<s>
Neural	B-Algorithm
Network	I-Algorithm
Quantum	I-Algorithm
States	I-Algorithm
(	O
NQS	O
or	O
NNQS	O
)	O
is	O
a	O
general	O
class	O
of	O
variational	O
quantum	O
states	O
parameterized	O
in	O
terms	O
of	O
an	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
.	O
</s>
<s>
It	O
was	O
first	O
introduced	O
in	O
2017	O
by	O
the	O
physicists	O
Giuseppe	O
Carleo	O
and	O
Matthias	O
Troyer	O
to	O
approximate	O
wave	O
functions	O
of	O
many-body	B-Algorithm
quantum	O
systems	O
.	O
</s>
<s>
where	O
is	O
an	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
of	O
parameters	O
(	O
weights	O
)	O
,	O
input	O
variables	O
(	O
)	O
and	O
one	O
complex-valued	O
output	O
corresponding	O
to	O
the	O
wave-function	O
amplitude	O
.	O
</s>
<s>
Since	O
,	O
for	O
a	O
general	O
artificial	B-Architecture
neural	I-Architecture
network	I-Architecture
,	O
computing	O
the	O
expectation	O
value	O
is	O
an	O
exponentially	O
costly	O
operation	O
in	O
,	O
stochastic	O
techniques	O
based	O
,	O
for	O
example	O
,	O
on	O
the	O
Monte	B-Algorithm
Carlo	I-Algorithm
method	I-Algorithm
are	O
used	O
to	O
estimate	O
,	O
analogously	O
to	O
what	O
is	O
done	O
in	O
Variational	O
Monte	O
Carlo	O
,	O
see	O
for	O
example	O
for	O
a	O
review	O
.	O
</s>
<s>
where	O
and	O
can	O
be	O
efficiently	O
computed	O
,	O
in	O
deep	B-Algorithm
networks	I-Algorithm
through	O
backpropagation	B-Algorithm
.	O
</s>
<s>
The	O
stochastic	O
approximation	O
of	O
the	O
gradients	O
is	O
then	O
used	O
to	O
minimize	O
the	O
energy	O
typically	O
using	O
a	O
stochastic	B-Algorithm
gradient	I-Algorithm
descent	I-Algorithm
approach	O
.	O
</s>
<s>
When	O
the	O
neural-network	O
parameters	O
are	O
updated	O
at	O
each	O
step	O
of	O
the	O
learning	O
procedure	O
,	O
a	O
new	O
set	O
of	O
samples	O
is	O
generated	O
,	O
in	O
an	O
iterative	O
procedure	O
similar	O
to	O
what	O
done	O
in	O
unsupervised	B-General_Concept
learning	I-General_Concept
.	O
</s>
<s>
Neural-Network	O
representations	O
of	O
quantum	O
wave	O
functions	O
share	O
some	O
similarities	O
with	O
variational	O
quantum	O
states	O
based	O
on	O
tensor	B-Application
networks	I-Application
.	O
</s>
