KEMBAR78
An Introduction to Quantum Computers Architecture | PPTX
Quantum
Computers
Architecture
Hamid Reza Bolhasani
PhD Student / Data Scientist
Computer Architecture
JAN 2020
1
Table of Contents
- History
- Classical vs Quantum Mechanics
- Breakdown of Classical Mechanics
- Quantum Mechanics Introduction
- Wave Function
- Quantum Bit (Qubit)
- Quantum Gates
- Quantum Computer
- Challenges
- Q & A
Richard Feynman
“I think I can safely say that no one understand quantum mechanics!”
1982: Feynman
proposed the first
idea.
1985: Deutsch
developed the
quantum Turing
Machine.
1994: Shor
Algorithm to factor
very large numbers
in polynomial time.
1997: Grover
proposed a
quantum search
algorithm.
…Future!
3
Classical Mechanics vs Quantum Mechanics
Mechanics: the study of the behavior of
physical bodies when subjected to forces or
displacements
Classical Mechanics: describing
the motion of macroscopic objects.
Macroscopic: measurable or
observable by naked eyes
Quantum Mechanics: describing
behavior of systems at atomic
length scales and smaller .
4
Classical Mechanics
5
position r = (x,y,z)
velocity v
Property Behaviour
mass momentum
Particles position  collisions
velocity
Waves wavelength  diffraction
frequency interference
x
m
F
k
x = 0
k
m(d2x/dt2) = kx
+A
A
x

time period  = 1/ 
position x(t) = Asin(t)
of particle
frequency  = /2 =
(of oscillation)
m
π2
1 k
Breakdown of Classical Mechanics
6
ePhotelectrons-
h
Metal surface
work function = F
e
Photoelectrons ejected with
kinetic energy:
Ek = h - F
a) Black Body Radiation b) Photoelectric Effect
Max Planck (1900) Albert Einstein (1921)
The Bohr Model of the Atom
7
E = E2  E1 = h
h
E1
E2
h
E1
E2
Absorption Emission
n2
n1
e
p+
Niels Bohr, 1913
i
s

e
p=h/s
p=mev
i
s
   







 cos1λλΔλ is
cm
h
e
The Compton Effect (1923) Electron Diffraction(1925)
Partial Wave Duality
8
Two Split Experiment
t
tx
jtxxV
x
tx
m 



 ),(
),()(
),(
2 2
22


Wave Function
(x,y,z) = (r) = (r,,)
Bit vs Qunatum Bit (Qubit)
9
1 0
1
0
≡
≡
1
1
0






0
0
1













2221
1211



S=(Sφ Sθ SR=const)
• Two states classical bit
• Equalities
• Two levels quantum system (qubit)
• Single qubit operations
Polarization vector:
Density matrix:
 //
)0()( iHtiHt
eet  

Computation with Qubit (I)
10
0 1
1 0
Classical Computation
Operations: logical
Valid operations:
AND =
0 i
-i 0
1 0
0 -1
1 1
1 -1
0 1
0
1
0 0
0 1
NOT =
0 1
1 0
in
out
out
in
in
1 0 0 0
0 1 0 0
0 0 0 1
0 0 1 0
1-bit
2-bit
Quantum Computation
Operations: unitary
Valid operations:
σX =
σy =
σz =
Hd =
CNOT =
√2
1
1-qubit
2-qubit
Computation with Qubit (II)
11
1
0
0
0
u11 u12
u21u22
Single qubit
c1
c2
c1
c2
Two qubits
H2 =
1
0
0
1,
|0,|1
H2
2 = H2H2 = ,
|00,|01,|10,|11
0
1
0
0
,
0
0
1
0
,
0
0
0
1
c1
c2
c3
c4
c1
c2
c3
c4
u11 u12 u13 u14
u21 u22 u23 u24
u31 u32 u33 u34
u41 u42 u43 u44
Hilbert
space
U| = U| =Operator
| = c1|0 + c2|1 = |
c1|00 + c2|01 +
c3|10 + c4|11
==
Arbitrary
state
Quantum Gates(I)
12
pure state → mixed state
Only 1 classical single-bit gate, but ∞single-qubit gates
H² = 1
Hadamard Gate (H)
Quantum Gates(II)
13
Quantum Algorithms (I)
14
• Factoring, discrete log [Shor 94]
• Unstructured search [Grover 96]
• Various hidden subgroup problems [Long List]
• Pell’s equation [Hallgren 02]
• Hidden shift problems [van Dam, Hallgren, Ip 03]
• Graph traversal [CCDFGS 03]
• Spatial search [AA 03, CG 03/04, AKR 04]
• Element distinctness [Ambainis 03]
• Various graph problems [DHHM 04, MSS 03,…]
• Testing matrix multiplication [Buhrman,Špalek 04]
• Hidden subgroup problem [Bacon, Childs, van Dam 05]
• Certain hidden shift problems [Childs, van Dam 05]
Quantum Algorithms (II)
15
Shor’s Algorithm
18819881292060796383869723946165043
98071635633794173827007633564229888
59715234665485319060606504743045317
38801130339671619969232120573403187
9550656996221305168759307650257059
4727721461074353025362
2307197304822463291469
5302097116459852171130
520711256363590397527
3980750864240649373971
2550055038649119906436
2342526708406385189575
946388957261768583317
Best classical algorithm
takes time
Shor’s quantum algorithm
takes time
Peter Shor
1994
Quantum Algorithms (II)
16
Shor’s Algorithm
Quantum Algorithms (III)
17
Grover’s Algorithm (1996)
n qubit
1qubit
Suppose we have a black box
with the property
Problem: find with as few queries as possible.
Quantum Algorithms (V)
18
Grover’s Algorithm
Repeated application of the Grover iterate
Grover’s algorithm:
1. start with
2. repeatedly apply Grover’s iterate to rotate to near
Quantum Algorithms (IV)
19
Grover’s Algorithm
We have identified marked item using only queries!𝑂 𝑛
Quantum Computers Architecture (I)
20
Quantum Computers Architecture (II)
21
• Ion traps and neutral atoms
E0
E1
E2
• Superconducting qubit
• Semiconductor charge qubit
• Spin qubit
Nuclear spin
(liquid state NMR,
solid state NMR)
I
Electron spin
S
SQUIDCooper pair box
Double QD
e
0 1
N pairs - 0 1N+1 pairs -
Single QD
F
i
E0
E1
e
• Photon based QC
P
0
1
Quantum Computers Architecture (III)
22
Trapped Ion
motion
head
target
pushing
laser
Quantum Computers Architecture (IV)
23
Individual Photon
A
B
|1 = |0A|1B + |1A|0B
Quantum
Entanglement!
send single
photons
weak
laser
Ultraviolet ()
X
c(2) nonlinear crystal
Quantum Computer Challenges
24
0 1
106 eV
CLASSICAL
|0
|1
10-6 eV
QUANTUM
- Dephasing
- Decoherence
- Control of Operations
- Isolation from environment
- Superpositions are very fragile!
QC Future Works…
25
- More Qubits: 64, 128, 192, 256, …
- Much Greater Connectivity
- Much Lower Error Rate
- Much Longer Coherence
- True Fault Tolerance
- Much Lower Cost
- Non-cryogenic Operating
Temperature
Thanks!Hamid Reza Bolhasani
bolhasani@gmail.com
Dec 2018

An Introduction to Quantum Computers Architecture

  • 1.
    Quantum Computers Architecture Hamid Reza Bolhasani PhDStudent / Data Scientist Computer Architecture JAN 2020 1
  • 2.
    Table of Contents -History - Classical vs Quantum Mechanics - Breakdown of Classical Mechanics - Quantum Mechanics Introduction - Wave Function - Quantum Bit (Qubit) - Quantum Gates - Quantum Computer - Challenges - Q & A
  • 3.
    Richard Feynman “I thinkI can safely say that no one understand quantum mechanics!” 1982: Feynman proposed the first idea. 1985: Deutsch developed the quantum Turing Machine. 1994: Shor Algorithm to factor very large numbers in polynomial time. 1997: Grover proposed a quantum search algorithm. …Future! 3
  • 4.
    Classical Mechanics vsQuantum Mechanics Mechanics: the study of the behavior of physical bodies when subjected to forces or displacements Classical Mechanics: describing the motion of macroscopic objects. Macroscopic: measurable or observable by naked eyes Quantum Mechanics: describing behavior of systems at atomic length scales and smaller . 4
  • 5.
    Classical Mechanics 5 position r= (x,y,z) velocity v Property Behaviour mass momentum Particles position  collisions velocity Waves wavelength  diffraction frequency interference x m F k x = 0 k m(d2x/dt2) = kx +A A x  time period  = 1/  position x(t) = Asin(t) of particle frequency  = /2 = (of oscillation) m π2 1 k
  • 6.
    Breakdown of ClassicalMechanics 6 ePhotelectrons- h Metal surface work function = F e Photoelectrons ejected with kinetic energy: Ek = h - F a) Black Body Radiation b) Photoelectric Effect Max Planck (1900) Albert Einstein (1921)
  • 7.
    The Bohr Modelof the Atom 7 E = E2  E1 = h h E1 E2 h E1 E2 Absorption Emission n2 n1 e p+ Niels Bohr, 1913 i s  e p=h/s p=mev i s             cos1λλΔλ is cm h e The Compton Effect (1923) Electron Diffraction(1925)
  • 8.
    Partial Wave Duality 8 TwoSplit Experiment t tx jtxxV x tx m      ),( ),()( ),( 2 2 22   Wave Function (x,y,z) = (r) = (r,,)
  • 9.
    Bit vs QunatumBit (Qubit) 9 1 0 1 0 ≡ ≡ 1 1 0       0 0 1              2221 1211    S=(Sφ Sθ SR=const) • Two states classical bit • Equalities • Two levels quantum system (qubit) • Single qubit operations Polarization vector: Density matrix:  // )0()( iHtiHt eet   
  • 10.
    Computation with Qubit(I) 10 0 1 1 0 Classical Computation Operations: logical Valid operations: AND = 0 i -i 0 1 0 0 -1 1 1 1 -1 0 1 0 1 0 0 0 1 NOT = 0 1 1 0 in out out in in 1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 1-bit 2-bit Quantum Computation Operations: unitary Valid operations: σX = σy = σz = Hd = CNOT = √2 1 1-qubit 2-qubit
  • 11.
    Computation with Qubit(II) 11 1 0 0 0 u11 u12 u21u22 Single qubit c1 c2 c1 c2 Two qubits H2 = 1 0 0 1, |0,|1 H2 2 = H2H2 = , |00,|01,|10,|11 0 1 0 0 , 0 0 1 0 , 0 0 0 1 c1 c2 c3 c4 c1 c2 c3 c4 u11 u12 u13 u14 u21 u22 u23 u24 u31 u32 u33 u34 u41 u42 u43 u44 Hilbert space U| = U| =Operator | = c1|0 + c2|1 = | c1|00 + c2|01 + c3|10 + c4|11 == Arbitrary state
  • 12.
    Quantum Gates(I) 12 pure state→ mixed state Only 1 classical single-bit gate, but ∞single-qubit gates H² = 1 Hadamard Gate (H)
  • 13.
  • 14.
    Quantum Algorithms (I) 14 •Factoring, discrete log [Shor 94] • Unstructured search [Grover 96] • Various hidden subgroup problems [Long List] • Pell’s equation [Hallgren 02] • Hidden shift problems [van Dam, Hallgren, Ip 03] • Graph traversal [CCDFGS 03] • Spatial search [AA 03, CG 03/04, AKR 04] • Element distinctness [Ambainis 03] • Various graph problems [DHHM 04, MSS 03,…] • Testing matrix multiplication [Buhrman,Špalek 04] • Hidden subgroup problem [Bacon, Childs, van Dam 05] • Certain hidden shift problems [Childs, van Dam 05]
  • 15.
    Quantum Algorithms (II) 15 Shor’sAlgorithm 18819881292060796383869723946165043 98071635633794173827007633564229888 59715234665485319060606504743045317 38801130339671619969232120573403187 9550656996221305168759307650257059 4727721461074353025362 2307197304822463291469 5302097116459852171130 520711256363590397527 3980750864240649373971 2550055038649119906436 2342526708406385189575 946388957261768583317 Best classical algorithm takes time Shor’s quantum algorithm takes time Peter Shor 1994
  • 16.
  • 17.
    Quantum Algorithms (III) 17 Grover’sAlgorithm (1996) n qubit 1qubit Suppose we have a black box with the property Problem: find with as few queries as possible.
  • 18.
    Quantum Algorithms (V) 18 Grover’sAlgorithm Repeated application of the Grover iterate Grover’s algorithm: 1. start with 2. repeatedly apply Grover’s iterate to rotate to near
  • 19.
    Quantum Algorithms (IV) 19 Grover’sAlgorithm We have identified marked item using only queries!𝑂 𝑛
  • 20.
  • 21.
    Quantum Computers Architecture(II) 21 • Ion traps and neutral atoms E0 E1 E2 • Superconducting qubit • Semiconductor charge qubit • Spin qubit Nuclear spin (liquid state NMR, solid state NMR) I Electron spin S SQUIDCooper pair box Double QD e 0 1 N pairs - 0 1N+1 pairs - Single QD F i E0 E1 e • Photon based QC P 0 1
  • 22.
    Quantum Computers Architecture(III) 22 Trapped Ion motion head target pushing laser
  • 23.
    Quantum Computers Architecture(IV) 23 Individual Photon A B |1 = |0A|1B + |1A|0B Quantum Entanglement! send single photons weak laser Ultraviolet () X c(2) nonlinear crystal
  • 24.
    Quantum Computer Challenges 24 01 106 eV CLASSICAL |0 |1 10-6 eV QUANTUM - Dephasing - Decoherence - Control of Operations - Isolation from environment - Superpositions are very fragile!
  • 25.
    QC Future Works… 25 -More Qubits: 64, 128, 192, 256, … - Much Greater Connectivity - Much Lower Error Rate - Much Longer Coherence - True Fault Tolerance - Much Lower Cost - Non-cryogenic Operating Temperature
  • 26.