Summary Advanced Concepts in Quantum Computing (TUM) - Cheatsheet

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