<s>
In	O
quantum	B-Architecture
computing	I-Architecture
,	O
the	O
variational	B-Algorithm
quantum	I-Algorithm
eigensolver	I-Algorithm
(	O
VQE	O
)	O
is	O
a	O
quantum	B-Device
algorithm	I-Device
for	O
quantum	O
chemistry	O
,	O
quantum	B-Device
simulations	I-Device
and	O
optimization	O
problems	O
.	O
</s>
<s>
It	O
is	O
a	O
hybrid	O
algorithm	O
that	O
uses	O
both	O
classical	O
computers	O
and	O
quantum	B-Architecture
computers	I-Architecture
to	O
find	O
the	O
ground	O
state	O
of	O
a	O
given	O
physical	O
system	O
.	O
</s>
<s>
Given	O
a	O
guess	O
or	O
ansatz	O
,	O
the	O
quantum	B-Architecture
processor	I-Architecture
calculates	O
the	O
expectation	O
value	O
of	O
the	O
system	O
with	O
respect	O
to	O
an	O
observable	O
,	O
often	O
the	O
Hamiltonian	O
,	O
and	O
a	O
classical	O
optimizer	O
is	O
used	O
to	O
improve	O
the	O
guess	O
.	O
</s>
<s>
The	O
algorithm	O
has	O
also	O
found	O
applications	O
in	O
quantum	B-Device
machine	I-Device
learning	I-Device
and	O
has	O
been	O
further	O
substantiated	O
by	O
general	O
hybrid	O
algorithms	O
between	O
quantum	O
and	O
classical	O
computers	O
.	O
</s>
<s>
In	O
gate-based	O
quantum	B-Architecture
computing	I-Architecture
,	O
the	O
ansatz	O
is	O
given	O
by	O
a	O
parametrized	O
quantum	B-Application
circuit	I-Application
,	O
whose	O
parameters	O
can	O
be	O
updated	O
after	O
each	O
run	O
.	O
</s>
<s>
Classical	O
optimizers	O
using	O
gradient	B-Algorithm
descent	I-Algorithm
can	O
be	O
used	O
for	O
this	O
purpose	O
.	O
</s>
<s>
By	O
running	O
the	O
circuit	O
many	O
times	O
and	O
constantly	O
updating	O
the	O
parameters	O
to	O
find	O
the	O
global	O
minima	O
of	O
the	O
expectation	O
value	O
of	O
the	O
desired	O
observable	O
,	O
one	O
can	O
approach	O
the	O
ground	O
state	O
of	O
the	O
given	O
system	O
and	O
store	O
it	O
in	O
a	O
quantum	B-Architecture
processors	I-Architecture
as	O
a	O
series	O
of	O
quantum	O
gate	O
instructions	O
.	O
</s>
<s>
As	O
of	O
2022	O
,	O
the	O
variational	B-Algorithm
quantum	I-Algorithm
eigensolver	I-Algorithm
can	O
only	O
simulate	O
small	O
molecules	O
like	O
the	O
helium	O
hydride	O
ion	O
or	O
the	O
beryllium	O
hydride	O
molecule	O
.	O
</s>
<s>
In	O
2020	O
,	O
a	O
12	O
qubit	O
simulation	O
of	O
a	O
hydrogen	O
chain	O
(	O
H12	O
)	O
was	O
demonstrated	O
using	O
Google	B-Application
's	I-Application
Sycamore	B-Device
quantum	I-Device
processor	I-Device
.	O
</s>
