<s>
Quantum	B-Device
programming	I-Device
is	O
the	O
process	O
of	O
assembling	B-Language
sequences	O
of	O
instructions	O
,	O
called	O
quantum	B-Application
circuits	I-Application
,	O
that	O
are	O
capable	O
of	O
running	O
on	O
a	O
quantum	B-Architecture
computer	I-Architecture
.	O
</s>
<s>
Quantum	B-Device
programming	I-Device
languages	I-Device
help	O
express	O
quantum	B-Device
algorithms	I-Device
using	O
high-level	O
constructs	O
.	O
</s>
<s>
The	O
field	O
is	O
deeply	O
rooted	O
in	O
the	O
open-source	B-License
philosophy	O
and	O
as	O
a	O
result	O
most	O
of	O
the	O
quantum	O
software	O
discussed	O
in	O
this	O
article	O
is	O
freely	O
available	O
as	O
open-source	B-Application
software	I-Application
.	O
</s>
<s>
Quantum	O
instruction	O
sets	O
are	O
used	O
to	O
turn	O
higher	O
level	O
algorithms	O
into	O
physical	O
instructions	O
that	O
can	O
be	O
executed	O
on	O
quantum	B-Architecture
processors	I-Architecture
.	O
</s>
<s>
cQASM	O
,	O
also	O
known	O
as	O
common	O
QASM	O
,	O
is	O
a	O
hardware-agnostic	O
quantum	O
assembly	B-Language
language	I-Language
which	O
guarantees	O
the	O
interoperability	O
between	O
all	O
the	O
quantum	O
compilation	O
and	O
simulation	O
tools	O
.	O
</s>
<s>
Quil	B-Device
is	O
an	O
instruction	O
set	O
architecture	O
for	O
quantum	B-Architecture
computing	I-Architecture
that	O
first	O
introduced	O
a	O
shared	O
quantum/classical	O
memory	O
model	O
.	O
</s>
<s>
Many	O
quantum	B-Device
algorithms	I-Device
(	O
including	O
quantum	O
teleportation	O
,	O
quantum	B-Device
error	I-Device
correction	I-Device
,	O
simulation	O
,	O
and	O
optimization	O
algorithms	O
)	O
require	O
a	O
shared	O
memory	O
architecture	O
.	O
</s>
<s>
OpenQASM	B-Device
is	O
the	O
intermediate	O
representation	O
introduced	O
by	O
IBM	O
for	O
use	O
with	O
Qiskit	O
and	O
the	O
IBM	B-Device
Q	I-Device
Experience	I-Device
.	O
</s>
<s>
It	O
is	O
designed	O
to	O
represent	O
continuous-variable	O
quantum	B-Device
programs	I-Device
that	O
can	O
run	O
on	O
photonic	O
quantum	O
hardware	O
.	O
</s>
<s>
Quantum	O
software	B-Application
development	I-Application
kits	I-Application
provide	O
collections	O
of	O
tools	O
to	O
create	O
and	O
manipulate	O
quantum	B-Device
programs	I-Device
.	O
</s>
<s>
They	O
also	O
provide	O
the	O
means	O
to	O
simulate	O
the	O
quantum	B-Device
programs	I-Device
or	O
prepare	O
them	O
to	O
be	O
run	O
using	O
cloud-based	B-General_Concept
quantum	I-General_Concept
devices	I-General_Concept
and	O
self-hosted	O
quantum	O
devices	O
.	O
</s>
<s>
The	O
following	O
software	B-Application
development	I-Application
kits	I-Application
can	O
be	O
used	O
to	O
run	O
quantum	B-Application
circuits	I-Application
on	O
prototype	O
quantum	O
devices	O
,	O
as	O
well	O
as	O
on	O
simulators	O
.	O
</s>
<s>
An	O
open-source	B-License
project	O
created	O
by	O
for	O
designing	O
photonic	O
quantum	B-Application
circuits	I-Application
and	O
developing	O
quantum	B-Device
algorithms	I-Device
,	O
based	O
on	O
Python	B-Language
.	O
</s>
<s>
Simulations	O
are	O
run	O
either	O
on	O
the	O
user	O
's	O
own	O
computer	O
or	O
on	O
the	O
cloud	B-Architecture
.	O
</s>
<s>
Perceval	O
is	O
also	O
used	O
to	O
connect	O
to	O
Quandela	O
's	O
cloud-based	B-Architecture
photonic	B-Device
quantum	I-Device
processor	I-Device
.	O
</s>
<s>
An	O
Open	B-License
Source	I-License
suite	O
of	O
tools	O
developed	O
by	O
D-Wave	O
.	O
</s>
<s>
Written	O
mostly	O
in	O
the	O
Python	B-Language
programming	I-Language
language	I-Language
,	O
it	O
enables	O
users	O
to	O
formulate	O
problems	O
in	O
Ising	O
Model	O
and	O
Quadratic	O
Unconstrained	O
Binary	O
Optimization	O
formats	O
(	O
QUBO	O
)	O
.	O
</s>
<s>
Results	O
can	O
be	O
obtained	O
by	O
submitting	O
to	O
an	O
online	O
quantum	B-Architecture
computer	I-Architecture
in	O
Leap	O
,	O
D-Wave	O
'	O
s	O
real-time	O
Quantum	O
Application	O
Environment	O
,	O
customer-owned	O
machines	O
,	O
or	O
classical	O
samplers	O
.	O
</s>
<s>
An	O
Open	B-License
Source	I-License
project	O
developed	O
at	O
the	O
Institute	O
for	O
Theoretical	O
Physics	O
at	O
ETH	O
,	O
which	O
uses	O
the	O
Python	B-Language
programming	I-Language
language	I-Language
to	O
create	O
and	O
manipulate	O
quantum	B-Application
circuits	I-Application
.	O
</s>
<s>
Results	O
are	O
obtained	O
either	O
using	O
a	O
simulator	O
,	O
or	O
by	O
sending	O
jobs	O
to	O
IBM	B-Device
quantum	I-Device
devices	O
.	O
</s>
<s>
An	O
Open	B-License
Source	I-License
project	O
developed	O
by	O
IBM	O
.	O
</s>
<s>
Quantum	B-Application
circuits	I-Application
are	O
created	O
and	O
manipulated	O
using	O
Python	B-Language
.	O
</s>
<s>
Qiskit	O
is	O
based	O
on	O
the	O
OpenQASM	B-Device
standard	O
for	O
representing	O
quantum	B-Application
circuits	I-Application
.	O
</s>
<s>
An	O
open	B-License
source	I-License
full-stack	O
API	O
for	O
quantum	O
simulation	O
,	O
quantum	O
hardware	O
control	O
and	O
calibration	O
developed	O
by	O
multiple	O
research	O
laboratories	O
,	O
including	O
QRC	O
,	O
CQT	O
and	O
INFN	O
.	O
</s>
<s>
An	O
open	B-License
source	I-License
project	O
developed	O
by	O
Rigetti	O
,	O
which	O
uses	O
the	O
Python	B-Language
programming	I-Language
language	I-Language
to	O
create	O
and	O
manipulate	O
quantum	B-Application
circuits	I-Application
.	O
</s>
<s>
Forest	O
is	O
based	O
on	O
the	O
Quil	B-Device
instruction	O
set	O
.	O
</s>
<s>
A	O
quantum	B-Device
programming	I-Device
environment	O
and	O
optimizing	O
compiler	O
developed	O
by	O
Cambridge	O
Quantum	B-Architecture
Computing	I-Architecture
that	O
targets	O
simulators	O
and	O
several	O
quantum	O
hardware	O
back-ends	O
,	O
released	O
in	O
December	O
2018	O
.	O
</s>
<s>
An	O
open-source	B-License
Python	B-Language
library	O
developed	O
by	O
Xanadu	O
Quantum	O
Technologies	O
for	O
designing	O
,	O
simulating	O
,	O
and	O
optimizing	O
continuous	O
variable	O
(	O
CV	O
)	O
quantum	O
optical	O
circuits	O
.	O
</s>
<s>
Three	O
simulators	O
are	O
provided	O
-	O
one	O
in	O
the	O
Fock	O
basis	O
,	O
one	O
using	O
the	O
Gaussian	O
formulation	O
of	O
quantum	O
optics	O
,	O
and	O
one	O
using	O
the	O
TensorFlow	B-Language
machine	O
learning	O
library	O
.	O
</s>
<s>
An	O
open-source	B-License
Python	B-Language
library	O
developed	O
by	O
Xanadu	O
Quantum	O
Technologies	O
for	O
differentiable	B-Application
programming	I-Application
of	O
quantum	B-Architecture
computers	I-Architecture
.	O
</s>
<s>
PennyLane	O
provides	O
users	O
the	O
ability	O
to	O
create	O
models	O
using	O
TensorFlow	B-Language
,	O
NumPy	B-Application
,	O
or	O
PyTorch	B-Algorithm
,	O
and	O
connect	O
them	O
with	O
quantum	B-Architecture
computer	I-Architecture
backends	O
available	O
from	O
IBMQ	B-Device
,	O
Google	B-Application
Quantum	I-Application
,	O
Rigetti	O
,	O
Quantinuum	O
and	O
Alpine	O
Quantum	O
Technologies	O
.	O
</s>
<s>
A	O
project	O
developed	O
by	O
Microsoft	O
as	O
part	O
of	O
the	O
.NET	B-Application
Framework	I-Application
.	O
</s>
<s>
Quantum	B-Device
programs	I-Device
can	O
be	O
written	O
and	O
run	O
within	O
Visual	B-Application
Studio	I-Application
and	O
VSCode	O
using	O
the	O
quantum	B-Device
programming	I-Device
language	I-Device
Q#	O
.	O
</s>
<s>
Programs	O
developed	O
in	O
the	O
QDK	O
can	O
be	O
run	O
on	O
Microsoft	O
's	O
Azure	O
Quantum	O
,	O
and	O
run	O
on	O
quantum	B-Architecture
computers	I-Architecture
from	O
Quantinuum	O
,	O
IonQ	O
,	O
and	O
Pasqal	O
.	O
</s>
<s>
An	O
Open	B-License
Source	I-License
project	O
developed	O
by	O
Google	B-Application
,	O
which	O
uses	O
the	O
Python	B-Language
programming	I-Language
language	I-Language
to	O
create	O
and	O
manipulate	O
quantum	B-Application
circuits	I-Application
.	O
</s>
<s>
There	O
are	O
two	O
main	O
groups	O
of	O
quantum	B-Device
programming	I-Device
languages	I-Device
:	O
imperative	B-Application
quantum	B-Device
programming	I-Device
languages	I-Device
and	O
functional	B-Language
quantum	B-Device
programming	I-Device
languages	I-Device
.	O
</s>
<s>
The	O
most	O
prominent	O
representatives	O
of	O
the	O
imperative	B-Application
languages	I-Application
are	O
QCL	O
,	O
LanQ	O
and	O
Q|	O
SI>	O
.	O
</s>
<s>
Quantum	B-Device
Computation	I-Device
Language	I-Device
(	O
QCL	O
)	O
is	O
one	O
of	O
the	O
first	O
implemented	O
quantum	B-Device
programming	I-Device
languages	I-Device
.	O
</s>
<s>
Its	O
syntax	B-Application
resembles	O
the	O
syntax	B-Application
of	O
the	O
C	B-Language
programming	I-Language
language	I-Language
and	O
its	O
classical	O
data	O
types	O
are	O
similar	O
to	O
primitive	O
data	O
types	O
in	O
C	B-Language
.	O
One	O
can	O
combine	O
classical	O
code	O
and	O
quantum	B-Device
code	I-Device
in	O
the	O
same	O
program	O
.	O
</s>
<s>
Quantum	O
pseudocode	O
proposed	O
by	O
E	O
.	O
Knill	O
is	O
the	O
first	O
formalized	O
language	O
for	O
description	O
of	O
quantum	B-Device
algorithms	I-Device
.	O
</s>
<s>
It	O
was	O
introduced	O
and	O
,	O
moreover	O
,	O
was	O
tightly	O
connected	O
with	O
a	O
model	O
of	O
quantum	O
machine	O
called	O
Quantum	B-Architecture
Random	I-Architecture
Access	I-Architecture
Machine	I-Architecture
(	O
QRAM	O
)	O
.	O
</s>
<s>
A	O
language	O
developed	O
by	O
Microsoft	O
to	O
be	O
used	O
with	O
the	O
Quantum	O
Development	B-Application
Kit	I-Application
.	O
</s>
<s>
Q|	O
SI>	O
is	O
a	O
platform	O
embedded	O
in	O
.Net	B-Application
language	O
supporting	O
quantum	B-Device
programming	I-Device
in	O
a	O
quantum	O
extension	O
of	O
while-language	O
.	O
</s>
<s>
This	O
platform	O
includes	O
a	O
compiler	O
of	O
the	O
quantum	O
while-language	O
and	O
a	O
chain	O
of	O
tools	O
for	O
the	O
simulation	O
of	O
quantum	B-Architecture
computation	I-Architecture
,	O
optimisation	O
of	O
quantum	B-Application
circuits	I-Application
,	O
termination	O
analysis	O
of	O
quantum	B-Device
programs	I-Device
,	O
and	O
verification	O
of	O
quantum	B-Device
programs	I-Device
.	O
</s>
<s>
Q	O
Language	O
is	O
the	O
second	O
implemented	O
imperative	B-Application
quantum	B-Device
programming	I-Device
language	I-Device
.	O
</s>
<s>
Q	O
Language	O
was	O
implemented	O
as	O
an	O
extension	O
of	O
C++	O
programming	O
language	O
.	O
</s>
<s>
New	O
operators	O
can	O
be	O
defined	O
using	O
C++	O
class	O
mechanism	O
.	O
</s>
<s>
Quantum	O
Guarded	B-Application
Command	I-Application
Language	I-Application
(	O
qGCL	O
)	O
was	O
defined	O
by	O
P	O
.	O
Zuliani	O
in	O
his	O
PhD	O
thesis	O
.	O
</s>
<s>
It	O
is	O
based	O
on	O
Guarded	B-Application
Command	I-Application
Language	I-Application
created	O
by	O
Edsger	O
Dijkstra	O
.	O
</s>
<s>
It	O
can	O
be	O
described	O
as	O
a	O
language	O
of	O
quantum	B-Device
programs	I-Device
specification	O
.	O
</s>
<s>
Quantum	O
Macro	O
Assembler	B-Language
(	O
QMASM	O
)	O
is	O
a	O
low-level	O
language	O
specific	O
to	O
quantum	O
annealers	O
such	O
as	O
the	O
D-Wave	O
.	O
</s>
<s>
Scaffold	O
is	O
C-like	O
language	O
,	O
that	O
compiles	O
to	O
QASM	O
and	O
OpenQASM	B-Device
.	O
</s>
<s>
It	O
is	O
built	O
on	O
top	O
of	O
the	O
LLVM	B-Application
Compiler	O
Infrastructure	O
to	O
perform	O
optimizations	O
on	O
Scaffold	O
code	O
before	O
generating	O
a	O
specified	O
instruction	O
set	O
.	O
</s>
<s>
Silq	O
is	O
a	O
high-level	O
programming	O
language	O
for	O
quantum	B-Architecture
computing	I-Architecture
with	O
a	O
strong	O
static	O
type	O
system	O
,	O
developed	O
at	O
ETH	O
Zürich	O
.	O
</s>
<s>
The	O
Logic	O
of	O
Quantum	B-Device
Programs	I-Device
(	O
LQP	O
)	O
is	O
a	O
dynamic	O
quantum	O
logic	O
,	O
capable	O
of	O
expressing	O
important	O
features	O
of	O
quantum	O
measurements	O
and	O
unitary	O
evolutions	O
of	O
multi-partite	O
states	O
,	O
and	O
provides	O
logical	O
characterizations	O
of	O
various	O
forms	O
of	O
entanglement	O
.	O
</s>
<s>
The	O
logic	O
has	O
been	O
used	O
to	O
specify	O
and	O
verify	O
the	O
correctness	O
of	O
various	O
protocols	O
in	O
quantum	B-Architecture
computation	I-Architecture
.	O
</s>
<s>
Efforts	O
are	O
underway	O
to	O
develop	O
functional	B-Language
programming	I-Language
languages	I-Language
for	O
quantum	B-Architecture
computing	I-Architecture
.	O
</s>
<s>
Functional	B-Language
programming	I-Language
languages	I-Language
are	O
well-suited	O
for	O
reasoning	O
about	O
programs	O
.	O
</s>
<s>
Examples	O
include	O
Selinger	O
's	O
QPL	O
,	O
and	O
the	O
Haskell-like	B-Language
language	O
QML	O
by	O
Altenkirch	O
and	O
Grattage	O
.	O
</s>
<s>
Higher-order	O
quantum	B-Device
programming	I-Device
languages	I-Device
,	O
based	O
on	O
lambda	B-Language
calculus	I-Language
,	O
have	O
been	O
proposed	O
by	O
van	O
Tonder	O
,	O
Selinger	O
and	O
Valiron	O
and	O
by	O
Arrighi	O
and	O
Dowek	O
.	O
</s>
<s>
QFC	O
and	O
QPL	O
are	O
two	O
closely	O
related	O
quantum	B-Device
programming	I-Device
languages	I-Device
defined	O
by	O
Peter	O
Selinger	O
.	O
</s>
<s>
They	O
differ	O
only	O
in	O
their	O
syntax	B-Application
:	O
QFC	O
uses	O
a	O
flow	O
chart	O
syntax	B-Application
,	O
whereas	O
QPL	O
uses	O
a	O
textual	O
syntax	B-Application
.	O
</s>
<s>
Selinger	O
gives	O
a	O
denotational	B-Application
semantics	I-Application
for	O
these	O
languages	O
in	O
a	O
category	O
of	O
superoperators	O
.	O
</s>
<s>
QML	O
is	O
a	O
Haskell-like	B-Language
quantum	B-Device
programming	I-Device
language	I-Device
by	O
Altenkirch	O
and	O
Grattage	O
.	O
</s>
<s>
An	O
operational	O
semantics	O
for	O
QML	O
is	O
given	O
in	O
terms	O
of	O
quantum	B-Application
circuits	I-Application
,	O
while	O
a	O
denotational	B-Application
semantics	I-Application
is	O
presented	O
in	O
terms	O
of	O
superoperators	O
,	O
and	O
these	O
are	O
shown	O
to	O
agree	O
.	O
</s>
<s>
Both	O
the	O
operational	O
and	O
denotational	B-Application
semantics	I-Application
have	O
been	O
implemented	O
(	O
classically	O
)	O
in	O
Haskell	B-Language
.	O
</s>
<s>
LIQUi|	O
>	O
(	O
pronounced	O
liquid	O
)	O
is	O
a	O
quantum	O
simulation	O
extension	O
on	O
the	O
F#	B-Operating_System
programming	O
language	O
.	O
</s>
<s>
LIQUi|	O
>	O
seeks	O
to	O
allow	O
theorists	O
to	O
experiment	O
with	O
quantum	B-Device
algorithm	I-Device
design	O
before	O
physical	O
quantum	B-Architecture
computers	I-Architecture
are	O
available	O
for	O
use	O
.	O
</s>
<s>
LIQUi|	O
>	O
can	O
be	O
used	O
to	O
translate	O
a	O
quantum	B-Device
algorithm	I-Device
written	O
in	O
the	O
form	O
of	O
a	O
high-level	O
program	O
into	O
the	O
low-level	O
machine	O
instructions	O
for	O
a	O
quantum	O
device	O
.	O
</s>
<s>
Quantum	O
lambda	B-Language
calculi	I-Language
are	O
extensions	O
of	O
the	O
classical	O
lambda	B-Language
calculus	I-Language
introduced	O
by	O
Alonzo	O
Church	O
and	O
Stephen	O
Cole	O
Kleene	O
in	O
the	O
1930s	O
.	O
</s>
<s>
The	O
purpose	O
of	O
quantum	O
lambda	B-Language
calculi	I-Language
is	O
to	O
extend	O
quantum	B-Device
programming	I-Device
languages	I-Device
with	O
a	O
theory	O
of	O
higher-order	B-Language
functions	I-Language
.	O
</s>
<s>
The	O
first	O
attempt	O
to	O
define	O
a	O
quantum	O
lambda	B-Language
calculus	I-Language
was	O
made	O
by	O
Philip	O
Maymin	O
in	O
1996	O
.	O
</s>
<s>
His	O
lambda-q	O
calculus	O
is	O
powerful	O
enough	O
to	O
express	O
any	O
quantum	B-Architecture
computation	I-Architecture
.	O
</s>
<s>
However	O
,	O
this	O
language	O
can	O
efficiently	O
solve	O
NP-complete	O
problems	O
,	O
and	O
therefore	O
appears	O
to	O
be	O
strictly	O
stronger	O
than	O
the	O
standard	O
quantum	O
computational	O
models	O
(	O
such	O
as	O
the	O
quantum	O
Turing	O
machine	O
or	O
the	O
quantum	B-Application
circuit	I-Application
model	O
)	O
.	O
</s>
<s>
In	O
2003	O
,	O
André	O
van	O
Tonder	O
defined	O
an	O
extension	O
of	O
the	O
lambda	B-Language
calculus	I-Language
suitable	O
for	O
proving	O
correctness	O
of	O
quantum	B-Device
programs	I-Device
.	O
</s>
<s>
He	O
also	O
provided	O
an	O
implementation	O
in	O
the	O
Scheme	B-Language
programming	I-Language
language	I-Language
.	O
</s>
<s>
In	O
2004	O
,	O
Selinger	O
and	O
Valiron	O
defined	O
a	O
strongly	O
typed	O
lambda	B-Language
calculus	I-Language
for	O
quantum	B-Architecture
computation	I-Architecture
with	O
a	O
type	O
system	O
based	O
on	O
linear	O
logic	O
.	O
</s>
<s>
It	O
is	O
implemented	O
as	O
an	O
embedded	O
language	O
,	O
using	O
Haskell	B-Language
as	O
the	O
host	O
language	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
quantum	B-Device
programs	I-Device
written	O
in	O
Quipper	O
are	O
written	O
in	O
Haskell	B-Language
using	O
provided	O
libraries	O
.	O
</s>
