Quantum computers, quantum computations

1. Quantum computers, quantum computations

H. Gomonay
National Technical University of Ukraine
JGU, Mainz, Germany

2. Take-home message

The quest for a quantum computer reminds me
of the endless quests for WIMPs, strings,
sparticles, magnetic monopoles, etc. Succeed
they or not, they bring to development of new
knowledges and technologies, push the most
talented people into science and keep fun from
research. Same as it ever was.

3. Motivation

Moore’s law
Meters
Nanometers
40 years
Electronic lamp
Microprocessor 80486dx2

4. Outline

History
Principles of quantum computation
Di Vincenzo criteria
Superconducting qubit
Some algorithms
Architecture
Challenges and problems

5. History in facts

1935 – A. Einstein doubts in adequacy of
quantum mechanics & introduces entangled
states
1982 – R. Feynman predicts
possibility of quantum computations
2007 – D-Wave Systems presents
16 qubit quantum processor
Orion

6.

2012 – S. Haroche & D. J. Wineland winn
Nobel prize for for ground-breaking
experimental
methods
that
enable
measuring and manipulation of individual
quantum systems"
2015 – Google tests the D-Wave
2X quantum annealer, ~1000 qb

7. History in diagrams

Classical vs quantum:
speed up

8. What is beyond?

Down to small size = forward to quantum physics

9. Quantum Mechanics: Quantum Information

Quantum Mechanics
Measurement
Hilbert space
Schrödinger’s equation
Quantum key
distribution
Entanglement
Bell-EPR correlations
Multiple particle
interference
Quantum
computer
Quantum
algorithm
Decoherence
Quantum error
correction
Error correcting
codes
Data compression
Cryptography
Computer
(Turing)
Shannon’s
theorem
Maxwell’s
demon
Statistical
mechanics
Information Theory

10. What is all about or new applications of quantum physics

“Hacking” crypto
Keeping secrets
Data search speed up
Bioinformatics
Outer space opening
Fundamental
problems
Factorization of 256-digit
number:
Classic – 2N 1070 years
Quantum – N2 ~ 10 seconds

11. What is QC?

D-Wave
QC is the physical device that utilizes
quantum properties for information
processing

12. Classical  Quantum

Classical Quantum
Classical
Software
Input-output
Interface
Algorithms
Boolean logic
(Principle of
excluded middle)
Quantum
System codes
Physical basis
Quantum logic
(Superposition &
hidden symmetry)
Hardware

13. Algorithm complexity

Input
Classic C
Easy
L n
Hard
L 2
d
n
Quantum C
Hard
L n
d

14. Qubit = Quantum bit

i
cos 0 e sin 1
1
1
0
Bit
0 1
0
Qubit

15. Entangled states (EPR)

AB
1
0
2
A
1B 1
1 B
A
0
B
0 B
B
AB
A
0 A
1 A

16. Interference – Schrödinger's Cat

U
0 + 1
1
1
1
ˆ
H
1 1
2

17. Quantum parallelelism

18. Parallel quantum algorithm

in
a 0 1 b 1 0
out
a f (01) b f (10)
f
2n 1
c
x 0
2n 1
x
cx f ( x )
f
x
x 0

19. Universal gate set

Operation
x, y
x, y f ( x)
Gates:
NOT
Hadamar
XOR
1
NOT
0 1;1 0
0 0 1 / 2
1 0 1 / 2
0
1
00 00 ; 01 01
10 11 ; 11 10
0
Hadamar

20. Principles of quantum computation

Computation: unitary evolution
n
Hˆ Bzi (t ) ˆ zi Bxi (t ) ˆ xi J ij (t ) ˆ i ˆ j
i 1
i j
i ˆ
out exp H (t )dt in
Readout: measurement
Pˆ out 0 0 1 ... 1
Avoiding decoherence

21. Di Vincenzo criteria

Selectivity (addressing each qubit)
High sensitivity = Good control
Large decoherence time
( decoh/ gate >104)
Readout Measurability
Scalability (>100 qubits)

22. Quantum computer by Cirac & Zoller (1995)

Quantum computer
by Cirac & Zoller (1995)

23. Ions in trap

24. Qubit: micro or macro?

Measurement duration:
t ~ op ~ R1 ~ 10 9 s
Limitations:
E t
Energy splitting:
E B B
Qubit = 1 electron spin:
B ~ 10 23 J/T
-3 – 10-7
2
k~10
Measured
E E k
2
19
E
/
k
~
10
J
R
Min splitting
B E / B ~10 4 T
Min field
Impossible! We need macrospin!

25. Superconductors: macroatoms

Qubit: charge or phase
Control: magnetic flux
Readout: SQUID, SET
T=10 mK
1 qubit gate — ns
Qubit size 1 mcm
Josephson junction

26. Superconducting qubit: overcoming decoherence

(Shnyrkov, Mooji, D-wave Systems)
Shnyrkov et al, 2007
decoh s, T 1 K

27. Flux qubit: theory

250
e= ...
U ( , e ), a.u.
200
0
150
3/4 0
1/2 0
100
1/4 0
50
0
0
-2
~ 10 10 B
8
U SIS ( , e )
10
-1
0
/ 0
( e )
2L
2
I ct (0) 0
2
cos 2
0
1
2

28. … & experiment

…&
experiment
qubit
gate

29. V-I SQUID (V.Shnyrkov, G. Tsoi, 1990)

VT
Nb-Nb
classic
T 0,35 K
f 6 MHz
e = 0 /2
0
e = 0
quantum
Irf

30. Quantum coherence

ScS-контакт, m= 26, C= 8 pF, L= 3,83

31. Single-qubit gate

10
10
10
2
| 2 |
2|
|
| |
UU(
( ) )
U
U
U
88
8
1
0,20
1 1 1
0,6 0 0
0,8
0,98
2
e = 1.002 0
e = 1.001 0
e = 0
666
EEE
22E
2
1 E1
E
1
444EEE
0 00
0,5
0,5
0,5
1,0
1,0
1,0
/ 0
//
00
1,5
1,5
1,5

32. Rabi oscillations

Experimental results for the charge-phase qubit placed in the region of the maximum electric
field at continuous microwave irradiation with w0=7.27 GHz.
Set of the curves of the voltage-current phase shift T ( e/ 0) in the tank circuit. (V.
Shnyrkov, D. Born, A. Soroka, W. Krech 2003)

33. 2-qubit gate (DiVincenzo et al, IBM qubit)

34. Find the period: Shor’s algorithm

2n 1
x f ( x)
x 0
x
x a f ( x)
f ( x)
x a
a
Hˆ
y
x
f ( x a ) f ( x)

35. Hidden symmetry

2n 1 2n 1
( 1)
H
xy
y f ( x)
y 0 x 0
2n 1 2n 1
( 1)
xy
(1 ( 1) ) y f ( x)
ay
y 0 x 0
ay=0 - amplification; ay=1 -
depression

36. Database search

Classic algorithm : 2n =N
Quantum algorithm: 2n/2 = N
Unsorted database
s
Merlin
N
1
N
x 0
x
1
N
0..00
w ??..?
... 1..11

37. Grover’ algorithm

Input
Flip (Merlin)
Uw 1 2 w w
Mirroring
U s 2 s s 1

38. Grover’ algorithm: experiment

39. Architecture

4-level system
QIR=Quantum Intermediate Representation
QASM=Quantum Assembly Language
QPOL=Quantum Physical Operations Language
QCC=Quantum Computer Compiler

40. Quantum computer: challenges

Decoherence (state instability)
Scaling (few number of qubits)
Input-output control
Extreme conditions (T=10 mK, …)
New math algorithms development
Consumer friendly implementation
Weak measurement

41. Quantum abyss

Есть
Надо
~5
# кубитов
>1000
<100
# операций
>109
Шум
Технологии
?
Ошибки
Алгоритмы
41

42. When, Where, Who & hoW?

When, Where, Who & hoW?
2 qb — 1999, 7 qb — 2001, 16 qb — 2007,
NP — 2012,1000 qb —2015, on-table -- 20xx?
~ 1000 experimental groups over the world
Physics, math, computer science, engineering?
Semi- or super-conductors or?

43. Alumni

Sergii Strelchuk
Vadym Kliuchnikov
Junior Research Fellow @ Centre for
Quantum Information and Foundations,
UC
http://www.qi.damtp.cam.ac.uk/node/72
Post doc researcher @ Microsoft
Research
http://research.microsoft.com/enus/people/vadym/

44. QUANTUM COMPUTING

JOIN THE TEAM!