<s>
Quantum	B-Device
image	I-Device
processing	I-Device
(	O
QIMP	O
)	O
is	O
using	O
quantum	B-Architecture
computing	I-Architecture
or	O
quantum	O
information	O
processing	O
to	O
create	O
and	O
work	O
with	O
quantum	B-Device
images	I-Device
.	O
</s>
<s>
Due	O
to	O
some	O
of	O
the	O
properties	O
inherent	O
to	O
quantum	B-Architecture
computation	I-Architecture
,	O
notably	O
entanglement	O
and	O
parallelism	B-Operating_System
,	O
it	O
is	O
hoped	O
that	O
QIMP	O
technologies	O
will	O
offer	O
capabilities	O
and	O
performances	O
that	O
surpass	O
their	O
traditional	O
equivalents	O
,	O
in	O
terms	O
of	O
computing	O
speed	O
,	O
security	O
,	O
and	O
minimum	O
storage	O
requirements	O
.	O
</s>
<s>
A	O
.	O
Y	O
.	O
Vlasov	O
's	O
work	O
in	O
1997	O
focused	O
on	O
the	O
use	O
of	O
a	O
quantum	O
system	O
to	O
recognize	O
orthogonal	B-Application
images	O
.	O
</s>
<s>
This	O
was	O
followed	O
by	O
efforts	O
using	O
quantum	B-Device
algorithms	I-Device
to	O
search	O
specific	O
patterns	O
in	O
binary	B-Algorithm
images	I-Algorithm
and	O
detect	O
the	O
posture	O
of	O
certain	O
targets	O
.	O
</s>
<s>
Later	O
on	O
,	O
in	O
2005	O
,	O
Latorre	O
proposed	O
another	O
kind	O
of	O
representation	O
,	O
called	O
the	O
Real	O
Ket	O
,	O
whose	O
purpose	O
was	O
to	O
encode	O
quantum	B-Device
images	I-Device
as	O
a	O
basis	O
for	O
further	O
applications	O
in	O
QIMP	O
.	O
</s>
<s>
Furthermore	O
,	O
in	O
2010	O
Venegas-Andraca	O
and	O
Ball	O
presented	O
a	O
method	O
for	O
storing	O
and	O
retrieving	O
binary	B-Language
geometrical	I-Language
shapes	I-Language
in	O
quantum	O
mechanical	O
systems	O
in	O
which	O
it	O
is	O
shown	O
that	O
maximally	O
entangled	O
qubits	O
can	O
be	O
used	O
to	O
reconstruct	O
images	O
without	O
using	O
any	O
additional	O
information	O
.	O
</s>
<s>
A	O
survey	O
of	O
quantum	B-Device
image	I-Device
representation	O
has	O
been	O
published	O
in	O
.	O
</s>
<s>
Furthermore	O
,	O
the	O
recently	O
published	O
book	O
Quantum	B-Device
Image	I-Device
Processing	I-Device
provides	O
a	O
comprehensive	O
introduction	O
to	O
quantum	B-Device
image	I-Device
processing	I-Device
,	O
which	O
focuses	O
on	O
extending	O
conventional	O
image	O
processing	O
tasks	O
to	O
the	O
quantum	B-Architecture
computing	I-Architecture
frameworks	O
.	O
</s>
<s>
It	O
summarizes	O
the	O
available	O
quantum	B-Device
image	I-Device
representations	O
and	O
their	O
operations	O
,	O
reviews	O
the	O
possible	O
quantum	B-Device
image	I-Device
applications	O
and	O
their	O
implementation	O
,	O
and	O
discusses	O
the	O
open	O
questions	O
and	O
future	O
development	O
trends	O
.	O
</s>
<s>
A	O
lot	O
of	O
the	O
effort	O
in	O
QIMP	O
has	O
been	O
focused	O
on	O
designing	O
algorithms	O
to	O
manipulate	O
the	O
position	O
and	O
color	O
information	O
encoded	B-Algorithm
using	O
flexible	O
representation	O
of	O
quantum	B-Device
images	I-Device
(	O
FRQI	O
)	O
and	O
its	O
many	O
variants	O
.	O
</s>
<s>
For	O
instance	O
,	O
FRQI-based	O
fast	O
geometric	O
transformations	O
including	O
(	O
two-point	O
)	O
swapping	O
,	O
flip	O
,	O
(	O
orthogonal	B-Application
)	O
rotations	O
and	O
restricted	O
geometric	O
transformations	O
to	O
constrain	O
these	O
operations	O
to	O
a	O
specified	O
area	O
of	O
an	O
image	O
were	O
initially	O
proposed	O
.	O
</s>
<s>
Recently	O
,	O
NEQR-based	O
quantum	B-Device
image	I-Device
translation	O
to	O
map	O
the	O
position	O
of	O
each	O
picture	B-Algorithm
element	I-Algorithm
in	O
an	O
input	O
image	O
into	O
a	O
new	O
position	O
in	O
an	O
output	O
image	O
and	O
quantum	B-Device
image	I-Device
scaling	O
to	O
resize	O
a	O
quantum	B-Device
image	I-Device
were	O
discussed	O
.	O
</s>
<s>
By	O
using	O
the	O
basic	O
quantum	O
gates	O
and	O
the	O
aforementioned	O
operations	O
,	O
so	O
far	O
,	O
researchers	O
have	O
contributed	O
to	O
quantum	B-Device
image	I-Device
feature	O
extraction	O
,	O
quantum	B-Device
image	I-Device
segmentation	B-Algorithm
,	O
quantum	B-Device
image	I-Device
morphology	O
,	O
quantum	B-Device
image	I-Device
comparison	O
,	O
quantum	B-Device
image	I-Device
filtering	O
,	O
quantum	B-Device
image	I-Device
classification	O
,	O
quantum	B-Device
image	I-Device
stabilization	O
,	O
among	O
others	O
.	O
</s>
<s>
Similarly	O
,	O
these	O
advancements	O
have	O
led	O
to	O
many	O
applications	O
in	O
the	O
areas	O
of	O
watermarking	B-General_Concept
,	O
encryption	O
,	O
and	O
steganography	O
etc.	O
,	O
which	O
form	O
the	O
core	O
security	O
technologies	O
highlighted	O
in	O
this	O
area	O
.	O
</s>
<s>
By	O
encoding	B-Algorithm
and	O
processing	O
the	O
image	O
information	O
in	O
quantum-mechanical	O
systems	O
,	O
a	O
framework	O
of	O
quantum	B-Device
image	I-Device
processing	I-Device
is	O
presented	O
,	O
where	O
a	O
pure	O
quantum	O
state	O
encodes	O
the	O
image	O
information	O
:	O
to	O
encode	O
the	O
pixel	B-Algorithm
values	O
in	O
the	O
probability	O
amplitudes	O
and	O
the	O
pixel	B-Algorithm
positions	O
in	O
the	O
computational	O
basis	O
states	O
.	O
</s>
<s>
Given	O
an	O
image	O
,	O
where	O
represents	O
the	O
pixel	B-Algorithm
value	O
at	O
position	O
with	O
and	O
,	O
a	O
vector	O
with	O
elements	O
can	O
be	O
formed	O
by	O
letting	O
the	O
first	O
elements	O
of	O
be	O
the	O
first	O
column	O
of	O
,	O
the	O
next	O
elements	O
the	O
second	O
column	O
,	O
etc	O
.	O
</s>
<s>
In	O
the	O
quantum	B-Architecture
computing	I-Architecture
,	O
the	O
linear	O
transformation	O
can	O
be	O
represented	O
as	O
with	O
the	O
input	O
image	O
state	O
and	O
the	O
output	O
image	O
state	O
.	O
</s>
<s>
Some	O
basic	O
and	O
commonly	O
used	O
image	O
transforms	O
(	O
e.g.	O
,	O
the	O
Fourier	B-Algorithm
,	O
Hadamard	B-Algorithm
,	O
and	O
Haar	O
wavelet	O
transforms	O
)	O
can	O
be	O
expressed	O
in	O
the	O
form	O
,	O
with	O
the	O
resulting	O
image	O
and	O
a	O
row	O
(	O
column	O
)	O
transform	O
matrix	O
.	O
</s>
<s>
The	O
corresponding	O
unitary	B-Algorithm
operator	I-Algorithm
can	O
then	O
be	O
written	O
as	O
.	O
</s>
<s>
Several	O
commonly	O
used	O
two-dimensional	O
image	O
transforms	O
,	O
such	O
as	O
the	O
Haar	O
wavelet	O
,	O
Fourier	B-Algorithm
,	O
and	O
Hadamard	B-Algorithm
transforms	I-Algorithm
,	O
are	O
experimentally	O
demonstrated	O
on	O
a	O
quantum	B-Architecture
computer	I-Architecture
,	O
with	O
exponential	O
speedup	O
over	O
their	O
classical	O
counterparts	O
.	O
</s>
<s>
In	O
addition	O
,	O
a	O
novel	O
highly	O
efficient	O
quantum	B-Device
algorithm	I-Device
is	O
proposed	O
and	O
experimentally	O
implemented	O
for	O
detecting	O
the	O
boundary	O
between	O
different	O
regions	O
of	O
a	O
picture	O
:	O
It	O
requires	O
only	O
one	O
single-qubit	O
gate	O
in	O
the	O
processing	O
stage	O
,	O
independent	O
of	O
the	O
size	O
of	O
the	O
picture	O
.	O
</s>
