<s>
A	O
qutrit	B-Device
(	O
or	O
quantum	B-Device
trit	I-Device
)	O
is	O
a	O
unit	O
of	O
quantum	O
information	O
that	O
is	O
realized	O
by	O
a	O
3-level	O
quantum	O
system	O
,	O
that	O
may	O
be	O
in	O
a	O
superposition	O
of	O
three	O
mutually	O
orthogonal	O
quantum	O
states	O
.	O
</s>
<s>
The	O
qutrit	B-Device
is	O
analogous	O
to	O
the	O
classical	O
radix-3	O
trit	B-Algorithm
,	O
just	O
as	O
the	O
qubit	O
,	O
a	O
quantum	O
system	O
described	O
by	O
a	O
superposition	O
of	O
two	O
orthogonal	O
states	O
,	O
is	O
analogous	O
to	O
the	O
classical	O
radix-2	O
bit	O
.	O
</s>
<s>
There	O
is	O
ongoing	O
work	O
to	O
develop	O
quantum	B-Architecture
computers	I-Architecture
using	O
qutrits	B-Device
and	O
qubits	O
with	O
multiple	O
states	O
.	O
</s>
<s>
A	O
qutrit	B-Device
has	O
three	O
orthonormal	O
basis	O
states	O
or	O
vectors	O
,	O
often	O
denoted	O
,	O
,	O
and	O
in	O
Dirac	O
or	O
bra	O
–	O
ket	O
notation	O
.	O
</s>
<s>
These	O
are	O
used	O
to	O
describe	O
the	O
qutrit	B-Device
as	O
a	O
superposition	O
state	O
vector	O
in	O
the	O
form	O
of	O
a	O
linear	O
combination	O
of	O
the	O
three	O
orthonormal	O
basis	O
states	O
:	O
</s>
<s>
Qutrits	B-Device
require	O
a	O
Hilbert	O
space	O
of	O
higher	O
dimension	O
,	O
namely	O
the	O
three-dimensional	O
spanned	O
by	O
the	O
qutrit	B-Device
's	O
basis	O
,	O
which	O
can	O
be	O
realized	O
by	O
a	O
three-level	O
quantum	O
system	O
.	O
</s>
<s>
An	O
n-qutrit	O
register	O
can	O
represent	O
3n	O
different	O
states	O
simultaneously	O
,	O
i.e.	O
,	O
a	O
superposition	O
state	O
vector	O
in	O
3n-dimensional	O
complex	O
Hilbert	O
space	O
.	O
</s>
<s>
Qutrits	B-Device
have	O
several	O
peculiar	O
features	O
when	O
used	O
for	O
storing	O
quantum	O
information	O
.	O
</s>
<s>
In	O
reality	O
,	O
manipulating	O
qutrits	B-Device
directly	O
might	O
be	O
tricky	O
,	O
and	O
one	O
way	O
to	O
do	O
that	O
is	O
by	O
using	O
an	O
entanglement	O
with	O
a	O
qubit	O
.	O
</s>
<s>
The	O
quantum	O
logic	O
gates	O
operating	O
on	O
single	O
qutrits	B-Device
are	O
unitary	B-Algorithm
matrices	I-Algorithm
and	O
gates	O
that	O
act	O
on	O
registers	O
of	O
qutrits	B-Device
are	O
unitary	B-Algorithm
matrices	I-Algorithm
(	O
the	O
elements	O
of	O
the	O
unitary	O
groups	O
U(3 )	O
and	O
U(3n )	O
respectively	O
)	O
.	O
</s>
<s>
The	O
global	O
phase	O
shift	O
gate	O
for	O
the	O
qutrit	B-Device
is	O
where	O
the	O
phase	O
factor	O
is	O
called	O
the	O
global	O
phase	O
.	O
</s>
<s>
This	O
phase	O
gate	O
performs	O
the	O
mapping	O
and	O
together	O
with	O
the	O
8	O
rotation	O
operators	O
is	O
capable	O
of	O
expressing	O
any	O
single-qutrit	O
gate	O
in	O
U(3 )	O
,	O
as	O
a	O
series	O
circuit	O
of	O
at	O
most	O
9	O
gates	O
.	O
</s>
