<s>
Quantum	B-Device
machine	I-Device
learning	I-Device
is	O
the	O
integration	O
of	O
quantum	B-Device
algorithms	I-Device
within	O
machine	O
learning	O
programs	O
.	O
</s>
<s>
The	O
most	O
common	O
use	O
of	O
the	O
term	O
refers	O
to	O
machine	O
learning	O
algorithms	O
for	O
the	O
analysis	O
of	O
classical	O
data	O
executed	O
on	O
a	O
quantum	B-Architecture
computer	I-Architecture
,	O
i.e.	O
</s>
<s>
While	O
machine	O
learning	O
algorithms	O
are	O
used	O
to	O
compute	O
immense	O
quantities	O
of	O
data	O
,	O
quantum	B-Device
machine	I-Device
learning	I-Device
utilizes	O
qubits	O
and	O
quantum	O
operations	O
or	O
specialized	O
quantum	O
systems	O
to	O
improve	O
computational	O
speed	O
and	O
data	O
storage	O
done	O
by	O
algorithms	O
in	O
a	O
program	O
.	O
</s>
<s>
These	O
routines	O
can	O
be	O
more	O
complex	O
in	O
nature	O
and	O
executed	O
faster	O
on	O
a	O
quantum	B-Architecture
computer	I-Architecture
.	O
</s>
<s>
Furthermore	O
,	O
quantum	B-Device
algorithms	I-Device
can	O
be	O
used	O
to	O
analyze	O
quantum	O
states	O
instead	O
of	O
classical	O
data	O
.	O
</s>
<s>
Beyond	O
quantum	B-Architecture
computing	I-Architecture
,	O
the	O
term	O
"	O
quantum	B-Device
machine	I-Device
learning	I-Device
"	O
is	O
also	O
associated	O
with	O
classical	O
machine	O
learning	O
methods	O
applied	O
to	O
data	O
generated	O
from	O
quantum	O
experiments	O
(	O
i.e.	O
</s>
<s>
machine	B-Device
learning	I-Device
of	I-Device
quantum	I-Device
systems	I-Device
)	O
,	O
such	O
as	O
learning	O
the	O
phase	O
transitions	O
of	O
a	O
quantum	O
system	O
or	O
creating	O
new	O
quantum	O
experiments	O
.	O
</s>
<s>
Quantum	B-Device
machine	I-Device
learning	I-Device
also	O
extends	O
to	O
a	O
branch	O
of	O
research	O
that	O
explores	O
methodological	O
and	O
structural	O
similarities	O
between	O
certain	O
physical	O
systems	O
and	O
learning	O
systems	O
,	O
in	O
particular	O
neural	O
networks	O
.	O
</s>
<s>
For	O
example	O
,	O
some	O
mathematical	O
and	O
numerical	O
techniques	O
from	O
quantum	O
physics	O
are	O
applicable	O
to	O
classical	O
deep	B-Algorithm
learning	I-Algorithm
and	O
vice	O
versa	O
.	O
</s>
<s>
Quantum-enhanced	O
machine	O
learning	O
refers	O
to	O
quantum	B-Device
algorithms	I-Device
that	O
solve	O
tasks	O
in	O
machine	O
learning	O
,	O
thereby	O
improving	O
and	O
often	O
expediting	O
classical	O
machine	O
learning	O
techniques	O
.	O
</s>
<s>
Such	O
algorithms	O
typically	O
require	O
one	O
to	O
encode	O
the	O
given	O
classical	O
data	O
set	O
into	O
a	O
quantum	B-Architecture
computer	I-Architecture
to	O
make	O
it	O
accessible	O
for	O
quantum	O
information	O
processing	O
.	O
</s>
<s>
Subsequently	O
,	O
quantum	O
information	O
processing	O
routines	O
are	O
applied	O
and	O
the	O
result	O
of	O
the	O
quantum	B-Architecture
computation	I-Architecture
is	O
read	O
out	O
by	O
measuring	O
the	O
quantum	O
system	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
outcome	O
of	O
the	O
measurement	O
of	O
a	O
qubit	O
reveals	O
the	O
result	O
of	O
a	O
binary	B-General_Concept
classification	I-General_Concept
task	O
.	O
</s>
<s>
While	O
many	O
proposals	O
of	O
quantum	B-Device
machine	I-Device
learning	I-Device
algorithms	O
are	O
still	O
purely	O
theoretical	O
and	O
require	O
a	O
full-scale	O
universal	O
quantum	B-Architecture
computer	I-Architecture
to	O
be	O
tested	O
,	O
others	O
have	O
been	O
implemented	O
on	O
small-scale	O
or	O
special	O
purpose	O
quantum	O
devices	O
.	O
</s>
<s>
A	O
number	O
of	O
quantum	B-Device
algorithms	I-Device
for	O
machine	O
learning	O
are	O
based	O
on	O
the	O
idea	O
of	O
amplitude	O
encoding	O
,	O
that	O
is	O
,	O
to	O
associate	O
the	O
amplitudes	O
of	O
a	O
quantum	O
state	O
with	O
the	O
inputs	O
and	O
outputs	O
of	O
computations	O
.	O
</s>
<s>
The	O
goal	O
of	O
algorithms	O
based	O
on	O
amplitude	O
encoding	O
is	O
to	O
formulate	O
quantum	B-Device
algorithms	I-Device
whose	O
resources	O
grow	O
polynomially	O
in	O
the	O
number	O
of	O
qubits	O
,	O
which	O
amounts	O
to	O
a	O
logarithmic	O
time	O
complexity	O
in	O
the	O
number	O
of	O
amplitudes	O
and	O
thereby	O
the	O
dimension	O
of	O
the	O
input	O
.	O
</s>
<s>
Many	O
quantum	B-Device
machine	I-Device
learning	I-Device
algorithms	O
in	O
this	O
category	O
are	O
based	O
on	O
variations	O
of	O
the	O
quantum	B-Algorithm
algorithm	I-Algorithm
for	I-Algorithm
linear	I-Algorithm
systems	I-Algorithm
of	I-Algorithm
equations	I-Algorithm
(	O
colloquially	O
called	O
HHL	O
,	O
after	O
the	O
paper	O
's	O
authors	O
)	O
which	O
,	O
under	O
specific	O
conditions	O
,	O
performs	O
a	O
matrix	O
inversion	O
using	O
an	O
amount	O
of	O
physical	O
resources	O
growing	O
only	O
logarithmically	O
in	O
the	O
dimensions	O
of	O
the	O
matrix	O
.	O
</s>
<s>
Quantum	O
matrix	O
inversion	O
can	O
be	O
applied	O
to	O
machine	O
learning	O
methods	O
in	O
which	O
the	O
training	O
reduces	O
to	O
solving	O
a	O
linear	O
system	O
of	O
equations	O
,	O
for	O
example	O
in	O
least-squares	O
linear	O
regression	O
,	O
the	O
least-squares	O
version	O
of	O
support	B-Algorithm
vector	I-Algorithm
machines	I-Algorithm
,	O
and	O
Gaussian	O
processes	O
.	O
</s>
<s>
VQAs	O
are	O
one	O
of	O
the	O
most	O
studied	O
quantum	B-Device
algorithms	I-Device
as	O
researchers	O
expect	O
that	O
all	O
the	O
needed	O
applications	O
for	O
the	O
quantum	B-Architecture
computer	I-Architecture
will	O
be	O
using	O
the	O
VQAs	O
and	O
also	O
VQAs	O
seem	O
to	O
fulfill	O
the	O
expectation	O
for	O
gaining	O
quantum	O
supremacy	O
.	O
</s>
<s>
VQAs	O
is	O
a	O
mixed	O
quantum-classical	O
approach	O
where	O
the	O
quantum	B-Architecture
processor	I-Architecture
prepares	O
quantum	O
states	O
and	O
measurement	O
is	O
made	O
and	O
the	O
optimization	O
is	O
done	O
by	O
a	O
classical	O
computer	O
.	O
</s>
<s>
Variational	O
Quantum	O
Circuits	O
also	O
known	O
as	O
Parametrized	O
Quantum	O
Circuits	O
(	O
PQCs	O
)	O
are	O
based	O
on	O
Variational	O
Quantum	B-Device
Algorithms	I-Device
(	O
VQAs	O
)	O
.	O
</s>
<s>
Researchers	O
are	O
extensively	O
studying	O
VQCs	O
,	O
as	O
it	O
uses	O
the	O
power	O
of	O
quantum	B-Architecture
computation	I-Architecture
to	O
learn	O
in	O
a	O
short	O
time	O
and	O
also	O
use	O
fewer	O
parameters	O
than	O
its	O
classical	O
counterparts	O
.	O
</s>
<s>
Pattern	O
reorganization	O
is	O
one	O
of	O
the	O
important	O
task	O
of	O
machine	O
learning	O
,	O
binary	B-General_Concept
classification	I-General_Concept
is	O
one	O
of	O
the	O
tool	O
or	O
algorithms	O
to	O
find	O
pattern	O
.	O
</s>
<s>
Binary	B-General_Concept
classification	I-General_Concept
is	O
used	O
in	O
supervised	B-General_Concept
learning	I-General_Concept
and	O
in	O
unsupervised	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
In	O
quantum	B-Device
machine	I-Device
learning	I-Device
,	O
classical	O
bits	O
are	O
converted	O
in	O
qubits	O
and	O
they	O
are	O
map	O
to	O
Hilbert	O
space	O
,	O
complex	O
value	O
data	O
are	O
used	O
in	O
quantum	O
binary	B-General_Concept
classifier	I-General_Concept
to	O
used	O
the	O
advantage	O
of	O
Hilbert	O
space	O
.	O
</s>
<s>
By	O
exploiting	O
,	O
the	O
quantum	O
mechanic	O
properties	O
such	O
as	O
superposition	O
,	O
entanglement	O
,	O
interference	O
the	O
quantum	O
binary	B-General_Concept
classifier	I-General_Concept
produces	O
the	O
accurate	O
result	O
in	O
short	O
period	O
of	O
time	O
.	O
</s>
<s>
Another	O
approach	O
to	O
improving	O
classical	O
machine	O
learning	O
with	O
quantum	O
information	O
processing	O
uses	O
amplitude	B-Algorithm
amplification	I-Algorithm
methods	O
based	O
on	O
Grover	B-Algorithm
's	I-Algorithm
search	I-Algorithm
algorithm	O
,	O
which	O
has	O
been	O
shown	O
to	O
solve	O
unstructured	O
search	O
problems	O
with	O
a	O
quadratic	O
speedup	O
compared	O
to	O
classical	O
algorithms	O
.	O
</s>
<s>
These	O
quantum	O
routines	O
can	O
be	O
employed	O
for	O
learning	O
algorithms	O
that	O
translate	O
into	O
an	O
unstructured	O
search	O
task	O
,	O
as	O
can	O
be	O
done	O
,	O
for	O
instance	O
,	O
in	O
the	O
case	O
of	O
the	O
k-medians	B-Algorithm
and	O
the	O
k-nearest	B-General_Concept
neighbors	I-General_Concept
algorithms	I-General_Concept
.	O
</s>
<s>
Another	O
application	O
is	O
a	O
quadratic	O
speedup	O
in	O
the	O
training	O
of	O
perceptron	B-Algorithm
.	O
</s>
<s>
An	O
example	O
of	O
amplitude	B-Algorithm
amplification	I-Algorithm
being	O
used	O
in	O
a	O
machine	O
learning	O
algorithm	O
is	O
Grover	B-Algorithm
's	I-Algorithm
search	I-Algorithm
algorithm	O
minimization	O
.	O
</s>
<s>
In	O
which	O
a	O
subroutine	O
uses	O
Grover	B-Algorithm
's	I-Algorithm
search	I-Algorithm
algorithm	O
to	O
find	O
an	O
element	O
less	O
than	O
some	O
previously	O
defined	O
element	O
.	O
</s>
<s>
Grover	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
can	O
then	O
find	O
an	O
element	O
such	O
that	O
our	O
condition	O
is	O
met	O
.	O
</s>
<s>
This	O
minimization	O
is	O
notably	O
used	O
in	O
quantum	O
k-medians	B-Algorithm
,	O
and	O
it	O
has	O
a	O
speed	O
up	O
of	O
at	O
least	O
compared	O
to	O
classical	O
versions	O
of	O
k-medians	B-Algorithm
,	O
where	O
is	O
the	O
number	O
of	O
data	O
points	O
and	O
is	O
the	O
number	O
of	O
clusters	O
.	O
</s>
<s>
Amplitude	B-Algorithm
amplification	I-Algorithm
is	O
often	O
combined	O
with	O
quantum	B-Algorithm
walks	I-Algorithm
to	O
achieve	O
the	O
same	O
quadratic	O
speedup	O
.	O
</s>
<s>
Quantum	B-Algorithm
walks	I-Algorithm
have	O
been	O
proposed	O
to	O
enhance	O
Google	O
's	O
PageRank	O
algorithm	O
as	O
well	O
as	O
the	O
performance	O
of	O
reinforcement	O
learning	O
agents	O
in	O
the	O
projective	O
simulation	O
framework	O
.	O
</s>
<s>
Reinforcement	O
learning	O
is	O
a	O
branch	O
of	O
machine	O
learning	O
distinct	O
from	O
supervised	O
and	O
unsupervised	B-General_Concept
learning	I-General_Concept
,	O
which	O
also	O
admits	O
quantum	O
enhancements	O
.	O
</s>
<s>
Quantum	B-Algorithm
annealing	I-Algorithm
is	O
an	O
optimization	O
technique	O
used	O
to	O
determine	O
the	O
local	O
minima	O
and	O
maxima	O
of	O
a	O
function	O
over	O
a	O
given	O
set	O
of	O
candidate	O
functions	O
.	O
</s>
<s>
The	O
process	O
can	O
be	O
distinguished	O
from	O
Simulated	B-Algorithm
annealing	I-Algorithm
by	O
the	O
Quantum	O
tunneling	O
process	O
,	O
by	O
which	O
particles	O
tunnel	O
through	O
kinetic	O
or	O
potential	O
barriers	O
from	O
a	O
high	O
state	O
to	O
a	O
low	O
state	O
.	O
</s>
<s>
Quantum	B-Algorithm
annealing	I-Algorithm
starts	O
from	O
a	O
superposition	O
of	O
all	O
possible	O
states	O
of	O
a	O
system	O
,	O
weighted	O
equally	O
.	O
</s>
<s>
The	O
noise	O
tolerance	O
will	O
be	O
improved	O
by	O
using	O
the	O
quantum	O
perceptron	B-Algorithm
and	O
the	O
quantum	B-Algorithm
algorithm	I-Algorithm
on	O
the	O
currently	O
accessible	O
quantum	O
hardware	O
.	O
</s>
<s>
Typically	O
,	O
a	O
neuron	O
has	O
two	O
operations	O
:	O
the	O
inner	O
product	O
and	O
an	O
activation	B-Algorithm
function	I-Algorithm
.	O
</s>
<s>
As	O
opposed	O
to	O
the	O
activation	B-Algorithm
function	I-Algorithm
,	O
which	O
is	O
typically	O
nonlinear	O
,	O
the	O
inner	O
product	O
is	O
a	O
linear	O
process	O
.	O
</s>
<s>
With	O
quantum	B-Architecture
computing	I-Architecture
,	O
linear	O
processes	O
may	O
be	O
easily	O
accomplished	O
additionally	O
,	O
due	O
to	O
the	O
simplicity	O
of	O
implementation	O
,	O
the	O
threshold	O
function	O
is	O
preferred	O
by	O
the	O
majority	O
of	O
quantum	O
neurons	O
for	O
activation	B-Algorithm
functions	I-Algorithm
.	O
</s>
<s>
Pattern	O
reorganization	O
is	O
one	O
of	O
the	O
important	O
task	O
of	O
machine	O
learning	O
,	O
binary	B-General_Concept
classification	I-General_Concept
is	O
one	O
of	O
the	O
tool	O
or	O
algorithms	O
to	O
find	O
pattern	O
.	O
</s>
<s>
Binary	B-General_Concept
classification	I-General_Concept
is	O
used	O
in	O
supervised	B-General_Concept
learning	I-General_Concept
and	O
in	O
unsupervised	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
In	O
quantum	B-Device
machine	I-Device
learning	I-Device
,	O
classical	O
bits	O
are	O
converted	O
in	O
qubits	O
and	O
they	O
are	O
map	O
to	O
Hilbert	O
space	O
,	O
complex	O
value	O
data	O
are	O
used	O
in	O
quantum	O
binary	B-General_Concept
classifier	I-General_Concept
to	O
used	O
the	O
advantage	O
of	O
Hilbert	O
space	O
.	O
</s>
<s>
By	O
exploiting	O
,	O
the	O
quantum	O
mechanic	O
properties	O
such	O
as	O
superposition	O
,	O
entanglement	O
,	O
interference	O
the	O
quantum	O
binary	B-General_Concept
classifier	I-General_Concept
produces	O
the	O
accurate	O
result	O
in	O
short	O
period	O
of	O
time	O
.	O
</s>
<s>
Sampling	B-Algorithm
from	O
high-dimensional	O
probability	O
distributions	O
is	O
at	O
the	O
core	O
of	O
a	O
wide	O
spectrum	O
of	O
computational	O
techniques	O
with	O
important	O
applications	O
across	O
science	O
,	O
engineering	O
,	O
and	O
society	O
.	O
</s>
<s>
Examples	O
include	O
deep	B-Algorithm
learning	I-Algorithm
,	O
probabilistic	O
programming	O
,	O
and	O
other	O
machine	O
learning	O
and	O
artificial	O
intelligence	O
applications	O
.	O
</s>
<s>
Sampling	B-Algorithm
from	O
generic	O
probabilistic	O
models	O
is	O
hard	O
:	O
algorithms	O
relying	O
heavily	O
on	O
sampling	B-Algorithm
are	O
expected	O
to	O
remain	O
intractable	O
no	O
matter	O
how	O
large	O
and	O
powerful	O
classical	O
computing	O
resources	O
become	O
.	O
</s>
<s>
Even	O
though	O
quantum	B-Algorithm
annealers	I-Algorithm
,	O
like	O
those	O
produced	O
by	O
D-Wave	O
Systems	O
,	O
were	O
designed	O
for	O
challenging	O
combinatorial	O
optimization	O
problems	O
,	O
it	O
has	O
been	O
recently	O
recognized	O
as	O
a	O
potential	O
candidate	O
to	O
speed	O
up	O
computations	O
that	O
rely	O
on	O
sampling	B-Algorithm
by	O
exploiting	O
quantum	O
effects	O
.	O
</s>
<s>
Some	O
research	O
groups	O
have	O
recently	O
explored	O
the	O
use	O
of	O
quantum	B-Algorithm
annealing	I-Algorithm
hardware	O
for	O
training	O
Boltzmann	B-Algorithm
machines	I-Algorithm
and	O
deep	O
neural	O
networks	O
.	O
</s>
<s>
The	O
standard	O
approach	O
to	O
training	O
Boltzmann	B-Algorithm
machines	I-Algorithm
relies	O
on	O
the	O
computation	O
of	O
certain	O
averages	O
that	O
can	O
be	O
estimated	O
by	O
standard	O
sampling	B-Algorithm
techniques	O
,	O
such	O
as	O
Markov	B-General_Concept
chain	I-General_Concept
Monte	I-General_Concept
Carlo	I-General_Concept
algorithms	O
.	O
</s>
<s>
Another	O
possibility	O
is	O
to	O
rely	O
on	O
a	O
physical	O
process	O
,	O
like	O
quantum	B-Algorithm
annealing	I-Algorithm
,	O
that	O
naturally	O
generates	O
samples	O
from	O
a	O
Boltzmann	O
distribution	O
.	O
</s>
<s>
The	O
D-Wave	O
2X	O
system	O
hosted	O
at	O
NASA	O
Ames	O
Research	O
Center	O
has	O
been	O
recently	O
used	O
for	O
the	O
learning	O
of	O
a	O
special	O
class	O
of	O
restricted	O
Boltzmann	B-Algorithm
machines	I-Algorithm
that	O
can	O
serve	O
as	O
a	O
building	O
block	O
for	O
deep	B-Algorithm
learning	I-Algorithm
architectures	O
.	O
</s>
<s>
Complementary	O
work	O
that	O
appeared	O
roughly	O
simultaneously	O
showed	O
that	O
quantum	B-Algorithm
annealing	I-Algorithm
can	O
be	O
used	O
for	O
supervised	B-General_Concept
learning	I-General_Concept
in	O
classification	O
tasks	O
.	O
</s>
<s>
The	O
same	O
device	O
was	O
later	O
used	O
to	O
train	O
a	O
fully	O
connected	O
Boltzmann	B-Algorithm
machine	I-Algorithm
to	O
generate	O
,	O
reconstruct	O
,	O
and	O
classify	O
down-scaled	O
,	O
low-resolution	O
handwritten	O
digits	O
,	O
among	O
other	O
synthetic	O
datasets	O
.	O
</s>
<s>
In	O
both	O
cases	O
,	O
the	O
models	O
trained	O
by	O
quantum	B-Algorithm
annealing	I-Algorithm
had	O
a	O
similar	O
or	O
better	O
performance	O
in	O
terms	O
of	O
quality	O
.	O
</s>
<s>
The	O
ultimate	O
question	O
that	O
drives	O
this	O
endeavour	O
is	O
whether	O
there	O
is	O
quantum	O
speedup	O
in	O
sampling	B-Algorithm
applications	O
.	O
</s>
<s>
Experience	O
with	O
the	O
use	O
of	O
quantum	B-Algorithm
annealers	I-Algorithm
for	O
combinatorial	O
optimization	O
suggests	O
the	O
answer	O
is	O
not	O
straightforward	O
.	O
</s>
<s>
Reverse	O
annealing	O
has	O
been	O
used	O
as	O
well	O
to	O
solve	O
a	O
fully	O
connected	O
quantum	O
restricted	O
Boltzmann	B-Algorithm
machine	I-Algorithm
.	O
</s>
<s>
Inspired	O
by	O
the	O
success	O
of	O
Boltzmann	B-Algorithm
machines	I-Algorithm
based	O
on	O
classical	O
Boltzmann	O
distribution	O
,	O
a	O
new	O
machine	O
learning	O
approach	O
based	O
on	O
quantum	O
Boltzmann	O
distribution	O
of	O
a	O
transverse-field	O
Ising	O
Hamiltonian	O
was	O
recently	O
proposed	O
.	O
</s>
<s>
Due	O
to	O
the	O
non-commutative	O
nature	O
of	O
quantum	O
mechanics	O
,	O
the	O
training	O
process	O
of	O
the	O
quantum	O
Boltzmann	B-Algorithm
machine	I-Algorithm
can	O
become	O
nontrivial	O
.	O
</s>
<s>
This	O
problem	O
was	O
,	O
to	O
some	O
extent	O
,	O
circumvented	O
by	O
introducing	O
bounds	O
on	O
the	O
quantum	O
probabilities	O
,	O
allowing	O
the	O
authors	O
to	O
train	O
the	O
model	O
efficiently	O
by	O
sampling	B-Algorithm
.	O
</s>
<s>
It	O
is	O
possible	O
that	O
a	O
specific	O
type	O
of	O
quantum	O
Boltzmann	B-Algorithm
machine	I-Algorithm
has	O
been	O
trained	O
in	O
the	O
D-Wave	O
2X	O
by	O
using	O
a	O
learning	O
rule	O
analogous	O
to	O
that	O
of	O
classical	O
Boltzmann	B-Algorithm
machines	I-Algorithm
.	O
</s>
<s>
Quantum	B-Algorithm
annealing	I-Algorithm
is	O
not	O
the	O
only	O
technology	O
for	O
sampling	B-Algorithm
.	O
</s>
<s>
In	O
a	O
prepare-and-measure	O
scenario	O
,	O
a	O
universal	O
quantum	B-Architecture
computer	I-Architecture
prepares	O
a	O
thermal	O
state	O
,	O
which	O
is	O
then	O
sampled	O
by	O
measurements	O
.	O
</s>
<s>
This	O
can	O
reduce	O
the	O
time	O
required	O
to	O
train	O
a	O
deep	O
restricted	O
Boltzmann	B-Algorithm
machine	I-Algorithm
,	O
and	O
provide	O
a	O
richer	O
and	O
more	O
comprehensive	O
framework	O
for	O
deep	B-Algorithm
learning	I-Algorithm
than	O
classical	O
computing	O
.	O
</s>
<s>
The	O
same	O
quantum	O
methods	O
also	O
permit	O
efficient	O
training	O
of	O
full	O
Boltzmann	B-Algorithm
machines	I-Algorithm
and	O
multi-layer	O
,	O
fully	O
connected	O
models	O
and	O
do	O
not	O
have	O
well-known	O
classical	O
counterparts	O
.	O
</s>
<s>
This	O
provides	O
an	O
exponential	O
reduction	O
in	O
computational	O
complexity	O
in	O
probabilistic	O
inference	O
,	O
and	O
,	O
while	O
the	O
protocol	O
relies	O
on	O
a	O
universal	O
quantum	B-Architecture
computer	I-Architecture
,	O
under	O
mild	O
assumptions	O
it	O
can	O
be	O
embedded	O
on	O
contemporary	O
quantum	B-Algorithm
annealing	I-Algorithm
hardware	O
.	O
</s>
<s>
Quantum	O
analogues	O
or	O
generalizations	O
of	O
classical	O
neural	O
nets	O
are	O
often	O
referred	O
to	O
as	O
quantum	B-Device
neural	I-Device
networks	I-Device
.	O
</s>
<s>
Quantum	B-Device
neural	I-Device
networks	I-Device
are	O
often	O
defined	O
as	O
an	O
expansion	O
on	O
Deutsch	O
's	O
model	O
of	O
a	O
quantum	O
computational	O
network	O
.	O
</s>
<s>
Quantum	B-Device
neural	I-Device
networks	I-Device
apply	O
the	O
principals	O
quantum	O
information	O
and	O
quantum	B-Architecture
computation	I-Architecture
to	O
classical	O
neurocomputing	O
.	O
</s>
<s>
A	O
quantum	B-Device
neural	I-Device
network	I-Device
has	O
computational	O
capabilities	O
to	O
decrease	O
the	O
number	O
of	O
steps	O
,	O
qubits	O
used	O
,	O
and	O
computation	O
time	O
.	O
</s>
<s>
Quantum	B-Device
neural	I-Device
networks	I-Device
take	O
advantage	O
of	O
the	O
hierarchical	O
structures	O
,	O
and	O
for	O
each	O
subsequent	O
layer	O
,	O
the	O
number	O
of	O
qubits	O
from	O
the	O
preceding	O
layer	O
is	O
decreased	O
by	O
a	O
factor	O
of	O
two	O
.	O
</s>
<s>
Such	O
process	O
can	O
be	O
accomplished	O
applying	O
full	B-Algorithm
Tomography	I-Algorithm
on	O
the	O
state	O
to	O
reduce	O
it	O
all	O
the	O
way	O
down	O
to	O
one	O
qubit	O
and	O
then	O
processed	O
it	O
in	O
subway	O
.	O
</s>
<s>
Similar	O
to	O
conventional	B-Algorithm
feed-forward	I-Algorithm
neural	O
networks	O
,	O
the	O
last	O
module	O
is	O
a	O
fully	O
connected	O
layer	O
with	O
full	O
connections	O
to	O
all	O
activations	O
in	O
the	O
preceding	O
layer	O
.	O
</s>
<s>
Dissipative	O
QNNs	O
(	O
DQNNs	O
)	O
are	O
constructed	O
from	O
layers	O
of	O
qubits	O
coupled	O
by	O
perceptron	B-Algorithm
called	O
building	O
blocks	O
,	O
which	O
have	O
an	O
arbitrary	O
unitary	O
design	O
.	O
</s>
<s>
Each	O
node	O
in	O
the	O
network	O
layer	O
of	O
a	O
DQNN	O
is	O
given	O
a	O
distinct	O
collection	O
of	O
qubits	O
,	O
and	O
each	O
qubit	O
is	O
also	O
given	O
a	O
unique	O
quantum	O
perceptron	B-Algorithm
unitary	O
to	O
characterize	O
it	O
.	O
</s>
<s>
When	O
performing	O
a	O
broad	O
supervised	B-General_Concept
learning	I-General_Concept
task	O
,	O
DQNN	O
are	O
used	O
to	O
learn	O
a	O
unitary	O
matrix	O
connecting	O
the	O
input	O
and	O
output	O
quantum	O
states	O
.	O
</s>
<s>
Inspired	O
by	O
the	O
extremely	O
successful	O
classical	O
Generative	O
adversarial	O
network(GAN )	O
,	O
dissipative	O
quantum	O
generative	B-Algorithm
adversarial	I-Algorithm
network	I-Algorithm
(	O
DQGAN	O
)	O
is	O
introduced	O
for	O
unsupervised	B-General_Concept
learning	I-General_Concept
of	O
the	O
unlabeled	O
training	O
data	O
.	O
</s>
<s>
Hidden	O
quantum	O
Markov	O
models	O
(	O
HQMMs	O
)	O
are	O
a	O
quantum-enhanced	O
version	O
of	O
classical	O
Hidden	O
Markov	O
Models	O
(	O
HMMs	O
)	O
,	O
which	O
are	O
typically	O
used	O
to	O
model	O
sequential	O
data	O
in	O
various	O
fields	O
like	O
robotics	O
and	O
natural	B-Language
language	I-Language
processing	I-Language
.	O
</s>
<s>
In	O
the	O
most	O
general	O
case	O
of	O
quantum	B-Device
machine	I-Device
learning	I-Device
,	O
both	O
the	O
learning	O
device	O
and	O
the	O
system	O
under	O
study	O
,	O
as	O
well	O
as	O
their	O
interaction	O
,	O
are	O
fully	O
quantum	O
.	O
</s>
<s>
Going	O
beyond	O
the	O
specific	O
problem	O
of	O
learning	O
states	O
and	O
transformations	O
,	O
the	O
task	O
of	O
clustering	B-Algorithm
also	O
admits	O
a	O
fully	O
quantum	O
version	O
,	O
wherein	O
both	O
the	O
oracle	O
which	O
returns	O
the	O
distance	O
between	O
data-points	O
and	O
the	O
information	O
processing	O
device	O
which	O
runs	O
the	O
algorithm	O
are	O
quantum	O
.	O
</s>
<s>
The	O
need	O
for	O
models	O
that	O
can	O
be	O
understood	O
by	O
humans	O
emerges	O
in	O
quantum	B-Device
machine	I-Device
learning	I-Device
in	O
analogy	O
to	O
classical	O
machine	O
learning	O
and	O
drives	O
the	O
research	O
field	O
of	O
explainable	O
quantum	B-Device
machine	I-Device
learning	I-Device
(	O
or	O
XQML	O
in	O
analogy	O
to	O
XAI/XML	O
)	O
.	O
</s>
<s>
The	O
term	O
"	O
quantum	B-Device
machine	I-Device
learning	I-Device
"	O
sometimes	O
refers	O
to	O
classical	O
machine	O
learning	O
performed	O
on	O
data	O
from	O
quantum	O
systems	O
.	O
</s>
<s>
A	O
basic	O
example	O
of	O
this	O
is	O
quantum	B-Algorithm
state	I-Algorithm
tomography	I-Algorithm
,	O
where	O
a	O
quantum	O
state	O
is	O
learned	O
from	O
measurement	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
concept	O
class	O
could	O
be	O
the	O
set	O
of	O
disjunctive	B-Application
normal	I-Application
form	I-Application
(	O
DNF	O
)	O
formulas	O
on	O
n	O
bits	O
or	O
the	O
set	O
of	O
Boolean	O
circuits	O
of	O
some	O
constant	O
depth	O
.	O
</s>
<s>
This	O
passive	O
learning	O
type	O
is	O
also	O
the	O
most	O
common	O
scheme	O
in	O
supervised	B-General_Concept
learning	I-General_Concept
:	O
a	O
learning	O
algorithm	O
typically	O
takes	O
the	O
training	O
examples	O
fixed	O
,	O
without	O
the	O
ability	O
to	O
query	O
the	O
label	O
of	O
unlabelled	O
examples	O
.	O
</s>
<s>
The	O
earliest	O
experiments	O
were	O
conducted	O
using	O
the	O
adiabatic	O
D-Wave	O
quantum	B-Architecture
computer	I-Architecture
,	O
for	O
instance	O
,	O
to	O
detect	O
cars	O
in	O
digital	O
images	O
using	O
regularized	O
boosting	O
with	O
a	O
nonconvex	O
objective	O
function	O
in	O
a	O
demonstration	O
in	O
2009	O
.	O
</s>
<s>
Many	O
experiments	O
followed	O
on	O
the	O
same	O
architecture	O
,	O
and	O
leading	O
tech	O
companies	O
have	O
shown	O
interest	O
in	O
the	O
potential	O
of	O
quantum	B-Device
machine	I-Device
learning	I-Device
for	O
future	O
technological	O
implementations	O
.	O
</s>
<s>
In	O
2013	O
,	O
Google	O
Research	O
,	O
NASA	O
,	O
and	O
the	O
Universities	O
Space	O
Research	O
Association	O
launched	O
the	O
Quantum	B-Application
Artificial	I-Application
Intelligence	I-Application
Lab	I-Application
which	O
explores	O
the	O
use	O
of	O
the	O
adiabatic	O
D-Wave	O
quantum	B-Architecture
computer	I-Architecture
.	O
</s>
<s>
Using	O
a	O
different	O
annealing	O
technology	O
based	O
on	O
nuclear	O
magnetic	O
resonance	O
(	O
NMR	O
)	O
,	O
a	O
quantum	O
Hopfield	B-Algorithm
network	I-Algorithm
was	O
implemented	O
in	O
2009	O
that	O
mapped	O
the	O
input	O
data	O
and	O
memorized	O
data	O
to	O
Hamiltonians	O
,	O
allowing	O
the	O
use	O
of	O
adiabatic	O
quantum	B-Architecture
computation	I-Architecture
.	O
</s>
<s>
NMR	O
technology	O
also	O
enables	O
universal	O
quantum	B-Architecture
computing	I-Architecture
,	O
and	O
it	O
was	O
used	O
for	O
the	O
first	O
experimental	O
implementation	O
of	O
a	O
quantum	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
to	O
distinguish	O
hand	O
written	O
number	O
‘	O
6’	O
and	O
‘	O
9’	O
on	O
a	O
liquid-state	O
quantum	B-Architecture
computer	I-Architecture
in	O
2015	O
.	O
</s>
<s>
Once	O
the	O
vectors	O
are	O
defined	O
on	O
the	O
feature	O
space	O
,	O
the	O
quantum	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
was	O
implemented	O
to	O
classify	O
the	O
unknown	O
input	O
vector	O
.	O
</s>
<s>
The	O
readout	O
avoids	O
costly	O
quantum	B-Algorithm
tomography	I-Algorithm
by	O
reading	O
out	O
the	O
final	O
state	O
in	O
terms	O
of	O
direction	O
(	O
up/down	O
)	O
of	O
the	O
NMR	O
signal	O
.	O
</s>
<s>
Using	O
non-linear	O
photonics	O
to	O
implement	O
an	O
all-optical	O
linear	O
classifier	O
,	O
a	O
perceptron	B-Algorithm
model	O
was	O
capable	O
of	O
learning	O
the	O
classification	O
boundary	O
iteratively	O
from	O
training	O
data	O
through	O
a	O
feedback	O
rule	O
.	O
</s>
<s>
A	O
core	O
building	O
block	O
in	O
many	O
learning	O
algorithms	O
is	O
to	O
calculate	O
the	O
distance	O
between	O
two	O
vectors	O
:	O
this	O
was	O
first	O
experimentally	O
demonstrated	O
for	O
up	O
to	O
eight	O
dimensions	O
using	O
entangled	O
qubits	O
in	O
a	O
photonic	O
quantum	B-Architecture
computer	I-Architecture
in	O
2015	O
.	O
</s>
<s>
Recently	O
,	O
based	O
on	O
a	O
neuromimetic	O
approach	O
,	O
a	O
novel	O
ingredient	O
has	O
been	O
added	O
to	O
the	O
field	O
of	O
quantum	B-Device
machine	I-Device
learning	I-Device
,	O
in	O
the	O
form	O
of	O
a	O
so-called	O
quantum	O
memristor	O
,	O
a	O
quantized	O
model	O
of	O
the	O
standard	O
classical	O
memristor	O
.	O
</s>
<s>
A	O
quantum	O
memristor	O
would	O
implement	O
nonlinear	O
interactions	O
in	O
the	O
quantum	O
dynamics	O
which	O
would	O
aid	O
the	O
search	O
for	O
a	O
fully	O
functional	O
quantum	B-Device
neural	I-Device
network	I-Device
.	O
</s>
<s>
Since	O
2016	O
,	O
IBM	O
has	O
launched	O
an	O
online	O
cloud-based	O
platform	O
for	O
quantum	O
software	O
developers	O
,	O
called	O
the	O
IBM	B-Device
Q	I-Device
Experience	I-Device
.	O
</s>
<s>
This	O
platform	O
consists	O
of	O
several	O
fully	O
operational	O
quantum	B-Architecture
processors	I-Architecture
accessible	O
via	O
the	O
IBM	O
Web	O
API	O
.	O
</s>
<s>
New	O
architectures	O
are	O
being	O
explored	O
on	O
an	O
experimental	O
basis	O
,	O
up	O
to	O
32	O
qubits	O
,	O
utilizing	O
both	O
trapped-ion	O
and	O
superconductive	O
quantum	B-Architecture
computing	I-Architecture
methods	O
.	O
</s>
<s>
The	O
work	O
also	O
demonstrated	O
that	O
the	O
generation	O
of	O
fair	O
random	O
numbers	O
with	O
a	O
gate	O
quantum	B-Architecture
computer	I-Architecture
is	O
a	O
non-trivial	O
task	O
on	O
NISQ	O
devices	O
,	O
and	O
QRNGs	O
are	O
therefore	O
typically	O
much	O
more	O
difficult	O
to	O
utilize	O
in	O
practice	O
than	O
PRNGs	O
.	O
</s>
<s>
While	O
machine	O
learning	O
itself	O
is	O
now	O
not	O
only	O
a	O
research	O
field	O
but	O
an	O
economically	O
significant	O
and	O
fast	O
growing	O
industry	O
and	O
quantum	B-Architecture
computing	I-Architecture
is	O
a	O
well	O
established	O
field	O
of	O
both	O
theoretical	O
and	O
experimental	O
research	O
,	O
quantum	B-Device
machine	I-Device
learning	I-Device
remains	O
a	O
purely	O
theoretical	O
field	O
of	O
studies	O
.	O
</s>
<s>
Attempts	O
to	O
experimentally	O
demonstrate	O
concepts	O
of	O
quantum	B-Device
machine	I-Device
learning	I-Device
remain	O
insufficient	O
.	O
</s>
<s>
Many	O
of	O
the	O
leading	O
scientists	O
that	O
extensively	O
publish	O
in	O
the	O
field	O
of	O
quantum	B-Device
machine	I-Device
learning	I-Device
warn	O
about	O
the	O
extensive	O
hype	O
around	O
the	O
topic	O
and	O
are	O
very	O
restrained	O
if	O
asked	O
about	O
its	O
practical	O
uses	O
in	O
the	O
foreseeable	O
future	O
.	O
</s>
<s>
This	O
is	O
an	O
extremely	O
new	O
scientific	O
field	O
,	O
"	O
-	O
physicist	O
Maria	O
Schuld	O
of	O
Canada-based	O
quantum	B-Architecture
computing	I-Architecture
startup	O
Xanadu	O
.	O
</s>
<s>
“	O
When	O
mixing	O
machine	O
learning	O
with	O
‘	O
quantum	O
,	O
’	O
you	O
catalyse	O
a	O
hype-condensate.	O
”	O
-	O
Jacob	O
Biamonte	O
a	O
contributor	O
to	O
the	O
theory	O
of	O
quantum	B-Architecture
computation	I-Architecture
.	O
</s>
<s>
"	O
There	O
is	O
a	O
lot	O
more	O
work	O
that	O
needs	O
to	O
be	O
done	O
before	O
claiming	O
quantum	B-Device
machine	I-Device
learning	I-Device
will	O
actually	O
work	O
,	O
"	O
-	O
computer	O
scientist	O
Iordanis	O
Kerenidis	O
,	O
the	O
head	O
of	O
quantum	B-Device
algorithms	I-Device
at	O
the	O
Silicon	O
Valley-based	O
quantum	B-Architecture
computing	I-Architecture
startup	O
QC	O
Ware	O
.	O
</s>
<s>
"	O
I	O
have	O
not	O
seen	O
a	O
single	O
piece	O
of	O
evidence	O
that	O
there	O
exists	O
a	O
meaningful	O
[	O
machine	O
learning ]	O
task	O
for	O
which	O
it	O
would	O
make	O
sense	O
to	O
use	O
a	O
quantum	B-Architecture
computer	I-Architecture
and	O
not	O
a	O
classical	O
computer	O
,	O
"	O
-	O
physicist	O
Ryan	O
Sweke	O
of	O
the	O
Free	O
University	O
of	O
Berlin	O
in	O
Germany	O
.	O
</s>
<s>
“	O
Do	O
n't	O
fall	O
for	O
the	O
hype	O
!	O
”	O
-	O
Frank	O
Zickert	O
,	O
who	O
is	O
the	O
author	O
of	O
probably	O
the	O
most	O
practical	O
book	O
related	O
to	O
the	O
subject	O
beware	O
that	O
”	O
quantum	B-Architecture
computers	I-Architecture
are	O
far	O
away	O
from	O
advancing	O
machine	O
learning	O
for	O
their	O
representation	O
ability	O
”	O
,	O
and	O
even	O
speaking	O
about	O
evaluation	O
and	O
optimization	O
for	O
any	O
kind	O
of	O
useful	O
task	O
quantum	O
supremacy	O
is	O
not	O
yet	O
achieved	O
.	O
</s>
