n
j
n
n
n
j
H
G
(4)
Step 3
: Swa
p
op
eratio
n i
s
u
s
e
d
, the
state
0
|
is
co
nve
r
ted a
n
y
M
|
state, the final
state is obtai
ned:
1
2
0
2
|
|
2
1
|
n
j
n
j
M
Q
(5)
The p
r
ovin
g
sh
ows th
at
the q
uantu
m
expressio
n
1
2
0
2
|
|
2
1
|
n
j
n
j
M
Q
of the
pre
s
ente
d
grayscale ima
ges h
e
re ca
n be conv
erted from a
seri
es
of qu
antum unita
ry
transfo
rmatio
n and from t
he initial qua
ntum state
1
2
0
|
n
,
the basi
s
is
provide
d
for the next
appli
c
ation of
the expressi
on.
Quan
tum
po
inter:
In cl
assical comp
uter, the p
o
inte
r is
used to i
ndicate the
a
ddre
s
s of
the memo
ry
unit sto
r
e
s
, the mem
o
ry u
n
it of
its a
ddress
can
be f
ound th
ro
ugh
a poi
nter,
which
mean
s that the add
re
ss
of a variable
is the
varia
b
le pointe
r
. In quantum
expre
ssi
on
s of
grayscal
e im
age
s, a
gray scale
rep
r
esents
8
bina
ry
stri
ng, p
o
siti
on in
dication
also i
s
a bi
n
a
ry
string, to dia
g
ram i
s
wh
ether ea
ch
pixel locatio
n
or gray inform
a
t
ion are bin
a
ry string
s in their
forms
of expression. F
o
r q
uantum
g
r
ay
scale im
age
s,
each pixel i
s
comp
osed of
the gray valu
e
and its lo
cati
on rep
r
e
s
e
n
tation, a com
b
ination of b
o
th is exactly
similar to th
e cla
ssi
c co
mputer
pointer, the
r
e
is the idea of
quantum poi
nter.
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ISSN: 25
02-4
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IJEECS
Vol.
2, No. 3, Jun
e
2016 : 675
– 683
678
2.2. Quantu
m Pointer Bidirection
a
lity
Quantum
poi
nter is differe
nt from the cl
assic p
o
inter.
In classical p
o
inter, the ad
dre
ss i
s
a pointe
r
, an
d this rep
r
e
s
e
n
tation is fixe
d. Ho
weve
r, t
he poi
nter i
s
not fi
xedin qu
antum poi
nter, it
is with
two
-
way dire
ctivity. In both
gray
value a
nd t
he po
sition
value, the
gra
y
value may
be
rep
r
e
s
ente
d
as a
pointe
r
, the po
sition v
a
lue m
a
y al
so be exp
r
e
ssed a
s
a
point
er, an
d this
choice
is dete
r
min
e
d
based o
n
th
e qua
ntum
sp
ecific i
m
age
pro
c
e
ssi
ng o
peratio
n. The
quantum
poi
nter
bidire
ction
a
lity is expresse
d specifically as follows:
1)
Whe
n
the
gray value of
quantum
gra
y
im
age i
s
u
s
ed t
o
repre
s
en
qua
ntum
pointe
r
, the
positio
n value
s
of the imag
e is the co
nte
n
t which the pointer p
o
ints to ;
2)
Whe
n
the p
o
sition valu
e
s
of qua
ntu
m
gr
ay imag
e rep
r
e
s
ent
quantum
poi
nter, the gray
values of the
image is the
conte
n
t whi
c
h
the pointer p
o
ints to.
In different image p
r
o
c
e
s
sing, both g
r
ay va
lue pointer or p
o
siti
on value poi
nter is
sele
cted
as
a pointe
r
o
n
the ba
sis o
f
which the
process is
relatively
sim
p
le, it is easily
impleme
n
ted.
For exam
ple
,
whe
n
the
same
gray
-scale pixel
g
r
ay value i
s
adju
s
t in
the im
a
ge,
gray ca
n be
as a poi
nter to find a point
er of t
he gra
y
, then gray value is directly change
d, the
gray which is co
rre
sp
ondi
n
g
to the poi
nter po
sition
i
s
cha
nge
d alo
n
g
with it. If the location i
s
as
a qu
antum
po
inter,
whi
c
h
convenie
n
t effects will
be
p
r
odu
ced
?
Here come
s to
th
e next
nature
of
quantum p
o
in
ter, whi
c
h is
sub-bl
ocks.
Quan
tum p
o
inter s
ub-b
l
ock prop
erties:
Qu
antu
m
pointe
r
su
b-blo
c
k refers to the
block divi
sion
and
combi
n
ation of poi
nters. Be
ca
use
the pointe
r
expre
ssi
on i
s
a bina
ry stri
ng,
whi
c
h
con
s
i
s
ts of 0
and
1,
acco
rdin
g to
the pa
rtition
of 0 an
d 1, a
nd
qu
antum
pointer can b
e
divided on
different types.
Whe
n
the p
o
s
ition value
i
s
use
d
a
s
qua
ntum pointe
r
and i
s
faced
with
more
pixels, t
he poi
nter
ca
n be divid
ed i
n
to blo
c
ks
(or split). Simila
rly, when the
gray
scale val
ue
is u
s
e
d
as qu
antum
pointe
r
, it ca
n
rep
r
e
s
ent a
bi
n
a
ry string of
which
is
re
presenti
ng
g
r
ay ca
n be
divided, the p
o
sition
s different gray scal
e will be divid
ed into a larg
e sub
-
blo
c
ks.
2.3. Quantu
m Gra
y
scale Image Stora
g
e
1) Stor
age Based on Qu
a
n
tum Gray
Pointer
In the prop
osed expre
s
sio
n
,
M
|
is used t
o
encode the
gray scale i
n
formatio
n, it is
assume
d that
the g
r
a
datio
n info
rmation
is a
s
qua
ntu
m
pointe
r
. In
a fixed g
r
ay
scale
imag
e, e
a
ch
pixel has g
r
a
y
scale info
rmation, and
some pixel
g
r
ayscale of these pixels i
s
the sam
e
. Gray
pointer
with the sa
me gra
y
value points to pixel
location with the
same g
r
ay-scale info
rmati
on,
the building
relation
ship is
no long
er the
one to one
rel
a
tionship in the cla
s
sic im
age, but it is the
one to
ma
ny rel
a
tionship,
the o
n
e
to
many relatio
n
shi
p
ma
ke
s the
pixel be
witho
u
t a
si
ngle
cha
nge, afte
r the pixel
sub
-
blo
c
ks
ca
n b
e
forme
d
, large scal
e tra
n
s
form
ation i
s
made. Be
cau
s
e
the gray value chan
ge
s
betwe
en
0
-
2
55, the p
o
sit
i
on of the
same g
r
ay va
lue is for
uni
fied
stora
ge, 256
units of qua
ntum stat
e
s
mo
st only be ne
eded for
storage.
Let
}
,
|
,
,
|
,
{|
|
2
1
im
i
i
i
p
p
p
P
, here,
i
P
|
collectio
n is u
s
ed to re
pre
s
e
n
t all the
positio
n state
s
of
whi
c
h
grayscale valu
e M
i
corre
s
p
ondin
g
to, an
d
im
p
|
represent
s vari
ou
s
locatio
n
s of g
r
ay value M
i
, the corre
s
po
nding po
sitio
n
of each gra
y
value is assume
d to be m,
1
2
0
2
n
m
, quantum sto
r
ed exp
r
e
ssi
o
n
of gray pixe
l with the co
rresp
ondi
ng grayscale value
M
i
is in equati
on (6
).
im
i
i
p
M
m
Q
|
|
1
|
(6)
M
i
must correspon
d P
i
, and
i
Q
|
is sub-expression
of the
expre
ssion
1
2
0
2
|
|
2
1
|
n
j
n
j
M
Q
, it also corre
s
po
nd
s to a compon
ent wit
h
a gray valu
e.
2) Stor
age Based on Qu
a
n
tum Positio
n
Pointer
Quantum
po
sition pointe
r
stora
ge
relie
s main
ly on th
e su
b-blocks
of quantu
m
p
o
inter,
the sub
-
blo
ck of location in
formation bit
s
is di
vided to
achieve the
purp
o
se of the block sto
r
in
g
image pixel in
formation.
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A Quantum
Pointer Sign
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u
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Wu
)
679
Pixel position is
r
e
p
r
es
en
te
d
as
n
n
v
v
v
h
h
h
P
j
2
1
2
1
|
|
|
|
, where
n
h
h
h
2
1
|
and
n
v
v
v
2
1
|
are
re
sp
ecti
vely Qubit e
x
pressio
n
of
the po
sition
bits in th
e
x dire
ction a
nd y
dire
ction. Q
u
antum p
o
sitio
n
poi
nter i
s
d
e
termin
ed
by the p
o
sitio
n
string
exp
r
e
s
sion,
whi
c
h
the
bigge
st mat
c
h qua
ntum b
i
ts is d
e
termi
ned in
n
n
v
v
v
h
h
h
2
1
2
1
|
,
|
. The maximum m
a
tching
quantum bit string is that the entire im
a
ge pixels
a
r
e
divided into a numbe
r of different ch
un
ks.
In chu
n
ks,
ch
unk i
s
divided
into differe
nt
pieces
by loo
k
ing fo
r m
a
tching
strin
g
, it impleme
n
ts t
he
sub
-
blo
c
ks
of quantum
poi
nter, the g
r
a
y
scal
e
imag
e
storage i
s
completed
ba
sed on
qua
ntu
m
locatio
n
point
er.
3) Stor
age Based on Qu
a
n
tum Positio
n
Pointer
Storage
ba
se
d on
qua
ntu
m
mixed p
o
in
ter: Fro
m
the
descri
p
tion
of two q
uantum
pointe
r
,
there i
s
a
po
ssi
bility of bo
th com
b
inatio
ns. In
q
uantu
m
gray
point
ers, fo
r the
same g
r
ay, th
e
locatio
n
of th
eir remai
n
s
can be
divide
d into
sub
-
bl
ocks; th
ere
b
y the child p
o
i
n
ter of q
uant
um
positio
n is ge
nerate
d
. Accordin
g to the same re
as
o
n
, the pixel b
l
ock is pro
c
e
s
sed, if the gray
spe
c
ie
s are n
o
t particul
a
rly
much in the block,
or they
can be comb
ined ba
sed o
n
gray. This can
also
serve a
s
a future re
se
arch directio
n
in practi
cal a
pplication.
From
the
po
int of view
of two
qua
ntum
p
o
inter store
d
rep
r
e
s
entatio
n,
p
r
oce
s
sing
operation
s
a
r
e mad
e
for
d
i
fferent qu
ant
um imag
e, b
o
th have
adv
antage
s, to
choo
se the
m
o
s
t
approp
riate p
o
inters in vari
ous o
peration
s
is the key to quantum poi
nter appli
c
ati
ons.
3. Test and
Discus
s
ion
3.1. Grada
t
ion Trans
f
orm
a
tion
The g
r
ay-scal
e
tran
sfo
r
mat
i
on p
u
rp
ose i
s
to
ch
ange
a gray value
in the im
age,
and
all
gray
pixels o
f
gray val
u
e
s
mu
st chan
g
e
, all the
g
r
a
y
values hav
e chan
ged
a
c
cordi
ngly in
the
gray scale
co
rre
sp
ondi
ng p
o
sition.
First, the qu
antum imag
e
stora
ge is
comple
ted
ba
sed o
n
gray pointer, the
n
the gray
qubits of the i
m
age is p
r
o
c
essed. Be
cau
s
e the range
of gray value
s
is from 0 to
255, the nee
d
is
sho
w
in
g up
to an
8-bit
bin
a
ry st
ring.
Ch
ange
s in
gra
y
value are
chang
es
of ei
ght characte
rs 0
and 1. T
he o
r
iginal g
r
ay va
lues
are
co
m
pare
d
with
th
e targ
et gray
value, differe
nt bits a
r
e fo
und
betwe
en the two, and the
swap d
oor i
s
u
s
ed
to a
c
hiev
e conve
r
si
on
betwe
en 0 an
d 1.
Position
co
nv
ersion:
Position
conve
r
sio
n
is b
a
se
d
on the qua
ntum po
sition
pointer
transfo
rmatio
n, it is bel
ong
to the qu
ant
um imag
e
geo
me
tr
ic
tr
an
s
f
o
r
ma
tion
, th
e p
o
s
ition
mobile
is achieved
a
nd the a
s
soci
ated
tran
sformation is
cha
nged. A 8
8 grayscale im
a
ge is u
s
e
d
to
illustrate the
changing positions.
Figure 2. 8
8 origin
al grey i
m
age
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752
IJEECS
Vol.
2, No. 3, Jun
e
2016 : 675
– 683
680
Figure 2
is a
8
8 g
r
ayscal
e
image, e
a
ch
pixel identifie
s o
n
the
verti
c
al
and
ho
rizontal
coo
r
din
a
tes is sh
own
in Figure
2. Fo
r a
block 1 i
n
FIGURE, the positi
on is
}
011111
|
,
010111
|
,
011110
|
,
010110
{|
|
1
P
, and the position
of the block 2 i
s
}
001111
|
,
000111
|
,
001110
|
,
000110
{|
|
2
P
. The store
d
qubits of
the correspondi
ng
positio
n a
r
e
comp
ared in
positio
n 1
an
d po
sition
2,
010110
|
and
000110
|
,
011110
|
an
d
001110
|
,
010111
|
and
000111
|
,
011111
|
and
001111
|
is contrasted respectively, Only
the 2-th po
sit
i
on is differe
nt in two bits , and for e
a
ch q
ubit pai
r, only the 2-th origin
al qu
bit
transfo
rm
s from 1 to 0, transfo
rmatio
n can b
e
co
mpl
e
ted from the
origin
al po
sition to the target
positio
n.
Applica
t
ion Test:
Th
e d
e
scrib
ed o
p
e
r
ation in
Fig
u
re 3
is the
above
stored an
d
transfo
rmatio
n pro
c
e
ss.
Figure 3. Qua
n
tum bit swa
p
Firs
t, pos
i
tion
1
|
P
is
sto
r
ed.
La
teral vie
w
ex
chang
e is sho
w
n i
n
Fig
u
re
3, a d
o
tted b
o
x
is the first chi
l
d block of the quantum
p
o
inter, wh
i
c
h
is the first lay
e
r of a pointe
r
; se
con
d
su
b-
block i
s
a
se
lection
blo
ck,
the provid
ed
and
se
le
cte
d
qubit i
s
0
and 1; the th
ird sub
-
blo
ck is
comp
osed
of
"11"
su
b-bl
o
c
ks; th
e 4
-
th
sub
-
blo
c
k i
s
also
a
selecti
on bl
ock, it i
s
co
mpo
s
e
d
o
f
0
and 1. From the divisio
n
of the
sub
-
blo
c
ks, the n
eed
transfo
rm i
s
a first sub-blo
ck, a
rro
w in t
h
e
dashed
box
is a
1-0
con
v
ersio
n
, an
d
the 2
-
th, 3
-
th, 4-th
s
u
b-blocks
c
o
ns
titute a perfectl
y
matche
d
co
mbination
of
a mem
o
ry, a
s
i
s
sho
w
n
i
n
the
da
she
d
box b.
The
qubit
string
b
l
ock
stora
g
e
allo
ws u
s
to q
u
ickl
y find the
blo
c
ks th
at n
eed
to
cha
nge, t
he tran
sition i
s
im
pleme
n
te
d
betwe
en bits,
and differe
nt sub
-
blo
c
ks a
r
e divide
d into different im
age
s, whi
c
h
can al
so
ch
a
nge
the efficien
cy
of the ima
ge
pro
c
e
ssi
ng. A
fter t
he
compl
e
tion of the
image
co
nversion, it i
s
sho
w
n
in Figure 4.
Figure 4. 8
8 target g
r
ey image
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A Quantum
Pointer Sign
al Processin
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Rese
arch (Sh
u
y
ue
Wu
)
681
Figure 5 i
s
a
grou
p of m
o
b
ile photo
s
, th
e co
ntent im
age bl
ocks continuo
usly e
x
chan
ge
with the bl
an
k blo
c
ks to
reach the m
o
bile ma
ss, th
e re
quire im
age VI is
ob
tained from the
origin
al ima
g
e
I. Each
ima
ge i
s
a
16
16
gray-scale i
m
age,
while th
e entire ima
g
e
is
divided
in
to
16 blo
c
ks of
equal si
ze
s,
and then th
e entire
ima
ge is compl
e
ted by moving the blo
c
ks.
De
scription bl
ock moves i
s
the first step,
block 2 excha
nge
s with bla
n
k blo
c
k 16.
Figure 5. Orig
inal image, ta
rget imag
e an
d
middle ima
ge got by the image tra
n
sfo
r
mation
Pixel blocks 2 and 16 are made of 4
4 pixels. Based on the
expre
ssi
on (2), the
positio
n of each pixel is re
pre
s
ente
d
by the eight
quantum bits. T
he po
sition set of the block 16
and bl
ock 2
a
r
e a
s
follo
ws
(qua
ntum bit
string
is to
o l
ong a
nd i
s
n
o
t
marked i
n
Fi
gure,
Refe
ren
c
e
can b
e
se
en i
n
Figure 2)
01110011
|
,
01100011
|
,
01010011
|
,
01000011
|
,
01110010
|
,
01100010
|
,
01010010
|
,
01000010
|
01110001
|
,
01100001
|
,
01010001
|
,
01000001
|
,
01110000
|
,
01100000
|
,
01010000
|
,
01000000
|
|
16
P
(7)
01110111
|
,
01100111
|
,
01010111
|
,
01000111
|
,
01110110
|
,
01100110
|
,
01010110
|
,
01000110
|
01110101
|
,
01100101
|
,
01010101
|
,
01000101
|
,
01110100
|
,
01100100
|
,
01010100
|
,
01000100
|
|
2
P
(8)
The blocks
2
and 16 nee
d to
be ch
ang
e
d
,
the storag
e
of
bl
ock 2 and blo
c
k
16
are
only
listed. Figu
re
6 sho
w
s the storage of two
trans
fo
rm blo
c
ks, and the
need q
uantu
m
bit conversion
is achieved.
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IJEECS
Vol.
2, No. 3, Jun
e
2016 : 675
– 683
682
Figure 6. First transformati
on: excha
nge
betwee
n
16
and 2
Location liste
d set P16 a
n
d
P2 are
com
pare
d
in corresp
ondi
ng po
sition, only th
e dotted
line arro
w m
a
rked bit
s
are different in
the corr
e
s
p
o
nding p
o
sitio
n
of P2 set. Acco
rdi
ng to
the
excha
nge
of the da
sh
ed
arrows i
n
Fig
u
re 6,
the exch
ange will be able
to be co
mpleted betwee
n
block 16 a
nd
block 2.
Discus
s
ion:
Becau
s
e
qua
ntum poi
nter is a
dire
ctio
nal, we
only
need to
ch
an
ge the
positio
n of the pixel, an
d then the role of
qua
ntum po
sition
pointer
ca
n be to ch
ang
the
corre
s
p
ondin
g
positio
n of gray, whi
c
h is
a major adva
n
tage of qua
n
t
um pointer.
I to II conversion ca
n be
co
mpleted in Fi
gure
5,
then the othe
r tran
sform
a
tion
s is simil
a
r.
Total 5 co
nversi
on i
s
re
q
u
ired from th
e origi
nal im
age I to the target ima
ge
VI. The first step
transfo
rmatio
n is
compl
e
te
d in
Figu
re
6
;
the
c
onve
r
ted ex
cha
nge
s of
the
othe
r
fou
r
stores are
empathy.
Other q
uantu
m
image ge
o
m
etric tran
sformatio
n
is compa
r
ed, the
pixel movement and
transfo
rmatio
n are u
s
e
d
first in the q
uantum p
o
int
e
r form, it is no long
er t
o
cha
nge
ea
ch
individual pix
e
l, but pixel block si
ze
s vary in
units,
this ca
n re
d
u
ce u
nne
ce
ssary o
peratio
ns
redu
nda
ncy
and sim
p
lify
pro
c
ed
ures. Furthe
rmo
r
e,
the point role of quantum
pointer ca
n can
prod
uce a se
ries of chain
rea
c
tion
s, time is sh
o
r
ten to lock the o
p
e
rating rang
e
,
efficiency is
improve
d
for image p
r
o
c
e
s
sing o
peratio
ns..
4. Conclusio
n
A quantum e
x
pressio
n
of gray imag
e is pre
s
e
n
ted
according to
the gray prop
erty and
locatio
n
p
r
op
erty of g
r
ay i
m
age
pixel, a
nd a
ne
w
co
n
c
ept
of qu
ant
um p
o
inter is put
forwa
r
d
in
accordan
ce
with the ima
ge expressio
n
, bas
ed on
the quantu
m
pointer
property, grayscal
e
conve
r
si
on a
nd po
sition conversion b
e
made from
t
he qua
ntum theory of grayscale imag
e. The
different typ
e
of qua
ntu
m
pointe
r
is use
d
in
dif
f
erent ima
g
e
pro
c
e
s
sing
ope
ration
s, the
compl
e
xity of the ope
ration
is si
mplified.
As c
an b
e
se
en from
the e
x
ample, ba
se
d on th
e ima
ge
grayscal
e or the location
information
cha
nge,
the
conn
ectio
n
role of qu
ant
um pointe
r
can
compl
e
te the transfo
rmatio
n operation of
t
he entire im
age, the com
p
lexity is the half.
In this pape
r, a relatively simple rep
r
es
e
n
tation is prop
ose
d
for grayscale
image
s
quantum
expression. In the
cla
ssi
c
colo
r
image, the pi
xel has the t
w
o p
r
op
ertie
s
of the colo
r a
nd
positio
n. In a grayscal
e image, ea
ch pi
xel gray
valu
e and its lo
cation is both
rep
r
e
s
ente
d
, the
rang
e of
gray value
s
i
s
th
e
sm
aller,
whi
c
h
si
m
p
lifies
the represent
ation of th
e
e
x
pressio
n
. Th
e
expre
ssi
on e
x
tends to the
colo
r imag
e
is a di
re
ctio
n for future rese
arch. In
addition, a n
e
w
con
c
e
p
t of the qua
ntum p
o
iner i
s
p
r
o
p
o
se
d ba
se
d
on the p
r
o
p
o
s
ed
expre
s
si
on. The
pro
p
ose
d
quantum p
o
in
ter here is somewhat sim
ilar with cl
assical compute
r
pointer, but there are very
different, qua
ntum imag
es stored
repre
s
entatio
n
is more co
nveni
ent, so that t
he imag
e ha
s a
highe
r efficie
n
cy and a
nd
better re
sult
s in the pro
c
e
s
s of tran
sform
a
tion.
Ackn
o
w
l
e
dg
ements
This
study i
s
sp
on
sored
by the Sci
e
n
t
ific
Re
se
arch Proj
ect
(NO. 14A08
4)
of Hu
nan
Provinci
al Educatio
n De
pa
rtment, Chin
a
.
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IJEECS
ISSN:
2502-4
752
A Quantum
Pointer Sign
al Processin
g
Rese
arch (Sh
u
y
ue
Wu
)
683
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