DEMO ↑
DEMO
=> U : Clifford
operation
>
-
2 logical qubits
- 1 logical qubit
DEMO
DEMO
F 7
=
IP1 for a
= =
1
bits n
transform
H
+ a Hamiltonian
embedded into matrix
unitary
:
a
↓
Quantum
Eigenvalve Transform
for 117(11 =
(vBlockina
:
1
&
DEMO
H =
2, X; 14; >4 ; / n =
2 =
[14 % ) (til
~ as
long
as
eigenvalves
a re of reasonable scale
(Kj1Xj) ,
this
matrix U is
unitary (meaning UtU =
1) .
16
4 <i =:
GR(j) 14(4)
7 = reflection and rotation around the
y-axis
U contains block
"
a
sphere uphased itrate
for each
(> N
eigenspace
of it
#jiet
, instead of 2 with A .
A .
)
projector-controlled
Je := eiez _
I It
· :
phase-shift operation
:
with projection IT 103 <01 to It out U
pick of
=
.
. .
⑫
DEMO
Hamiltonian
10) H
rarunSo
Simulation
H
odd parity
I : :sinS
Value Transform
Quantum
Singular
values of
~>
transform all
singular a
general (possibly non-
of
Square) matrix A encoded i n to a block a
unitary matrix U
A =
WSVt =
En OnIwn)(Vel forWe
E -
(
) withw Example : u =
U= =
A =
FUT -
with F =
EnE" IWr) <Vul
Ut Fant -U) =
(Poly() : ) =
=
En Crown
En R(On)@1Wk) < VrI
namUFau) ( )
↳ =
: =>
-
Qubitization
block encoding +
with
Poly(A) =
En Poly (On) (wn) < Urel Signal processing
DEMO
=> U : Clifford
operation
>
-
2 logical qubits
- 1 logical qubit
DEMO
DEMO
F 7
=
IP1 for a
= =
1
bits n
transform
H
+ a Hamiltonian
embedded into matrix
unitary
:
a
↓
Quantum
Eigenvalve Transform
for 117(11 =
(vBlockina
:
1
&
DEMO
H =
2, X; 14; >4 ; / n =
2 =
[14 % ) (til
~ as
long
as
eigenvalves
a re of reasonable scale
(Kj1Xj) ,
this
matrix U is
unitary (meaning UtU =
1) .
16
4 <i =:
GR(j) 14(4)
7 = reflection and rotation around the
y-axis
U contains block
"
a
sphere uphased itrate
for each
(> N
eigenspace
of it
#jiet
, instead of 2 with A .
A .
)
projector-controlled
Je := eiez _
I It
· :
phase-shift operation
:
with projection IT 103 <01 to It out U
pick of
=
.
. .
⑫
DEMO
Hamiltonian
10) H
rarunSo
Simulation
H
odd parity
I : :sinS
Value Transform
Quantum
Singular
values of
~>
transform all
singular a
general (possibly non-
of
Square) matrix A encoded i n to a block a
unitary matrix U
A =
WSVt =
En OnIwn)(Vel forWe
E -
(
) withw Example : u =
U= =
A =
FUT -
with F =
EnE" IWr) <Vul
Ut Fant -U) =
(Poly() : ) =
=
En Crown
En R(On)@1Wk) < VrI
namUFau) ( )
↳ =
: =>
-
Qubitization
block encoding +
with
Poly(A) =
En Poly (On) (wn) < Urel Signal processing
