This document provides a comprehensive overview of quantum computer architecture, detailing the history and development of quantum mechanics and its distinct features compared to classical mechanics. It explains key concepts such as qubits, quantum gates, and algorithms like Shor's and Grover's, highlighting their significance in advancing computational capabilities. Additionally, it addresses the challenges faced in quantum computing and future aspirations for improving qubit technology and operational efficiency.

1. Quantum
Computers
Architecture
Hamid Reza Bolhasani
PhD Student / 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 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

4. 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

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 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)

7. 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)

8. Partial Wave Duality
8
Two Split Experiment
t
tx
jtxxV
x
tx
m 



 ),(
),()(
),(
2 2
22


Wave Function
(x,y,z) = (r) = (r,,)

9. 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  


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. Quantum Gates(II)
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’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

16. Quantum Algorithms (II)
16
Shor’s Algorithm

17. 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.

18. 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

19. Quantum Algorithms (IV)
19
Grover’s Algorithm
We have identified marked item using only queries!𝑂 𝑛

20. Quantum Computers Architecture (I)
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
0 1
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. Thanks!Hamid Reza Bolhasani
bolhasani@gmail.com
Dec 2018