I
nte
rna
t
io
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l J
o
urna
l o
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nfo
rm
a
t
ics a
nd
Co
m
m
un
ica
t
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n T
ec
hn
o
lo
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y
(
I
J
-
I
CT
)
Vo
l.
1
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,
No
.
2
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J
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n
e
20
2
6
,
p
p
.
578
~
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7
I
SS
N:
2252
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,
DOI
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1
0
.
1
1
5
9
1
/iji
ct
.
v
1
5
i
2
.
pp
578
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58
7
578
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ttp
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M
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Art
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nfo
AB
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RAC
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ticle
his
to
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y:
R
ec
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ed
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2
1
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2
0
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R
ev
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J
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1
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Acc
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Clas
sifica
ti
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is
a
m
a
jo
r
tas
k
in
d
a
ta
sc
ien
c
e
.
Da
ta
c
las
sifica
ti
o
n
is
re
q
u
ired
in
m
a
n
y
in
d
u
stries
su
c
h
a
s
h
e
a
lt
h
c
a
re
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tran
sp
o
rt,
a
n
d
fin
a
n
c
e
.
No
isy
in
term
e
d
iate
-
sc
a
le
q
u
a
n
t
u
m
(
NIS
Q
)
e
ra
.
Qu
a
n
tu
m
c
o
m
p
u
ters
a
re
c
a
p
a
b
le
o
f
so
lv
i
n
g
c
o
m
p
lex
d
a
ta
c
h
a
ll
e
n
g
e
s
a
n
d
c
a
n
b
e
u
se
d
f
o
r
t
h
e
c
las
sifica
ti
o
n
o
f
th
e
d
a
ta
with
m
in
imu
m
fe
a
tu
re
s.
In
th
is
re
g
a
r
d
,
q
u
a
n
tu
m
n
e
u
ra
l
n
e
two
rk
s
a
r
e
b
e
in
g
u
se
d
e
x
ten
si
v
e
ly
fo
r
d
a
ta
c
las
sifica
ti
o
n
.
I
n
th
is
p
a
p
e
r,
w
e
e
m
p
lo
y
v
a
riatio
n
a
l
q
u
a
n
tu
m
c
ircu
it
s
f
o
r
th
e
tas
k
o
f
m
u
lt
icla
ss
c
las
sifica
ti
o
n
.
A
h
y
b
rid
a
p
p
r
o
a
c
h
is
u
se
d
f
o
r
b
u
il
d
in
g
th
e
n
e
u
ra
l
n
e
two
rk
.
In
wh
ic
h
q
u
a
n
tu
m
c
ircu
it
s
a
re
u
se
d
fo
r
th
e
fe
e
d
f
o
rw
a
rd
a
rc
h
it
e
c
tu
re
,
wh
il
e
i
n
b
a
c
k
-
p
r
o
p
a
g
a
ti
o
n
,
p
a
ra
m
e
ters
a
r
e
u
p
d
a
ted
u
sin
g
a
c
las
sic
a
l
o
p
ti
m
ize
r
o
n
c
las
sic
a
l
c
o
m
p
u
ters
.
We
h
a
v
e
s
u
c
c
e
ss
fu
ll
y
d
e
m
o
n
st
ra
ted
m
u
lt
icla
ss
c
las
sifica
ti
o
n
u
sin
g
t
h
e
p
ro
p
o
se
d
a
p
p
ro
a
c
h
o
n
b
e
n
c
h
m
a
rk
d
a
ta
se
ts.
Ou
r
re
su
lt
s
s
h
o
w
t
h
a
t
v
a
riatio
n
a
l
q
u
a
n
t
u
m
c
ircu
it
(
VQC
)
a
re
a
p
ro
m
isin
g
c
a
n
d
id
a
te
f
o
r
c
las
sifica
ti
o
n
p
ro
b
lem
s
with
fe
we
r
fe
a
tu
re
s.
We
h
a
v
e
p
e
rfo
rm
e
d
e
x
p
e
rime
n
ts
o
n
I
n
tern
a
ti
o
n
a
l
Bu
sin
e
ss
M
a
c
h
in
e
s C
o
rp
o
ra
ti
o
n
(
IBM
)
q
u
a
n
tu
m
h
a
rd
wa
re
a
n
d
sim
u
lato
rs.
K
ey
w
o
r
d
s
:
Mu
lti
-
class
clas
s
if
icatio
n
Qu
an
tu
m
co
m
p
u
tin
g
Qu
an
tu
m
n
e
u
r
al
n
etwo
r
k
s
Var
iatio
n
al
q
u
an
tu
m
cir
cu
its
h
y
b
r
id
q
u
a
n
tu
m
-
class
ical
alg
o
r
ith
m
T
h
is i
s
a
n
o
p
e
n
a
c
c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Mu
h
am
m
ad
Ham
i
d
Dep
ar
tm
en
t o
f
C
o
m
p
u
ter
E
n
g
i
n
ee
r
in
g
,
Facu
lty
o
f
E
n
g
in
ee
r
in
g
an
d
T
ec
h
n
o
l
o
g
y
J
am
ia
Millia
I
s
lam
ia
Un
iv
er
s
it
y
J
am
ia
Nag
ar
,
New
Delh
i,
I
n
d
i
a
E
m
ail:
h
am
id
m
d
5
0
4
@
g
m
ail.
c
o
m
1.
I
NT
RO
D
UCT
I
O
N
Ar
tific
ial
in
tellig
en
ce
h
as
ex
p
er
ien
ce
d
ex
p
o
n
e
n
tial
g
r
o
wth
i
n
r
ec
en
t d
ec
ad
es,
lead
in
g
to
a
wid
e
r
an
g
e
o
f
ap
p
licatio
n
s
in
h
ea
lth
ca
r
e
,
ag
r
icu
ltu
r
e,
tr
an
s
p
o
r
tatio
n
,
f
i
n
an
ce
,
en
te
r
tain
m
en
t,
a
n
d
m
a
n
y
o
th
e
r
d
o
m
ain
s
.
Ho
wev
er
,
tr
ain
in
g
m
ac
h
in
e
le
ar
n
in
g
m
o
d
els
ty
p
ically
r
eq
u
i
r
es
s
u
b
s
tan
tial
co
m
p
u
tatio
n
al
r
eso
u
r
ce
s
an
d
tim
e.
So
m
etim
es
tr
ain
in
g
a
d
ee
p
lea
r
n
in
g
m
o
d
el
m
a
y
tak
e
s
ev
er
al
d
ay
s
an
d
e
v
en
a
m
o
n
th
.
Desp
i
te
r
ec
en
t
ad
v
a
n
ce
s
in
class
ical
co
m
p
u
ter
s
,
m
o
d
e
r
n
co
m
p
u
ter
s
ar
e
r
ea
c
h
in
g
t
h
eir
lim
its
in
im
p
lem
en
tin
g
m
ac
h
in
e
lear
n
in
g
in
d
if
f
er
en
t
ar
ea
s
.
R
esear
ch
er
s
an
d
co
m
p
u
ter
s
cien
tis
ts
ar
e
lo
o
k
in
g
f
o
r
a
n
alter
n
ativ
e
to
class
ical
co
m
p
u
tin
g
,
an
d
th
ey
s
ee
q
u
an
tu
m
co
m
p
u
ter
s
as
an
alter
n
ativ
e
s
o
lu
tio
n
to
o
v
er
co
m
e
th
is
p
r
o
b
lem
.
Qu
an
tu
m
co
m
p
u
ter
s
u
s
e
s
u
p
er
p
o
s
itio
n
,
en
tan
g
lem
en
t,
an
d
in
ter
f
er
en
ce
to
p
r
o
ce
s
s
in
f
o
r
m
atio
n
.
Qu
a
n
tu
m
co
m
p
u
ter
s
h
av
e
s
h
o
wn
s
p
ee
d
u
p
in
f
ac
to
r
izatio
n
o
f
n
u
m
b
er
s
[
1
]
a
n
d
s
ea
r
ch
i
n
g
in
u
n
s
tr
u
ctu
r
ed
d
ata
[
2
]
.
Qu
an
tu
m
m
ac
h
i
n
e
lear
n
in
g
(
QM
L
)
is
an
em
er
g
in
g
in
te
r
d
i
s
cip
lin
ar
y
r
esear
ch
ar
ea
th
at
in
teg
r
ates
p
r
in
cip
les f
r
o
m
q
u
a
n
tu
m
co
m
p
u
tin
g
an
d
m
ac
h
i
n
e
lear
n
in
g
t
o
ac
h
iev
e
co
m
p
u
tatio
n
al
a
d
v
a
n
tag
es o
v
er
class
ical
ap
p
r
o
ac
h
es.
Alth
o
u
g
h
QM
L
r
em
ain
s
in
its
n
ascen
t
s
tag
e,
a
d
iv
er
s
e
r
an
g
e
o
f
alg
o
r
ith
m
s
h
as
alr
ea
d
y
b
ee
n
p
r
o
p
o
s
ed
with
in
th
is
d
o
m
ain
.
QM
L
h
as
b
ee
n
in
v
esti
g
ate
d
ac
r
o
s
s
m
u
ltip
le
lear
n
in
g
p
ar
ad
ig
m
s
[
3
]
–
[
5
]
.
Qu
an
tu
m
s
u
p
p
o
r
t
v
ec
to
r
m
ac
h
in
e
(
QSVM)
[
6
]
,
q
u
an
tu
m
K
-
n
ea
r
est
n
eig
h
b
o
r
(
QK
-
NN)
[
7
]
ar
e
ex
am
p
les
o
f
alg
o
r
ith
m
s
th
at
ar
e
b
ein
g
u
s
ed
f
o
r
th
e
b
i
n
ar
y
class
if
icatio
n
task
.
Als
o
,
we
h
av
e
witn
es
s
ed
th
e
p
o
wer
o
f
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Mu
lticla
s
s
cla
s
s
ifica
tio
n
u
s
in
g
va
r
ia
tio
n
a
l q
u
a
n
tu
m
circu
it o
n
b
en
c
h
ma
r
k
d
a
ta
s
et
(
Mu
h
a
mma
d
Ha
mid
)
579
Hy
b
r
id
-
QC
NN
f
o
r
m
u
lti
-
class
class
if
icatio
n
task
s
[
8
]
.
I
n
th
i
s
s
eq
u
en
ce
,
B
lan
k
et
a
l
.
[
9
]
i
n
tr
o
d
u
ce
d
a
k
er
n
el
-
b
ased
q
u
an
t
u
m
class
if
ier
f
o
r
b
ig
d
ata
class
if
icatio
n
.
Ad
h
ik
ar
y
et
a
l.
[
1
0
]
em
p
lo
y
ed
a
n
N
-
lev
el
q
u
an
tu
m
s
y
s
tem
to
en
c
o
d
e
f
ea
tu
r
e
s
f
o
r
a
h
y
b
r
id
q
u
an
t
u
m
-
class
ical
(
HQC)
class
if
ier
,
d
em
o
n
s
tr
atin
g
its
ap
p
licatio
n
to
class
if
icatio
n
task
s
ac
r
o
s
s
m
u
ltip
le
d
atasets
.
Date
et
a
l.
[1
1
]
in
tr
o
d
u
ce
d
a
HQC
n
e
u
r
al
n
etwo
r
k
ar
c
h
itectu
r
e
f
o
r
b
in
ar
y
class
if
icatio
n
.
Su
b
s
eq
u
en
tly
,
in
[
1
2
]
,
th
e
au
th
o
r
s
ex
ten
d
ed
th
ese
m
eth
o
d
s
to
m
u
lti
-
class
p
r
o
b
lem
s
b
y
em
p
l
o
y
in
g
am
p
litu
d
e
e
n
co
d
in
g
f
o
r
th
r
ee
-
class
class
if
icat
i
o
n
.
Her
e
we
p
r
esen
t
a
m
ix
ed
q
u
a
n
tu
m
-
class
ical
-
b
ased
ap
p
r
o
ac
h
u
s
in
g
v
ar
iatio
n
al
q
u
a
n
tu
m
cir
cu
its
f
o
r
m
u
lti
-
class
cla
s
s
if
icatio
n
ta
s
k
s
o
n
I
R
I
S
an
d
w
h
ea
t
s
ee
d
d
ata
s
ets.
Ou
r
s
tu
d
y
m
ain
ly
co
n
tr
i
b
u
tes
to
m
u
lti
-
class
class
if
icatio
n
o
n
th
e
I
R
I
S
f
lo
wer
d
ataset
in
to
th
r
ee
class
es
with
o
n
ly
f
o
u
r
f
ea
tu
r
es
an
d
cl
ass
if
icatio
n
o
f
wh
ea
t
s
ee
d
with
o
n
ly
f
o
u
r
f
ea
tu
r
es in
to
th
r
ee
class
es.
T
h
is
p
ap
er
is
d
iv
id
ed
in
to
s
e
v
er
al
s
ec
tio
n
s
wh
ich
ar
e
as
f
o
llo
ws,
s
ec
tio
n
1
co
v
er
s
in
tr
o
d
u
ctio
n
.
I
n
s
ec
tio
n
2
,
we
h
av
e
co
v
er
e
d
r
elate
d
wo
r
k
o
n
m
u
lti
-
class
class
if
icatio
n
,
an
d
v
ar
iatio
n
al
q
u
an
tu
m
cir
cu
its
ar
e
ex
p
lain
ed
i
n
s
ec
tio
n
3
.
I
n
s
ec
tio
n
4
we
h
av
e
ex
p
lain
ed
o
u
r
p
r
o
p
o
s
ed
s
ch
em
e
an
d
d
ata
p
r
ep
ar
atio
n
m
eth
o
d
,
an
d
s
ec
tio
n
5
is
a
d
is
cu
s
s
io
n
ab
o
u
t r
esu
lts
an
d
f
in
ally
o
u
r
f
i
n
d
in
g
s
ar
e
co
n
clu
d
e
d
in
t
h
e
last
s
ec
tio
n
.
2.
RE
L
AT
E
D
WO
RK
S
Qu
an
tu
m
n
eu
r
al
n
etwo
r
k
s
h
av
e
b
ee
n
s
tu
d
ied
as
a
m
eth
o
d
f
o
r
class
if
y
in
g
clas
s
ical
d
ata.
I
t
i
s
th
e
m
o
s
t
ex
p
lo
r
ed
m
eth
o
d
f
o
r
class
if
icatio
n
with
q
u
an
t
u
m
co
m
p
u
ter
s
.
Wu
et
a
l
.
[
1
3
]
in
tr
o
d
u
ce
d
a
n
e
w
s
ca
lab
le
m
eth
o
d
u
s
in
g
q
u
an
tu
m
n
eu
r
al
n
etwo
r
k
s
f
o
r
class
if
icatio
n
.
I
n
wh
ich
s
m
all
q
u
an
tu
m
h
ar
d
war
e
is
u
s
ed
co
o
p
er
ativ
ely
.
T
h
e
en
tire
i
m
ag
e
is
s
eg
m
en
te
d
in
to
m
u
ltip
le
r
eg
io
n
s
,
an
d
f
ea
tu
r
es
f
r
o
m
ea
ch
r
eg
io
n
ar
e
ex
t
r
ac
ted
u
s
in
g
s
m
all
-
s
ca
le
q
u
an
tu
m
d
ev
ices.
E
x
tr
a
cted
lo
ca
l
f
ea
tu
r
es
ar
e
s
en
t
to
th
e
q
u
an
tu
m
d
ev
ice
to
p
er
f
o
r
m
p
r
ed
ictio
n
b
y
co
m
b
in
in
g
all
lo
ca
l
f
ea
t
u
r
es
i
n
p
a
r
allel.
T
h
e
y
c
o
n
d
u
cted
e
x
p
er
im
en
ts
an
d
e
v
alu
ated
th
e
o
u
tco
m
es
f
o
r
b
in
ar
y
c
lass
if
icatio
n
o
n
th
e
Mo
d
if
ie
d
Natio
n
al
I
n
s
titu
te
o
f
Stan
d
a
r
d
s
an
d
T
ec
h
n
o
lo
g
y
(
MN
I
ST
)
d
ig
it
d
ataset.
T
h
e
lim
itatio
n
in
th
is
ap
p
r
o
ac
h
is
its
ef
f
icien
cy
f
o
r
lar
g
er
o
r
m
o
r
e
co
m
p
lex
d
ata
s
ets.
Als
o
,
it
is
n
o
t
k
n
o
w
n
wh
eth
er
th
is
ap
p
r
o
ac
h
ca
n
b
e
u
s
ed
f
o
r
m
u
lticla
s
s
clas
s
if
icati
o
n
o
n
class
ical
d
ata.
I
n
an
o
th
er
p
ap
er
,
Wu
et
a
l
.
[
1
4
]
p
r
o
p
o
s
ed
a
v
ar
iatio
n
al
q
u
an
tu
m
m
u
lti
-
class
if
ier
b
ased
o
n
c
o
r
r
elatio
n
an
d
m
ea
s
u
r
em
en
t.
T
h
e
e
v
alu
atio
n
f
in
d
in
g
s
s
h
o
w
t
h
at
th
ey
attain
ed
en
h
an
ce
d
p
e
r
f
o
r
m
an
ce
with
m
in
im
al
q
u
an
tu
m
r
eso
u
r
ce
s
an
d
a
b
asic
an
s
atz.
T
h
e
lim
itatio
n
i
n
th
is
m
et
h
o
d
is
th
at
it
d
ep
e
n
d
s
o
n
q
u
an
tu
m
s
tate
to
m
o
g
r
ap
h
y
to
r
e
co
n
s
tr
u
ct
th
e
r
ea
d
o
u
t
s
tate,
wh
ich
ca
n
b
e
r
eso
u
r
ce
-
in
ten
s
iv
e
in
ter
m
s
o
f
b
o
t
h
q
u
an
t
u
m
cir
c
u
its
an
d
class
ical
co
m
p
u
tatio
n
f
o
r
s
tate
r
ec
o
n
s
tr
u
ctio
n
.
W
an
g
et
a
l
.
[
1
5
]
p
r
esen
te
d
o
n
-
ch
ip
p
ar
am
et
r
ized
q
u
an
tu
m
ci
r
cu
it
tr
ain
in
g
with
p
ar
am
eter
s
h
if
t.
T
h
ey
f
in
d
th
at
g
r
ad
ie
n
ts
o
b
tain
ed
b
y
p
ar
am
eter
s
h
if
t
h
av
e
lo
w
f
id
elity
,
wh
ich
ca
u
s
es
a
d
ec
r
ea
s
e
in
tr
ain
in
g
ac
cu
r
ac
y
.
T
o
ac
h
iev
e
th
is
,
th
ey
also
s
u
g
g
est
p
r
o
b
ab
ilis
tic
g
r
ad
ien
t
p
r
u
n
in
g
,
wh
ich
id
en
t
if
ies
g
r
ad
ien
ts
with
p
o
ten
tially
s
ig
n
if
ican
t
e
r
r
o
r
s
.
T
h
e
f
in
d
i
n
g
s
s
h
o
w
th
at
o
n
-
c
h
ip
tr
ain
in
g
ca
n
class
if
y
im
ag
e
s
in
to
two
an
d
f
o
u
r
class
es
with
ap
p
r
o
x
im
ately
9
0
%
an
d
6
0
%
ac
cu
r
ac
y
,
r
es
p
ec
tiv
ely
.
T
h
e
k
e
y
lim
itatio
n
s
o
f
th
is
ap
p
r
o
ac
h
r
ev
o
lv
e
a
r
o
u
n
d
th
e
s
en
s
itiv
ity
to
n
o
is
e,
p
o
ten
tial
d
r
awb
a
ck
s
o
f
g
r
a
d
ien
t
p
r
u
n
in
g
,
lim
i
ted
s
ca
lab
ilit
y
an
d
g
en
er
aliza
tio
n
,
an
d
th
e
d
e
p
en
d
en
ce
o
n
s
p
ec
if
ic
q
u
a
n
tu
m
h
ar
d
war
e.
C
h
alu
m
u
r
i
et
a
l
.
[
1
6
]
p
r
o
p
o
s
ed
a
q
u
an
t
u
m
m
u
lti
-
class
class
if
ier
(
QM
C
C
)
im
p
lem
en
ted
as
a
p
ar
am
eter
i
ze
d
cir
cu
it,
wh
e
r
e
s
tate
p
r
ep
a
r
atio
n
is
p
er
f
o
r
m
ed
v
ia
a
u
n
itar
y
o
p
er
atio
n
o
n
a
s
in
g
le
q
u
b
it.
T
h
r
ee
b
e
n
ch
m
ar
k
d
atasets
wer
e
u
s
ed
f
o
r
th
eir
q
u
an
tu
m
s
im
u
latio
n
s
:
th
e
W
ir
eless
I
n
d
o
o
r
L
o
ca
lizatio
n
,
B
an
k
n
o
te
Au
th
en
ticatio
n
(
B
NA)
,
an
d
th
e
I
r
is
d
ataset.
T
h
e
QM
C
C
m
o
d
el
id
en
tifie
d
th
e
I
r
is
,
B
NA,
an
d
W
I
L
d
atasets
with
an
ac
cu
r
ac
y
o
f
9
2
.
1
0
%
,
8
9
.
5
0
%
,
a
n
d
9
1
.
7
3
%
,
r
esp
ec
tiv
ely
.
T
h
e
lim
itatio
n
s
ar
e
th
at
t
h
e
m
o
d
el
m
i
g
h
t
b
e
p
r
o
n
e
to
o
v
e
r
f
itti
n
g
o
n
s
m
all
d
atasets
.
Sh
en
et
a
l
.
im
p
r
o
v
e
a
v
ar
iatio
n
al
alg
o
r
ith
m
[
1
7
]
th
at
g
en
er
ally
p
r
e
p
ar
es
th
e
en
co
d
ed
d
ata
to
s
o
lv
e
th
e
d
ata
en
co
d
in
g
p
r
o
b
lem
.
T
h
e
f
ash
io
n
-
MN
I
ST
d
ataset
is
en
co
d
ed
u
s
in
g
th
e
m
o
s
t
r
ec
en
t
tech
n
iq
u
e.
T
h
ey
p
r
o
v
id
e
a
p
r
o
o
f
o
f
co
n
ce
p
t
f
o
r
th
e
n
ea
r
-
ter
m
p
r
ac
ticality
o
f
o
u
r
d
ata
en
co
d
in
g
tech
n
iq
u
e
b
y
d
e
p
lo
y
in
g
b
asic
q
u
a
n
tu
m
v
ar
iati
o
n
al
class
if
ier
s
th
at
ar
e
tr
ain
ed
o
n
th
e
en
c
o
d
ed
d
at
aset
o
n
a
m
o
d
er
n
q
u
a
n
tu
m
co
m
p
u
ter
an
d
ac
h
iev
e
m
o
d
e
r
ate
a
cc
u
r
ac
y
.
T
h
e
m
ain
lim
itatio
n
s
o
f
th
e
ap
p
r
o
ac
h
in
clu
d
e
th
e
r
elian
ce
o
n
s
h
allo
w
cir
cu
its
,
wh
ich
m
ay
n
o
t
s
ca
le
well
to
m
o
r
e
co
m
p
lex
p
r
o
b
lem
s
.
3.
B
ACK
G
RO
UND
I
n
s
u
p
e
r
v
is
ed
lear
n
in
g
,
ea
ch
m
ac
h
in
e
lear
n
in
g
m
o
d
el
is
tr
ain
ed
u
s
in
g
lab
eled
tr
ain
in
g
d
ata.
Af
ter
tr
ain
i
n
g
th
e
alg
o
r
ith
m
g
e
n
er
at
es
a
m
o
d
el
ca
p
ab
le
o
f
p
r
ed
ict
in
g
th
e
lab
els
o
f
n
ew,
u
n
s
ee
n
d
ata.
T
h
e
in
h
er
en
t
u
n
p
r
e
d
ictab
ilit
y
o
f
q
u
an
tu
m
m
ec
h
an
ics
is
lev
er
ag
ed
d
u
r
i
n
g
tr
ain
in
g
to
en
h
an
ce
th
e
m
o
d
el,
as
m
ac
h
in
e
lear
n
in
g
h
ea
v
ily
d
ep
e
n
d
s
o
n
li
n
ea
r
alg
e
b
r
a.
T
h
ey
ca
n
b
e
u
s
ed
to
ad
d
r
ess
v
a
r
io
u
s
task
s
,
s
u
c
h
as
r
ein
f
o
r
ce
m
e
n
t
lear
n
in
g
,
s
u
p
er
v
is
ed
lear
n
i
n
g
,
an
d
u
n
s
u
p
er
v
is
ed
lear
n
in
g
[
1
8
]
.
Qu
a
n
tu
m
c
o
m
p
u
tin
g
co
n
ce
p
ts
h
av
e
en
ab
le
d
co
n
v
en
tio
n
al
r
a
n
d
o
m
ize
d
alg
o
r
ith
m
s
to
p
er
f
o
r
m
e
x
p
o
n
en
t
ially
f
aster
th
an
s
tan
d
ar
d
al
g
o
r
ith
m
s
wh
ich
is
an
o
th
er
tech
n
iq
u
e
f
o
r
c
o
m
p
let
in
g
th
e
QM
L
task
is
v
ar
iatio
n
q
u
an
tu
m
cir
cu
its
[
1
9
]
,
[
2
0
]
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
5
7
8
-
58
7
580
T
h
e
v
a
r
iatio
n
al
q
u
an
tu
m
cir
c
u
it
ca
n
b
e
u
s
ed
as
a
n
ar
tific
i
al
n
eu
r
al
n
etwo
r
k
.
I
t
is
also
k
n
o
wn
as
a
p
ar
am
eter
ized
q
u
an
t
u
m
cir
cu
it
,
with
its
p
ar
am
eter
s
s
er
v
in
g
a
s
th
e
n
eu
r
al
n
etwo
r
k
'
s
weig
h
ts
.
T
h
ese
p
ar
a
m
eter
s
ar
e
u
p
d
ated
o
n
th
e
class
ical
s
y
s
tem
in
ea
ch
ep
o
ch
.
T
h
e
q
u
an
t
u
m
cir
cu
its
ca
n
b
e
em
p
lo
y
ed
t
o
co
m
p
u
te
th
e
co
s
t
f
u
n
ctio
n
,
wh
ich
s
h
o
u
ld
b
e
k
e
p
t
as
s
im
p
le
as
p
o
s
s
ib
le
f
o
r
th
e
m
ac
h
in
e
-
lear
n
in
g
m
o
d
el
to
p
er
f
o
r
m
ef
f
ec
tiv
ely
.
W
e
u
s
e
a
clas
s
ical
co
m
p
u
ter
to
tu
n
e
th
e
p
ar
a
m
eter
s
.
T
h
is
ap
p
r
o
ac
h
m
ak
es
ex
ten
s
iv
e
u
s
e
o
f
p
ar
am
eter
ize
d
,
o
p
tim
ized
q
u
an
tu
m
g
ates.
Usu
ally
,
th
ese
q
u
an
t
u
m
g
ates
in
clu
d
e
s
in
g
le
-
q
u
b
it
r
o
tatio
n
s
g
ates
(
R
ₓ,
R
ᵧ
,
R
)
as
well
as
two
-
q
u
b
it
c
o
n
tr
o
lled
NOT
(
C
NOT
)
g
ates.
T
h
e
o
p
ti
m
ized
cir
cu
it
is
u
s
ed
f
o
r
clas
s
if
icatio
n
.
Fig
u
r
e
1
illu
s
tr
ates
th
e
o
v
er
all
v
iew
o
f
v
ar
iatio
n
al
q
u
an
tu
m
cir
cu
it
s
with
q
u
an
tu
m
an
d
class
ical
p
ar
ts
.
Gen
er
ally
,
v
ar
iatio
n
al
q
u
a
n
tu
m
cir
c
u
it
(
V
QC
)
ca
n
b
e
wr
itten
as:
U(
θ)
ψ
=
∏
n
=1
Uiψ
(
1
)
Her
e
U(
θ)
r
e
p
r
esen
ts
a
p
a
r
a
m
eter
ized
u
n
i
v
er
s
al
g
ate,
n
is
th
e
to
tal
n
u
m
b
er
o
f
g
ates,
a
n
d
ψ
is
th
e
in
p
u
t
q
u
an
tu
m
s
tate.
B
y
ad
ju
s
tin
g
th
e
p
a
r
am
eter
s
θ,
th
e
ac
tio
n
o
f
U
ca
n
b
e
m
o
d
if
ied
.
E
v
er
y
v
ar
iatio
n
al
alg
o
r
ith
m
co
n
s
is
ts
o
f
th
e
f
o
llo
win
g
s
tep
s
.
−
Data
en
co
d
in
g
-
A
cr
u
cial
p
ar
t
o
f
a
VQ
C
is
em
b
ed
d
in
g
class
ical
d
ata
in
to
a
q
u
an
tu
m
s
tat
e
b
ef
o
r
e
it
ca
n
b
e
p
r
o
ce
s
s
ed
b
y
th
e
cir
cu
it.
T
h
is
ca
n
b
e
ac
co
m
p
lis
h
ed
in
s
ev
er
al
way
s
,
with
b
asis
a
n
d
am
p
litu
d
e
en
co
d
in
g
b
ein
g
th
e
m
o
s
t p
o
p
u
lar
m
eth
o
d
s
.
−
An
s
atz
d
esig
n
-
T
h
is
s
tep
in
v
o
lv
es
th
e
d
esig
n
o
f
q
u
an
t
u
m
cir
cu
its
u
s
in
g
q
u
a
n
tu
m
g
at
es
an
d
m
a
k
in
g
q
u
b
its
in
to
s
u
p
er
p
o
s
itio
n
an
d
e
n
tan
g
lem
en
t.
−
Me
asu
r
em
en
t
-
Ap
p
l
y
th
e
m
ea
s
u
r
em
en
t to
co
llap
s
e
th
e
q
u
an
t
u
m
s
tate
in
to
eith
er
0
o
r
1
b
in
a
r
y
s
tate
.
−
Po
s
t
-
p
r
o
ce
s
s
in
g
-
I
t
is
th
e
m
ap
p
in
g
o
f
th
e
b
in
ar
y
o
u
tp
u
t
o
b
tain
ed
f
r
o
m
VQC
with
th
e
lab
els
o
f
th
e
d
ataset
f
o
r
class
if
icatio
n
.
W
e
ch
ec
k
h
er
e
if
th
e
p
r
ed
icted
la
b
els ar
e
co
r
r
ec
t o
r
n
o
t
.
−
Op
tim
izatio
n
-
I
n
th
is
s
tep
,
t
h
e
p
ar
am
eter
o
p
tim
izatio
n
is
d
o
n
e
class
ically
to
r
ed
u
ce
th
e
co
s
t
f
u
n
ctio
n
.
W
e
ca
n
u
s
e
an
y
class
ica
l
o
p
tim
izer
to
o
p
tim
ize
th
e
p
ar
am
eter
,
s
u
ch
as
g
r
ad
ien
t
d
escen
t
,
ADAM
,
o
r
s
to
ch
asti
c
g
r
ad
ien
t
d
escen
t
.
Fig
u
r
e
1
.
Diag
r
a
m
o
f
a
v
ar
iati
o
n
al
q
u
a
n
tu
m
cir
c
u
it with
in
p
u
t q
u
an
t
u
m
s
tates,
p
ar
am
eter
iz
ed
g
ates,
an
d
class
i
ca
l o
p
tim
izatio
n
lo
o
p
4.
M
E
T
H
O
D
S
A
VQC
co
m
b
in
ed
with
class
ical
o
p
tim
izatio
n
is
em
p
lo
y
ed
f
o
r
m
u
lti
-
class
class
if
icati
o
n
.
W
h
er
e
class
ical
d
ata
o
r
f
ea
tu
r
es
will
b
e
en
co
d
ed
to
q
u
a
n
tu
m
s
tates,
th
is
s
tep
is
also
k
n
o
wn
as
f
ea
tu
r
e
m
ap
p
in
g
.
T
h
e
q
u
an
tu
m
a
n
s
atz,
w
h
ich
co
n
s
is
ts
o
f
en
tan
g
lin
g
a
n
d
r
o
tatio
n
al
g
ates,
r
ec
eiv
es
th
ese
p
r
ep
ar
e
d
s
tates
as
an
in
p
u
t.
T
h
is
an
s
atz
is
p
ar
am
eter
ize
d
b
y
a
n
g
les
th
at
ca
n
b
e
ad
ju
s
t
ed
d
u
r
in
g
tr
ain
i
n
g
.
T
h
e
o
u
t
p
u
t
o
f
th
is
cir
c
u
it
is
m
ea
s
u
r
ed
to
y
ield
b
its
tr
in
g
s
th
at
r
ep
r
esen
t
class
if
icat
io
n
r
esu
lts
.
T
h
e
d
ataset
is
d
iv
id
ed
in
to
tr
ain
in
g
an
d
v
alid
atio
n
s
ets
f
o
r
m
o
d
el
tr
ai
n
in
g
.
T
h
e
tr
ain
i
n
g
s
et
co
n
tain
s
lab
eled
d
ata
a
n
d
is
u
s
ed
f
o
r
tr
ain
in
g
,
wh
ile
th
e
v
alid
atio
n
s
et
is
u
s
ed
to
ev
alu
ate
th
e
m
o
d
el’
s
p
er
f
o
r
m
an
ce
.
A
class
ical
o
p
tim
izatio
n
alg
o
r
i
th
m
is
em
p
lo
y
ed
to
m
in
im
ize
a
lo
s
s
f
u
n
ctio
n
,
w
h
ich
co
m
p
ar
es
p
r
ed
icted
o
u
t
p
u
ts
with
ac
tu
al
lab
els.
Du
r
i
n
g
o
p
tim
izatio
n
,
th
e
p
ar
am
eter
s
(
an
g
les)
o
f
th
e
q
u
an
tu
m
cir
cu
it
ar
e
r
ep
ea
ted
l
y
ad
ju
s
ted
to
m
in
im
ize
th
e
co
s
t
f
u
n
ctio
n
.
Af
ter
p
r
o
ce
s
s
in
g
th
r
o
u
g
h
th
e
q
u
an
tu
m
cir
cu
it,
m
ea
s
u
r
em
en
ts
ar
e
tak
en
f
r
o
m
th
e
q
u
b
its
.
T
h
e
r
es
u
ltin
g
b
its
tr
in
g
s
ar
e
in
ter
p
r
eted
as p
r
o
b
a
b
ilit
ies f
o
r
class
m
em
b
er
s
h
ip
f
o
r
class
if
i
ca
tio
n
task
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Mu
lticla
s
s
cla
s
s
ifica
tio
n
u
s
in
g
va
r
ia
tio
n
a
l q
u
a
n
tu
m
circu
it o
n
b
en
c
h
ma
r
k
d
a
ta
s
et
(
Mu
h
a
mma
d
Ha
mid
)
581
4
.
1
.
Da
t
a
p
re
pa
ra
t
i
o
n
L
et
u
s
ex
p
lo
r
e
o
u
r
d
atasets
.
Mo
s
tly
all
d
ata
s
cien
ti
s
ts
ar
e
f
a
m
iliar
with
th
e
I
r
is
d
ata
[
2
1
]
.
T
h
e
d
ata
s
et
co
m
p
r
is
es th
r
ee
cl
ass
es:
Vir
g
in
ica,
Ver
s
ico
lo
r
,
an
d
Seto
s
a,
ea
ch
o
f
wh
ich
h
as 5
0
in
s
tan
ce
s
.
T
h
e
d
ata
h
av
e
1
5
0
in
s
tan
ce
s
.
Fo
u
r
f
ea
tu
r
es
ar
e
p
r
esen
t
in
ea
ch
in
s
tan
ce
:
s
ep
al
len
g
th
,
s
ep
al
b
r
ea
d
th
,
p
eta
l
len
g
th
,
an
d
p
etal
wid
th
.
As
ea
ch
class
h
as
an
eq
u
al
n
u
m
b
er
o
f
in
s
tan
ce
s
,
t
h
e
d
ata
s
et
is
p
r
o
p
er
ly
b
alan
ce
d
.
Nex
t,
is
th
e
wh
ea
t
s
ee
d
s
d
ataset
[
2
2
]
.
T
h
is
d
ataset
co
n
tain
s
th
e
th
r
ee
class
es
o
f
wh
ea
t
s
ee
d
:
Kam
a,
R
o
s
a,
an
d
C
an
ad
ian
.
E
ac
h
class
o
f
7
0
in
s
tan
ce
s
ar
e
th
er
e.
T
h
e
to
tal
n
u
m
b
e
r
o
f
in
s
tan
c
es
in
th
e
d
ataset
i
s
2
1
0
.
T
h
er
e
ar
e
s
ev
en
f
ea
tu
r
es
p
r
esen
t
in
ea
ch
i
n
s
tan
ce
:
ar
ea
,
p
er
im
eter
,
le
n
g
th
o
f
k
e
r
n
el,
wid
th
o
f
k
er
n
el,
co
m
p
a
ctn
ess
,
asy
m
m
etr
y
co
ef
f
icien
t,
a
n
d
len
g
th
o
f
k
e
r
n
e
l
g
r
o
o
v
e.
T
h
is
d
ataset
is
also
b
alan
ce
d
.
B
o
th
d
ata
is
s
p
lit
in
to
a
tr
ain
in
g
an
d
test
s
e
t
o
f
r
atio
s
8
0
:2
0
u
s
in
g
s
ci
-
k
it
lib
r
ar
y
.
Fig
u
r
e
2
an
d
Fig
u
r
e
3
ar
e
v
is
u
aliza
tio
n
s
o
f
d
ata
p
o
in
ts
o
f
th
e
s
elec
ted
d
ata
s
et.
Fig
u
r
es
2
(
a)
-
2
(
b
)
a
r
e
v
is
u
aliza
tio
n
o
f
d
ata
p
o
in
t o
f
I
R
I
S f
lo
wer
d
ataset
an
d
w
h
ea
t
s
ee
d
s
.
(
a)
(
b
)
Fig
u
r
e
2
.
Vis
u
aliza
tio
n
o
f
d
ata
p
o
in
t o
f
I
R
I
S f
lo
wer
d
ataset
(
a)
an
d
w
h
ea
t
s
ee
d
s
(
b
)
4
.
2
.
Da
t
a
enco
din
g
a
nd
s
t
a
t
e
prepa
ra
t
io
n
Qu
an
tu
m
d
ata
e
n
co
d
in
g
is
th
e
p
r
o
ce
s
s
o
f
m
ap
p
in
g
class
ical
d
ata
in
t
o
q
u
an
tu
m
s
tates
s
o
th
at
a
q
u
an
tu
m
co
m
p
u
ter
ca
n
p
r
o
ce
s
s
it.
I
n
VQCs
,
it
is
o
n
e
o
f
th
e
m
o
s
t
im
p
o
r
ta
n
t
an
d
cr
u
cial
s
tep
s
f
o
r
ac
ce
ler
ated
QM
L
alg
o
r
ith
m
s
.
C
o
m
m
o
n
m
eth
o
d
s
o
f
q
u
an
tu
m
d
ata
e
n
co
d
i
n
g
ar
e
as f
o
llo
ws:
1
)
B
asis
E
n
co
d
in
g
:
B
asis
en
co
d
in
g
is
th
e
m
o
s
t
s
tr
aig
h
tf
o
r
war
d
ap
p
r
o
ac
h
f
o
r
r
ep
r
esen
ti
n
g
d
ata
in
q
u
a
n
tu
m
cir
cu
its
f
o
r
ar
ith
m
etic
task
s
.
T
h
is
m
eth
o
d
en
co
d
es
th
e
b
in
ar
y
r
ep
r
esen
tatio
n
o
f
class
ica
l
d
ata
d
ir
ec
tly
in
to
q
u
an
tu
m
b
asis
s
tates.
T
y
p
ically
,
n
q
u
b
its
ar
e
r
e
q
u
ir
e
d
to
r
ep
r
esen
t
n
class
ical
d
ata
p
o
in
ts
.
T
h
e
class
ical
d
ata
p
o
in
t x
=
(
x
1
,
x
2
,
.
.
.
.
x
n
)
will b
e
en
co
d
ed
as
ψx
=
⊗
n
i x
i
(
2
)
2
)
Am
p
litu
d
e
E
n
c
o
d
in
g
: T
h
e
am
p
litu
d
e
en
co
d
in
g
r
e
p
r
esen
ts
in
p
u
t d
ata
o
f
x
=
(
x
1
,
x
2
,
.
.
.
.
x
n
)
T
o
f
d
im
en
s
io
n
N
=
2
N
as a
m
p
litu
d
es o
f
an
n
-
q
u
b
it q
u
an
tu
m
s
tate
ϕ
(
x
)
as
U
ϕ
(
x
)
: x
∈
R
N
→
ϕ
(
x
)
=
1
/
N
*
Σ
N
i=1
x
i
I
(
3
)
wh
er
e
i is th
e
ith
co
m
p
u
tatio
n
al
b
asis
s
tate.
3
)
An
g
le
E
n
co
d
i
n
g
:
T
h
e
an
g
le
en
co
d
in
g
m
eth
o
d
r
ep
r
esen
ts
c
lass
ical
d
ata
as
th
e
r
o
tatio
n
an
g
les
(
in
r
ad
ian
s
)
o
f
q
u
b
it
g
ates.
T
o
en
co
d
e
n
d
ata
p
o
in
ts
,
we
n
ee
d
n
q
u
b
its
an
d
n
r
o
tatio
n
g
ates
o
f
R
x
,
R
y
, R
z
ac
tin
g
o
n
q
u
b
its
.
if
x
=
(
x
1
, x
2
,
.
.
.
.
x
n
)
th
en
s
tates will
b
e
p
r
e
p
ar
ed
as
:
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
5
7
8
-
58
7
582
ψ
x
=
⊗
n
i R
(x
i
)x
i
(
4
)
T
h
e
wo
r
s
t
-
ca
s
e
tim
e
co
m
p
le
x
ity
o
f
q
u
a
n
tu
m
en
co
d
in
g
is
ex
p
o
n
en
tial.
L
aRo
s
e
et
a
l
.
h
av
e
p
r
esen
ted
d
if
f
er
en
t
r
o
b
u
s
t
q
u
an
t
u
m
en
co
d
in
g
m
eth
o
d
s
s
u
ch
as
d
en
s
e
an
g
le
en
co
d
in
g
,
g
en
e
r
al
q
u
b
it
en
co
d
i
n
g
,
wav
ef
u
n
ctio
n
e
n
co
d
in
g
,
an
d
am
p
litu
d
e
en
co
d
i
n
g
an
d
th
eir
r
esu
lts
o
n
d
if
f
er
en
t
ch
an
n
els
[
2
3
]
.
An
g
le
co
d
in
g
an
d
d
en
s
e
an
g
le
c
o
d
in
g
ca
n
b
e
u
s
ed
t
o
d
ec
r
ea
s
e
a
q
u
a
n
tu
m
cir
cu
it’s
d
ep
t
h
.
No
wa
d
ay
s
,
th
e
r
e
ar
e
o
n
ly
a
ce
r
tain
n
u
m
b
er
o
f
q
u
b
its
in
n
o
is
y
in
ter
m
ed
iate
-
s
ca
le
q
u
an
tu
m
(
NI
S
Q
)
d
ev
ices.
W
e
s
h
o
u
ld
s
elec
t a
n
en
co
d
i
n
g
th
at
ca
n
cr
ea
te
a
b
alan
ce
b
etwe
en
a
n
u
m
b
er
o
f
q
u
b
its
an
d
cir
cu
it
d
ep
th
.
I
n
o
u
r
ca
s
e
f
o
r
d
ata
e
n
co
d
i
n
g
an
d
s
tate
p
r
ep
a
r
atio
n
we
h
av
e
u
s
ed
th
e
s
tan
d
a
r
d
Z
Z
Featu
r
e
Ma
p
f
r
o
m
th
e
Qis
k
it
lib
r
ar
y
.
T
h
e
f
ir
s
t
s
tep
is
to
n
o
r
m
alize
th
e
in
p
u
t
f
e
atu
r
es
b
etwe
en
0
an
d
1
.
E
ac
h
n
o
r
m
alize
d
f
ea
t
u
r
e
is
m
ap
p
ed
to
a
r
o
tatio
n
al
an
g
l
e
o
n
th
e
B
lo
ch
s
p
h
er
e
u
s
in
g
th
e
An
g
leE
m
b
ed
d
in
g
tech
n
iq
u
e.
On
ce
th
e
r
o
tatio
n
g
ates
en
co
d
e
th
e
d
ata,
en
tan
g
lin
g
g
ates
estab
lis
h
co
r
r
elatio
n
s
b
etwe
en
q
u
b
its
,
allo
win
g
th
e
m
o
d
el
to
lear
n
co
m
p
lex
d
e
p
en
d
e
n
cies.
T
o
en
co
d
e
4
f
ea
tu
r
es,
we
h
av
e
u
s
ed
4
q
u
b
its
.
Hen
ce
4
r
o
tatio
n
s
g
a
tes
will
b
e
r
eq
u
ir
ed
an
d
th
e
r
o
tatio
n
an
g
le
will
b
e
in
th
e
r
an
g
e
b
etwe
en
[
0
,
2
π]
.
Af
ter
th
e
r
o
tatio
n
s
,
en
tan
g
lem
en
t
is
ap
p
lied
b
etwe
en
p
air
s
o
f
q
u
b
its
u
s
in
g
C
Z
g
ates.
T
wo
r
ep
etitio
n
s
wer
e
em
p
lo
y
e
d
to
s
tr
ik
e
a
b
ala
n
ce
b
etwe
en
m
o
d
el
ac
cu
r
ac
y
an
d
co
m
p
u
tatio
n
al
co
s
t,
y
ield
in
g
a
cir
c
u
it
d
e
p
th
o
f
2
0
th
at
p
r
o
v
i
d
es
ef
f
ec
tiv
e
class
if
icatio
n
p
er
f
o
r
m
an
ce
wh
ile
k
ee
p
in
g
c
o
m
p
lex
ity
m
in
im
u
m
.
Fig
u
r
e
3
.
Deta
iled
q
u
an
tu
m
cir
cu
it illu
s
tr
atin
g
in
p
u
t state
p
r
ep
ar
atio
n
u
s
in
g
Z
Z
Featu
r
eM
a
p
,
in
clu
d
i
n
g
q
u
b
it
r
o
tatio
n
s
an
d
e
n
tan
g
lem
e
n
t
4
.
3
.
Circ
uit
des
ig
n a
nd
t
ra
ini
ng
Af
ter
th
e
s
tate
p
r
ep
ar
atio
n
,
we
will
d
esig
n
an
an
s
atz
f
o
r
class
if
icatio
n
.
T
h
e
an
s
atz
p
r
o
v
id
es
th
e
p
ar
am
eter
ized
s
tr
u
ct
u
r
e
n
ee
d
e
d
to
p
e
r
f
o
r
m
o
p
tim
izatio
n
v
ia
class
ical
o
p
tim
izer
s
.
T
h
ese
g
ates
in
th
e
an
s
atz
ar
e
p
ar
am
eter
ized
,
a
n
d
th
e
p
ar
am
eter
s
o
f
th
ese
g
ate
s
ar
e
wh
at
n
ee
d
to
b
e
o
p
tim
ized
d
u
r
in
g
tr
ain
in
g
to
m
i
n
im
ize
class
if
icatio
n
er
r
o
r
.
C
h
o
o
s
in
g
th
e
r
ig
h
t a
n
s
atz
is
cr
u
cial
f
o
r
t
h
e
p
er
f
o
r
m
an
ce
o
f
q
u
an
tu
m
m
o
d
els.
T
h
e
lay
er
s
in
class
ical
n
eu
r
al
n
etwo
r
k
s
ar
e
d
ir
ec
tly
s
im
ilar
to
th
is
an
s
atz.
E
ac
h
g
ate
in
th
is
cir
c
u
it
wo
r
k
s
as
a
n
o
d
e
in
t
h
e
n
eu
r
al
n
etwo
r
k
.
I
t
h
as
a
s
et
o
f
ad
ju
s
tab
le
weig
h
ts
.
T
h
e
g
a
p
b
etwe
en
th
e
p
r
e
d
ictio
n
s
an
d
th
e
k
n
o
wn
la
b
eled
d
ata
is
d
escr
ib
ed
b
y
th
e
co
s
t
f
u
n
ctio
n
.
T
o
m
in
im
ize
a
co
s
t
f
u
n
ctio
n
,
we
n
ee
d
t
o
o
p
tim
i
ze
th
e
weig
h
ts
.
I
n
Fig
u
r
e
4
o
u
r
cir
c
u
it
is
p
lo
tted
.
T
h
is
cir
cu
it
h
as
1
6
tr
ain
ab
le
p
ar
am
eter
s
,
n
u
m
b
er
ed
f
r
o
m
0
to
1
5
,
wh
ich
s
er
v
e
as
th
e
weig
h
ts
f
o
r
th
e
class
if
ier
.
T
h
is
ci
r
cu
it
will
ac
t
as
th
e
f
ee
d
-
f
o
r
war
d
lay
e
r
o
f
t
h
e
n
eu
r
al
n
etwo
r
k
.
T
h
e
tr
ain
in
g
i
n
clu
d
es
lear
n
in
g
th
e
tr
ain
ab
le
p
ar
am
eter
s
.
I
n
o
u
r
ca
s
e,
lear
n
ab
le
p
ar
am
eter
s
ar
e
r
o
tatio
n
s
,
an
g
les,
en
tan
g
lem
en
t
o
p
er
atio
n
s
,
etc.
o
f
th
e
q
u
an
tu
m
cir
cu
it.
Me
a
s
u
r
em
en
ts
f
r
o
m
th
e
q
u
an
t
u
m
cir
cu
it
ar
e
u
s
ed
to
co
m
p
u
te
t
h
e
lo
s
s
,
an
d
th
e
o
p
tim
izer
iter
ativ
ely
u
p
d
ates
th
e
p
ar
am
eter
s
to
r
ed
u
ce
th
e
d
i
s
cr
ep
an
c
y
b
etwe
en
p
r
ed
icted
an
d
ac
t
u
al
lab
els.
I
n
th
is
tr
ain
in
g
p
r
o
ce
s
s
co
n
s
tr
ain
ed
o
p
tim
izatio
n
b
y
lin
ea
r
ap
p
r
o
x
im
atio
n
(
C
OB
YL
A
)
o
p
tim
izer
is
u
s
ed
f
o
r
o
p
tim
izin
g
th
e
p
ar
a
m
eter
s
.
C
OB
YL
A
is
d
es
ig
n
ed
f
o
r
o
p
t
im
izin
g
n
o
n
-
lin
ea
r
,
non
-
d
if
f
er
e
n
tiab
le
f
u
n
ctio
n
s
.
I
t
is
a
g
r
ad
ie
n
t
-
f
r
ee
,
d
er
iv
ativ
e
-
f
r
ee
o
p
tim
izer
.
I
ts
s
im
p
licity
an
d
g
r
ad
ie
n
t
-
f
r
e
e
n
atu
r
e
m
ak
e
it
a
s
tr
o
n
g
co
n
t
en
d
er
f
o
r
q
u
an
t
u
m
o
p
tim
izati
o
n
task
s
,
esp
ec
ially
th
o
s
e
in
v
o
lv
in
g
v
a
r
iatio
n
al
m
eth
o
d
s
.
T
h
e
tr
ain
i
n
g
tim
e
will
in
cr
ea
s
e
if
we
s
elec
t
a
g
r
a
d
i
en
t
-
b
ased
o
p
tim
i
ze
r
.
H
o
wev
er
,
f
o
r
s
m
o
o
t
h
,
well
-
b
eh
av
ed
p
r
o
b
lem
s
,
o
r
p
r
o
b
lem
s
th
at
ca
n
ef
f
icien
tly
p
r
o
v
id
e
g
r
ad
ien
ts
,
o
th
er
o
p
tim
izer
s
lik
e
L
-
B
FGS
-
B
,
SP
S
A
o
r
ADAM
m
ig
h
t
o
f
f
e
r
f
aster
co
n
v
e
r
g
en
ce
an
d
b
etter
p
er
f
o
r
m
an
ce
[
2
4
]
.
T
h
e
s
to
ch
asti
c
o
p
tim
izer
s
u
c
h
as
s
im
u
ltan
eo
u
s
p
er
tu
r
b
atio
n
s
to
c
h
asti
c
ap
p
r
o
x
im
atio
n
(
SP
SA)
ca
n
also
b
e
u
s
ed
f
o
r
o
p
tim
izatio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Mu
lticla
s
s
cla
s
s
ifica
tio
n
u
s
in
g
va
r
ia
tio
n
a
l q
u
a
n
tu
m
circu
it o
n
b
en
c
h
ma
r
k
d
a
ta
s
et
(
Mu
h
a
mma
d
Ha
mid
)
583
No
w
we
h
a
v
e
o
u
r
f
ea
tu
r
es,
an
s
atz,
a
n
d
o
p
tim
izer
r
ea
d
y
,
we
ca
n
tr
ain
o
u
r
class
if
ier
.
T
h
e
h
y
p
er
p
ar
am
eter
s
th
at
we
h
a
v
e
tu
n
ed
to
ac
h
iev
e
o
p
tim
al
p
er
f
o
r
m
an
ce
f
o
r
tr
ain
in
g
a
v
ar
iatio
n
al
q
u
an
t
u
m
cir
cu
it.
4
q
u
b
its
ar
e
u
s
ed
to
e
n
co
d
e
4
f
ea
tu
r
es.
T
o
m
a
k
e
th
e
m
o
d
el
co
n
v
er
g
e
f
aster
we
h
av
e
u
s
ed
C
OB
YL
A
o
p
tim
izer
with
lear
n
in
g
r
ate
0
.
0
0
1
.
T
r
ain
i
n
g
is
p
er
f
o
r
m
ed
with
a
b
atch
s
ize
o
f
1
6
o
v
er
2
5
0
ep
o
c
h
s
.
W
e
ca
n
tr
ain
VQC
u
s
in
g
eith
er
a
s
im
u
lato
r
o
r
a
r
ea
l
q
u
a
n
tu
m
co
m
p
u
ter
.
Her
e
we
will
b
e
u
s
in
g
a
q
u
an
t
u
m
s
im
u
lato
r
as
p
r
esen
t
r
ea
l
q
u
an
tu
m
h
ar
d
war
e
is
n
o
is
y
.
Nea
r
th
e
en
d
o
f
th
e
2
5
0
iter
atio
n
s
o
f
tr
ain
in
g
,
th
e
co
s
t
f
u
n
ctio
n
is
n
o
t
co
n
v
er
g
in
g
,
we
ca
n
s
ee
in
Fig
u
r
e
5
,
in
d
icatin
g
th
at
th
e
m
o
d
el’
s
p
er
f
o
r
m
an
ce
will
n
o
t
ch
an
g
e
ev
en
af
te
r
in
cr
ea
s
in
g
th
e
n
u
m
b
er
o
f
iter
at
io
n
s
.
Fig
u
r
e
4
.
Par
am
etr
ize
d
q
u
a
n
tu
m
cir
cu
it u
s
ed
f
o
r
class
if
icatio
n
o
f
d
ataset
Fig
u
r
e
5
.
R
ep
r
esen
tatio
n
o
f
l
o
s
s
d
ec
ay
d
u
r
in
g
tr
ain
in
g
af
ter
ev
er
y
iter
atio
n
o
f
ir
is
d
ataset
Nex
t,
we
will
u
s
e
th
e
ab
o
v
e
f
ea
tu
r
e
m
ap
an
d
an
s
atz
f
o
r
th
e
wh
ea
t
s
ee
d
s
d
ata
s
et.
W
h
er
e
t
h
e
p
r
im
ar
y
task
is
to
class
if
y
th
e
class
o
f
s
ee
d
f
r
o
m
th
r
ee
class
es:
k
am
a,
R
o
s
a,
ca
n
ad
ian
.
T
h
e
r
e
ar
e
s
ev
en
f
ea
tu
r
es
in
ea
c
h
in
s
tan
ce
.
W
e
will
r
ed
u
ce
th
e
d
im
en
s
io
n
s
to
4
f
ea
t
u
r
es
u
s
in
g
p
r
in
cip
al
co
m
p
o
n
e
n
t
an
aly
s
is
(
PC
A)
[
2
5
]
wh
ile
p
r
eser
v
in
g
th
e
m
o
s
t
im
p
o
r
tan
t
v
ar
ian
ce
in
t
h
e
d
ata.
T
h
is
is
a
f
o
r
m
o
f
p
r
e
p
r
o
ce
s
s
in
g
th
at
h
elp
s
th
e
q
u
a
n
tu
m
m
o
d
el
wo
r
k
with
f
ewe
r
,
b
u
t
m
o
r
e
i
n
f
o
r
m
ativ
e,
d
im
en
s
io
n
s
.
Af
ter
p
er
f
o
r
m
in
g
PC
A,
th
e
d
ata
is
n
o
r
m
alize
d
to
th
e
r
an
g
e
[
-
π,
π]
,
wh
ich
is
n
e
ce
s
s
ar
y
f
o
r
r
ep
r
esen
tin
g
class
ical
v
alu
es
as
q
u
an
tu
m
g
ate
r
o
tatio
n
an
g
les.
An
8
0
:2
0
s
p
lit
is
u
s
ed
to
allo
ca
te
th
e
d
ataset
f
o
r
tr
ain
i
n
g
an
d
v
alid
atio
n
p
u
r
p
o
s
es.
Featu
r
es
ar
e
en
co
d
ed
u
s
in
g
Z
Z
Featu
r
eM
ap
,
wh
e
r
ea
s
th
e
o
u
tp
u
t
is
th
e
s
tr
in
g
o
f
p
r
e
d
icted
lab
els
b
ased
o
n
th
e
test
d
ata.
Fro
m
Fig
u
r
e
6
W
e
ca
n
s
ee
th
at
th
e
m
o
d
el
is
at
m
in
im
u
m
lo
s
s
in
1
0
0
ep
o
ch
s.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
7
7
6
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
,
Vo
l.
1
5
,
No
.
2
,
J
u
n
e
20
2
6
:
5
7
8
-
58
7
584
Fig
u
r
e
6
.
R
ep
r
esen
tatio
n
o
f
lo
s
s
d
ec
ay
d
u
r
in
g
tr
ain
in
g
af
ter
ev
er
y
iter
atio
n
o
f
s
ee
d
s
d
atase
t
5.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
Af
ter
tr
ain
in
g
c
o
m
p
letio
n
,
we
ac
h
iev
ed
a
h
ig
h
s
co
r
e
o
n
th
e
t
r
ain
s
et
an
d
test
s
et.
T
h
e
la
b
els
f
r
o
m
th
e
I
R
I
S
d
ataset
o
f
u
n
s
ee
n
d
ata
c
an
b
e
p
r
ed
icted
u
s
in
g
th
is
m
o
d
el.
I
n
th
is
s
itu
atio
n
,
wh
ile
d
e
s
ig
n
in
g
th
e
cir
c
u
it,
we
h
av
e
m
o
d
if
ie
d
th
e
r
ep
s
p
a
r
am
eter
,
wh
ic
h
d
ictates
h
o
w
m
an
y
tim
es
we
ad
d
a
q
u
an
tu
m
g
ate
t
o
th
e
cir
cu
it,
wh
ich
is
s
im
i
lar
to
ad
d
in
g
a
h
id
d
en
lay
er
in
th
e
class
ical
n
e
u
r
al
n
etwo
r
k
.
A
g
r
ea
ter
n
u
m
b
er
o
f
q
u
an
tu
m
g
ates
r
esu
lts
in
m
o
r
e
p
a
r
am
eter
s
a
n
d
m
o
r
e
en
tan
g
lem
en
t
o
p
er
at
io
n
s
.
T
h
e
m
o
d
el
is
th
er
ef
o
r
e
m
o
r
e
f
le
x
ib
le,
b
u
t
b
ec
o
m
es
m
o
r
e
co
m
p
lex
with
a
lar
g
er
n
u
m
b
er
o
f
p
ar
am
eter
s
an
d
it
ty
p
ically
tak
es
lo
n
g
er
t
im
e
to
tr
ain
.
E
v
e
n
a
m
in
o
r
ch
an
g
e
to
th
e
an
s
atz
m
ig
h
t
p
r
o
d
u
ce
im
p
r
o
v
e
d
o
u
tco
m
es;
th
is
in
d
icate
s
th
a
t
th
e
s
elec
tio
n
o
f
h
y
p
er
p
ar
am
eter
s
is
ju
s
t
as
im
p
o
r
tan
t
in
QM
L
as
it
i
s
in
cl
ass
ical
m
ac
h
in
e
lear
n
in
g
,
an
d
it
co
u
ld
tak
e
s
o
m
e
tim
e
to
f
in
d
th
e
b
est
v
alu
es.
As
I
r
is
d
ata
h
as
o
n
ly
f
o
u
r
f
ea
tu
r
es,
we
will
b
e
r
e
q
u
ir
e
d
to
u
s
e
o
n
ly
4
q
u
b
its
to
p
r
o
ce
s
s
all
th
e
d
ata,
alth
o
u
g
h
th
is
m
ig
h
t
n
o
t
alwa
y
s
b
e
th
e
ca
s
e.
I
f
a
d
ata
s
et
co
n
tain
s
m
o
r
e
f
ea
tu
r
es
th
an
a
m
o
d
er
n
q
u
an
tu
m
co
m
p
u
ter
ca
n
ac
co
m
m
o
d
ate,
th
en
we
r
ed
u
ce
th
e
n
u
m
b
e
r
o
f
f
ea
tu
r
es,
r
es
u
ltin
g
in
d
ec
r
ea
s
ed
p
er
f
o
r
m
an
ce
f
o
r
all
m
o
d
els.
W
e
h
av
e
ac
h
iev
ed
an
ac
c
u
r
ac
y
o
f
9
9
%
with
class
ical
s
u
p
p
o
r
t
v
ec
to
r
m
ac
h
i
n
e
(
SVM)
o
n
t
h
e
tr
ain
in
g
d
ata
an
d
9
7
%
on
th
e
v
alid
atio
n
d
ata
o
f
th
e
I
r
is
d
ata
s
et,
r
esp
ec
tiv
ely
,
wh
er
ea
s
we
ca
n
ac
h
iev
e
a
test
ac
cu
r
ac
y
o
f
8
9
%
an
d
tr
ai
n
in
g
ac
c
u
r
ac
y
o
f
9
0
%
u
s
in
g
VQC.
As
we
ca
n
s
ee
,
th
e
class
ical
s
u
p
p
o
r
t
v
ec
to
r
m
ac
h
in
e
p
r
o
d
u
ce
d
th
e
b
est
r
esu
l
ts
.
Desp
ite
u
s
in
g
o
n
ly
f
o
u
r
f
ea
tu
r
es,
th
e
tr
ain
ed
q
u
a
n
tu
m
m
o
d
el
d
em
o
n
s
tr
ates
g
o
o
d
ac
cu
r
ac
y
o
n
th
e
I
R
I
S
d
ataset.
Un
s
u
r
p
r
is
in
g
ly
,
class
ica
l
m
o
d
els
o
u
tp
er
f
o
r
m
th
eir
q
u
an
tu
m
v
er
s
io
n
s
;
n
o
n
eth
eless
,
class
ical
ML
h
as
ad
v
an
ce
d
s
ig
n
if
ican
tly
,
wh
e
r
e
as
q
u
an
tu
m
ML
h
as
y
et
to
ac
h
iev
e
th
at
d
eg
r
ee
o
f
m
atu
r
ity
.
T
h
r
ee
-
class
s
ee
d
s
cla
s
s
if
icatio
n
is
d
o
n
e
with
th
e
wh
ea
t
s
ee
d
s
d
ataset
with
th
e
s
am
e
cir
cu
its
.
Her
e
we
h
av
e
tr
ain
ed
o
u
r
v
ar
iatio
n
al
q
u
an
tu
m
cir
cu
it
with
a
lear
n
in
g
r
ate
o
f
0
.
0
1
,
b
atch
s
ize
1
6
,
an
d
C
OB
YL
A
o
p
tim
izer
wi
th
0
.
4
2
5
f
o
r
1
0
0
ep
o
ch
s
.
W
e
h
av
e
ac
h
iev
e
d
n
e
ar
ly
9
2
%
ac
c
u
r
ac
y
o
n
th
is
d
at
aset
with
o
n
ly
f
o
u
r
f
ea
tu
r
es.
I
n
T
a
b
le
1
we
h
av
e
li
s
ted
th
e
ac
cu
r
ac
ies o
n
d
if
f
er
e
n
t d
ataset.
T
h
is
s
tu
d
y
also
s
u
p
p
o
r
ts
v
ar
io
u
s
wo
r
k
f
o
r
m
u
lticlas
s
cla
s
s
i
f
icatio
n
u
s
in
g
q
u
an
t
u
m
n
eu
r
al
n
etwo
r
k
s
[
2
6
]
–
[
2
8
]
.
T
o
d
ay
,
m
an
y
q
u
an
tu
m
h
ar
d
wa
r
e
an
d
lib
r
ar
ies
a
r
e
av
ailab
le
f
o
r
d
esig
n
in
g
q
u
an
tu
m
cir
cu
its
an
d
v
er
if
y
in
g
r
esu
lts
o
n
r
ea
l
h
a
r
d
war
e
an
d
s
im
u
lato
r
s
.
Q
u
an
tu
m
co
m
p
u
tin
g
to
o
ls
i
n
clu
d
e
s
o
f
twar
e
d
ev
el
o
p
m
en
t
k
its
(
SDKs
)
lik
e
Qis
k
it,
C
ir
q
,
an
d
Pen
n
y
L
an
e,
as
well
as
clo
u
d
-
b
ased
p
latf
o
r
m
s
s
u
c
h
as
Am
az
o
n
B
r
ac
k
et
a
n
d
Go
o
g
le
Qu
an
t
u
m
E
n
g
in
e.
T
h
ese
to
o
ls
h
elp
d
e
v
elo
p
e
r
s
in
ter
f
ac
e
with
r
ea
l
q
u
a
n
tu
m
h
ar
d
war
e
[
2
9
]
,
[
30]
.
I
n
th
is
p
ap
er
,
we
h
av
e
u
s
ed
a
n
I
B
M
‘
s
tatev
ec
to
r
’
q
u
an
tu
m
s
im
u
lato
r
an
d
h
ar
d
war
e
f
o
r
ev
alu
atin
g
o
u
r
r
esu
lts
an
d
r
u
n
n
in
g
o
u
r
cir
cu
its
.
T
ab
le
1
.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
th
e
an
s
atz
o
n
d
if
f
er
e
n
t d
ataset
D
a
t
a
s
e
t
N
u
mb
e
r
o
f
c
l
a
sse
s
N
u
mb
e
r
o
f
f
e
a
t
u
r
e
s
Tr
a
n
i
n
g
A
c
c
u
r
a
c
y
Te
st
i
n
g
A
c
c
u
r
a
c
y
I
R
I
S
3
4
9
0
.
2
%
8
9
.
7
%
S
e
e
d
s
3
4
9
2
.
4
%
9
1
.
9
%
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J I
n
f
&
C
o
m
m
u
n
T
ec
h
n
o
l
I
SS
N:
2252
-
8
7
7
6
Mu
lticla
s
s
cla
s
s
ifica
tio
n
u
s
in
g
va
r
ia
tio
n
a
l q
u
a
n
tu
m
circu
it o
n
b
en
c
h
ma
r
k
d
a
ta
s
et
(
Mu
h
a
mma
d
Ha
mid
)
585
6.
CO
NCLU
SI
O
N
Ma
n
y
co
m
p
le
x
p
r
o
b
lem
s
th
at
ar
e
ch
allen
g
in
g
f
o
r
class
ical
co
m
p
u
ter
s
to
r
eso
lv
e
co
u
ld
b
e
r
eso
lv
ed
b
y
q
u
an
tu
m
co
m
p
u
ter
s
.
A
k
ey
a
d
v
an
tag
e
o
f
q
u
an
tu
m
co
m
p
u
ti
n
g
is
its
ab
ilit
y
to
p
er
f
o
r
m
q
u
an
tu
m
p
ar
allelis
m
.
Fo
r
ex
am
p
le,
with
n
d
im
en
s
io
n
s
,
a
q
u
an
tu
m
co
m
p
u
ter
ca
n
cr
ea
te
a
s
u
p
er
p
o
s
itio
n
o
f
all
2
n
p
o
s
s
ib
le
s
tates
s
im
u
ltan
eo
u
s
ly
,
wh
ile
a
clas
s
ical
co
m
p
u
ter
wo
u
ld
h
av
e
to
ex
am
in
e
ea
ch
s
tate
o
n
e
b
y
o
n
e.
I
n
h
ig
h
-
d
im
en
s
io
n
al
d
ata,
tr
ain
in
g
d
ee
p
n
eu
r
al
n
etwo
r
k
s
o
r
o
t
h
er
co
m
p
lex
m
o
d
els
in
v
o
lv
es
m
in
im
izin
g
lo
s
s
f
u
n
ctio
n
s
ov
er
m
a
n
y
p
ar
am
eter
s
.
Qu
a
n
t
u
m
o
p
tim
izatio
n
co
u
ld
s
p
ee
d
u
p
th
e
c
o
n
v
e
r
g
en
ce
o
f
th
ese
m
o
d
els
b
y
ex
p
lo
r
in
g
th
e
p
ar
am
eter
s
p
ac
e
m
o
r
e
ef
f
i
cien
tly
.
Qu
an
tu
m
f
ea
t
u
r
e
m
ap
s
ca
n
m
ap
h
ig
h
-
d
im
en
s
io
n
al
d
ata
in
to
a
q
u
an
tu
m
s
tate
th
at
m
ay
r
eq
u
ir
e
f
ewe
r
q
u
b
its
to
r
ep
r
esen
t,
a
ll
o
win
g
q
u
an
t
u
m
alg
o
r
ith
m
s
to
p
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