<s>
Quantum	B-Algorithm
annealing	I-Algorithm
(	O
QA	O
)	O
is	O
an	O
optimization	O
process	O
for	O
finding	O
the	O
global	O
minimum	O
of	O
a	O
given	O
objective	O
function	O
over	O
a	O
given	O
set	O
of	O
candidate	O
solutions	O
(	O
candidate	O
states	O
)	O
,	O
by	O
a	O
process	O
using	O
quantum	O
fluctuations	O
.	O
</s>
<s>
Quantum	B-Algorithm
annealing	I-Algorithm
is	O
used	O
mainly	O
for	O
problems	O
where	O
the	O
search	O
space	O
is	O
discrete	O
(	O
combinatorial	O
optimization	O
problems	O
)	O
with	O
many	O
local	O
minima	O
;	O
such	O
as	O
finding	O
the	O
ground	O
state	O
of	O
a	O
spin	O
glass	O
or	O
the	O
traveling	B-Algorithm
salesman	I-Algorithm
problem	I-Algorithm
.	O
</s>
<s>
The	O
term	O
"	O
quantum	B-Algorithm
annealing	I-Algorithm
"	O
was	O
first	O
proposed	O
in	O
1988	O
by	O
B	O
.	O
Apolloni	O
,	O
N	O
.	O
Cesa	O
Bianchi	O
and	O
D	O
.	O
De	O
Falco	O
as	O
a	O
quantum-inspired	O
classical	O
algorithm	O
.	O
</s>
<s>
It	O
was	O
formulated	O
in	O
its	O
present	O
form	O
by	O
T	O
.	O
Kadowaki	O
and	O
H	O
.	O
Nishimori	O
(	O
ja	O
)	O
in	O
"	O
Quantum	B-Algorithm
annealing	I-Algorithm
in	O
the	O
transverse	O
Ising	O
model	O
"	O
though	O
an	O
imaginary-time	O
variant	O
without	O
quantum	O
coherence	O
had	O
been	O
discussed	O
by	O
A	O
.	O
</s>
<s>
B	O
.	O
Finnila	O
,	O
M	O
.	O
A	O
.	O
Gomez	O
,	O
C	O
.	O
Sebenik	O
and	O
J	O
.	O
D	O
.	O
Doll	O
,	O
in	O
"	O
Quantum	B-Algorithm
annealing	I-Algorithm
is	O
a	O
new	O
method	O
for	O
minimizing	O
multidimensional	O
functions	O
"	O
.	O
</s>
<s>
Quantum	B-Algorithm
annealing	I-Algorithm
starts	O
from	O
a	O
quantum-mechanical	O
superposition	O
of	O
all	O
possible	O
states	O
(	O
candidate	O
states	O
)	O
with	O
equal	O
weights	O
.	O
</s>
<s>
The	O
amplitudes	O
of	O
all	O
candidate	O
states	O
keep	O
changing	O
,	O
realizing	O
a	O
quantum	B-Architecture
parallelism	I-Architecture
,	O
according	O
to	O
the	O
time-dependent	O
strength	O
of	O
the	O
transverse	O
field	O
,	O
which	O
causes	O
quantum	O
tunneling	O
between	O
states	O
.	O
</s>
<s>
If	O
the	O
rate	O
of	O
change	O
of	O
the	O
transverse	O
field	O
is	O
slow	O
enough	O
,	O
the	O
system	O
stays	O
close	O
to	O
the	O
ground	O
state	O
of	O
the	O
instantaneous	O
Hamiltonian	O
(	O
also	O
see	O
adiabatic	O
quantum	B-Architecture
computation	I-Architecture
)	O
.	O
</s>
<s>
If	O
the	O
rate	O
of	O
change	O
of	O
the	O
transverse	O
field	O
is	O
accelerated	O
,	O
the	O
system	O
may	O
leave	O
the	O
ground	O
state	O
temporarily	O
but	O
produce	O
a	O
higher	O
likelihood	O
of	O
concluding	O
in	O
the	O
ground	O
state	O
of	O
the	O
final	O
problem	O
Hamiltonian	O
,	O
i.e.	O
,	O
diabatic	O
quantum	B-Architecture
computation	I-Architecture
.	O
</s>
<s>
An	O
experimental	O
demonstration	O
of	O
the	O
success	O
of	O
quantum	B-Algorithm
annealing	I-Algorithm
for	O
random	O
magnets	O
was	O
reported	O
immediately	O
after	O
the	O
initial	O
theoretical	O
proposal	O
.	O
</s>
<s>
Quantum	B-Algorithm
annealing	I-Algorithm
can	O
be	O
compared	O
to	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
whose	O
"	O
temperature	O
"	O
parameter	O
plays	O
a	O
similar	O
role	O
to	O
QA	O
's	O
tunneling	O
field	O
strength	O
.	O
</s>
<s>
In	O
simulated	B-Algorithm
annealing	I-Algorithm
,	O
the	O
temperature	O
determines	O
the	O
probability	O
of	O
moving	O
to	O
a	O
state	O
of	O
higher	O
"	O
energy	O
"	O
from	O
a	O
single	O
current	O
state	O
.	O
</s>
<s>
In	O
quantum	B-Algorithm
annealing	I-Algorithm
,	O
the	O
strength	O
of	O
transverse	O
field	O
determines	O
the	O
quantum-mechanical	O
probability	O
to	O
change	O
the	O
amplitudes	O
of	O
all	O
states	O
in	O
parallel	O
.	O
</s>
<s>
Analytical	O
and	O
numerical	O
evidence	O
suggests	O
that	O
quantum	B-Algorithm
annealing	I-Algorithm
outperforms	O
simulated	B-Algorithm
annealing	I-Algorithm
under	O
certain	O
conditions	O
(	O
see	O
for	O
a	O
careful	O
analysis	O
,	O
and	O
,	O
for	O
a	O
fully	O
solvable	O
model	O
of	O
quantum	B-Algorithm
annealing	I-Algorithm
to	O
arbitrary	O
target	O
Hamiltonian	O
and	O
comparison	O
of	O
different	O
computation	O
approaches	O
)	O
.	O
</s>
<s>
It	O
has	O
been	O
demonstrated	O
experimentally	O
as	O
well	O
as	O
theoretically	O
,	O
that	O
quantum	B-Algorithm
annealing	I-Algorithm
can	O
indeed	O
outperform	O
thermal	O
annealing	O
(	O
simulated	B-Algorithm
annealing	I-Algorithm
)	O
in	O
certain	O
cases	O
,	O
especially	O
where	O
the	O
potential	O
energy	O
(	O
cost	O
)	O
landscape	O
consists	O
of	O
very	O
high	O
but	O
thin	O
barriers	O
surrounding	O
shallow	O
local	O
minima	O
.	O
</s>
<s>
It	O
is	O
speculated	O
that	O
in	O
a	O
quantum	B-Architecture
computer	I-Architecture
,	O
such	O
simulations	O
would	O
be	O
much	O
more	O
efficient	O
and	O
exact	O
than	O
that	O
done	O
in	O
a	O
classical	O
computer	O
,	O
because	O
it	O
can	O
perform	O
the	O
tunneling	O
directly	O
,	O
rather	O
than	O
needing	O
to	O
add	O
it	O
by	O
hand	O
.	O
</s>
<s>
Timeline	O
of	O
ideas	O
related	O
to	O
quantum	B-Algorithm
annealing	I-Algorithm
in	O
Ising	O
spin	O
glasses	O
:	O
</s>
<s>
1998	O
Formulation	O
of	O
quantum	B-Algorithm
annealing	I-Algorithm
and	O
numerical	O
test	O
demonstrating	O
its	O
advantages	O
in	O
Ising	O
glass	O
systems	O
;	O
</s>
<s>
1999	O
First	O
experimental	O
demonstration	O
of	O
quantum	B-Algorithm
annealing	I-Algorithm
in	O
LiHoYF	O
Ising	O
glass	O
magnets	O
;	O
</s>
<s>
2011	O
Superconducting-circuit	O
quantum	B-Algorithm
annealing	I-Algorithm
machine	O
built	O
and	O
marketed	O
by	O
D-Wave	O
Systems	O
.	O
</s>
<s>
In	O
2011	O
,	O
D-Wave	O
Systems	O
announced	O
the	O
first	O
commercial	O
quantum	B-Algorithm
annealer	I-Algorithm
on	O
the	O
market	O
by	O
the	O
name	O
D-Wave	O
One	O
and	O
published	O
a	O
paper	O
in	O
Nature	O
on	O
its	O
performance	O
.	O
</s>
<s>
In	O
May	O
2013	O
it	O
was	O
announced	O
that	O
a	O
consortium	O
of	O
Google	B-Application
,	O
NASA	O
Ames	O
and	O
the	O
non-profit	O
Universities	O
Space	O
Research	O
Association	O
purchased	O
an	O
adiabatic	O
quantum	B-Architecture
computer	I-Architecture
from	O
D-Wave	O
Systems	O
with	O
512	O
qubits	O
.	O
</s>
<s>
An	O
extensive	O
study	O
of	O
its	O
performance	O
as	O
quantum	B-Algorithm
annealer	I-Algorithm
,	O
compared	O
to	O
some	O
classical	O
annealing	O
algorithms	O
,	O
is	O
already	O
available	O
.	O
</s>
<s>
As	O
the	O
first	O
company	O
dedicated	O
to	O
producing	O
software	O
applications	O
for	O
commercially	O
available	O
quantum	B-Architecture
computers	I-Architecture
,	O
1QBit	O
's	O
research	O
and	O
development	O
arm	O
has	O
focused	O
on	O
D-Wave	O
'	O
s	O
quantum	B-Algorithm
annealing	I-Algorithm
processors	O
and	O
has	O
successfully	O
demonstrated	O
that	O
these	O
processors	O
are	O
suitable	O
for	O
solving	O
real-world	O
applications	O
.	O
</s>
<s>
Researchers	O
at	O
Google	B-Application
,	O
LANL	O
,	O
USC	O
,	O
Texas	O
A&M	O
,	O
and	O
D-Wave	O
are	O
working	O
to	O
find	O
such	O
problem	O
classes	O
.	O
</s>
<s>
In	O
December	O
2015	O
,	O
Google	B-Application
announced	O
that	O
the	O
D-Wave	O
2X	O
outperforms	O
both	O
simulated	B-Algorithm
annealing	I-Algorithm
and	O
Quantum	O
Monte	O
Carlo	O
by	O
up	O
to	O
a	O
factor	O
of	O
100,000,000	O
on	O
a	O
set	O
of	O
hard	O
optimization	O
problems	O
.	O
</s>
<s>
D-Wave	O
'	O
s	O
architecture	O
differs	O
from	O
traditional	O
quantum	B-Architecture
computers	I-Architecture
.	O
</s>
<s>
It	O
is	O
not	O
known	O
to	O
be	O
polynomially	O
equivalent	O
to	O
a	O
universal	O
quantum	B-Architecture
computer	I-Architecture
and	O
,	O
in	O
particular	O
,	O
cannot	O
execute	O
Shor	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
because	O
Shor	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
is	O
not	O
a	O
hillclimbing	O
process	O
.	O
</s>
<s>
Shor	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
requires	O
a	O
universal	O
quantum	B-Architecture
computer	I-Architecture
.	O
</s>
<s>
During	O
the	O
Qubits	O
2021	O
conference	O
held	O
by	O
D-Wave	O
,	O
it	O
was	O
announced	O
that	O
the	O
company	O
is	O
hard	O
at	O
work	O
developing	O
their	O
first	O
universal	O
quantum	B-Architecture
computers	I-Architecture
,	O
capable	O
of	O
running	O
Shor	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
in	O
addition	O
to	O
other	O
gate-model	O
algorithms	O
such	O
as	O
QAOA	O
and	O
VQE	O
.	O
</s>
<s>
"	O
A	O
cross-disciplinary	O
introduction	O
to	O
quantum	O
annealing-based	O
algorithms	O
"	O
presents	O
an	O
introduction	O
to	O
combinatorial	O
optimization	O
(	O
NP-hard	O
)	O
problems	O
,	O
the	O
general	O
structure	O
of	O
quantum	O
annealing-based	O
algorithms	O
and	O
two	O
examples	O
of	O
this	O
kind	O
of	O
algorithms	O
for	O
solving	O
instances	O
of	O
the	O
max-SAT	O
and	O
Minimum	O
Multicut	O
problems	O
,	O
together	O
with	O
an	O
overview	O
of	O
the	O
quantum	B-Algorithm
annealing	I-Algorithm
systems	O
manufactured	O
by	O
D-Wave	O
Systems	O
.	O
</s>
