dizzy hasnt understood it.

fairiesbelchingInternet and Web Development

Dec 11, 2013 (3 years and 8 months ago)

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Anyone who can contemplate
quantum mechanics without getting
dizzy hasn

t understood it.







--
Niels Bohr



The Quantum Information Revolution




Paul Kwiat



Kwiat’s

Quantum

Clan (2012)

Graduate Students:



Rebecca Holmes


Aditya

Sharma


Trent Graham


Brad Christensen


Kevin
Zielnicki


Mike
Wayne


Courtney
Byard


Undergraduates
:


Daniel
Kumor


David
Schmid


Jia

Jun (“JJ”) Wong


Cory
Alford


Joseph Nash


David Rhodes


Visit Prof:
Hee

Su Park

Post
-
Doc:

Jian

Wang



A New Science!

Quantum

Mechanics

Information

Science

Quantum Information Science

20th Century

21st Century


Quantum

Information

Fundamental physics

Decoherence

Quantum




捬c獳s捡c

Entanglement

Ultimate control over


污牧l


獹獴s浳

兵慮瑵Q 浥瑲潬潧y

䵥慳畲M浥湴猠扥b潮o

瑨攠捬c獳s捡c 汩l楴

Non
-
invasive measurements

Measurements on quantum

systems

Quantum cryptography

Secure key distribution


(even between


non
-
speaking parties)

Quantum computation

Factoring

Simulating other quantum

systems (>30bits)

Error correction

Quantum communciation

Teleportation

Linking separated

quantum systems

(

焮q湥瑷潲o

)

Quantum
Metrology

Quantum
Computing

Quantum
Cryptography


Things should
be made as
simple as
possible, but not
any simpler.


What
I

do…

Unravel the mysteries




of the universe…

Quantum Optics

Light

???

Quantum…

a.
very small

b.
very big (e.g., “quantum leap”)

c.
an
unsplittable

parcel/bundle of
energy

d.
a cool buzzword to get more
funding, more papers, more
people at your Sat. am physics
lecture, etc.

e.
all of the above

1905: Einstein made a ‘quantum
leap’ and proposed that light
was really made of particles
with tiny energy given by


E = h f = h c/
l

frequency

6.6 x 10
-
34
J
-
s

wavelength

Power input

Partially transmitting
mirror

How many photons per second are emitted from a

1
-
mW

laser (
l
=635nm
)?





How do we reconcile this notion that light comes in

packets


with
our view of an electromagnetic wave, e.g., from a laser??

photon
hc
E
l

1240eV-nm
2eV
635 nm
 
Power output: P = (# photons/sec) x E
photon

3
15 1
-19
10 J 1eV 1photon
(# photons/sec) 3.1 10 s
s 1.6 10 J 2eV
photon
P
E


     

Visible light

Physics 214: Lect. 7

Example
:
“Counting photons”

1
mW

red laser

3 x 10
15

photons/sec =



This is an incredibly huge number


your eye basically
cannot resolve this many individual photons (though
the rods can detect single photons!
).

And
you

MAY be able to see just one photon!!




3,000,000,000,000,000/sec



Formation of Optical Images

l
For large light intensities
, image
formation by an optical system can be
described by classical optics.

Exposure time

l

However,

for very low light intensities
, one can see the
statistical and random nature of image formation.


l

Use an extremely sensitive CCD camera that can detect single photons.

A. Rose, J. Opt. Sci. Am. 43, 715 (1953)

"God does not play
dice with
the universe."


It seems to me that the idea of a personal God is an
anthropological concept which I cannot take seriously.


Photon only detected in one output.

Equally likely to be transmitted or

reflected


cannot tell which
.

A
b
eamsplitter


But how do we *know* there’s
only ONE photon…

Quantum random
-
number generator
!


completely unpredictable


patented


commercially available

“0”

“1”


The important thing is
not to stop questioning.






-
A. Einstein

Quantum

Interrogation


Yes, yes, already, Warren! …

There
is

film in the camera!


The problem…

Measure



-
film





-
absorber



-
atom
without



-
exposing



-
heating



-
exciting it

WHY was Einstein’s 1905
proposal that light was made of
particles such a profound leap

that
almost no one believed him
?

Because everyone KNEW that light
was really waves.


One of the strangest features of QM:
all particles can behave like waves…

Interference of
waves (e.g.,
water, sound, …
)



Superposition (adding together)
of
waves

Waves add up:

“Constructive interference”

Waves cancel:

“Destructive interference”

Light:
Particle

or
Wave
?




1675: Newton

proved


the light was made
of

corpuscles


1818: French Academy science contest

l
Fresnel proposed
interference

of
light.

l
Judge Poisson
knew

light was made of
particles:

Fresnel

s ideas ridiculous


If
Fresnel ideas were correct, one would
see a bright spot in the middle of the
shadow of a disk.

Judge Arago decided to
actually do the experiment…



Conclusion (at the time):
Light
must

be a wave, since
particles don

t
interfere!


Only, now we know




that
they
must!

Single
-
Photon
Interference:

l
Question:

what if we reduce the
source intensity so that at most
one particle (photon)
is in the
apparatus
at a time?




Exposure time

l
Answer:

Just like in the

optical
image formation

, given enough time,
the
classical interference pattern

will gradually build up from a huge #
of seemingly random

events

!





Photons

?

Optical Interferometers

l
Interference arises when there are two (or more) ways
for something to happen, e.g.,
sound from two speakers
reaching your ear.

l
An interferometer is a device using mirrors and

beam
splitters


(half light is transmitted, half is reflected) to
give two separate paths
for light to get from the source
to
the detector
.


l
Two common types:



Mach
-
Zehnder
:




Michelson :




mirror

beam
-

splitter

beam
-

splitter

mirror

Quantum

Interrogation


Yes, yes, already, Warren! …

There
is

film in the camera!


The problem…

Measure



-
film





-
absorber



-
atom
without



-
exposing



-
heating



-
exciting it

The solution…

(
Elitzur

&
Vaidman
, 1993)

Use
dual
wave
-
particle nature of quantum
objects (

wavicles

)

Single photon always shows up at D1

(complete destructive interference to D2)

Now place an absorbing object in one arm…

50% chance that photon is absorbed by object

50% chance it isn

t


㈵┠%桡湣攠䐲晩牥猠





interaction
-
free measurement


of object

Quantum Interrogation


Optimizing
reflectivities



50% efficiency


By combining these techniques with the

quantum Zeno effect


(making repeated very
weak interactions), the efficiency can in
principle be pushed to 100%: no photons
absorbed by the absorbing object!






[85% demonstrated to date]


Imaging semi
-
transparent objects does
not

readily yield a gray
-
scale

Quantum
Metrology

Quantum
Computing

Quantum
Cryptography

Wpdrval





L&wz;xcuymnzx



Cryptography:


Make messages so that only the
intended recipient can understand
them…

1.
public key encryption: Standard, but
not provably secure; relies on
difficulty of factoring (e.g., 15 = 3x5)

2.
secret key encryption: PROVABLY
secure as long as


a.
no one else has the key

b.
the key is never reused

Quantum Cryptography = Quantum Key Distribution

ALICE

BOB

Cipher:

…0110010110100010…

XOR(Cipher,Key)




Message

EVE

KEY:

…010001010011101001…

Quantum Cryptography

Cryptography

XOR(Message,Key)




Cipher

Quantum Cryptography:

Use a different property of light



polarization!

Prob
(horizontally polarized photon pass horizontal polarizer): 1

Polarization:

--
the
oscillation direction of the
light

--
property of each photon

--
can measure with polarizers, calcite, etc.

Prob
(horizontally polarized photon pass vertical polarizer): 0

Prob
(diagonally pol. photon pass horizontal polarizer): 1/2

Prob
(diagonally pol. photon pass vertical polarizer): 1/2

How to Make “Entangled” Coins

We don’t know WHICH crystal created the pair of
photons, but we know they both came from the
same

crystal


they

MUST have the same polarization.

“Spontaneous

DownConversion
”:

high energy
parent photon can
split into two
daughter photons

(with same
polarization)



Eve cannot

瑡t


瑨攠汩湥l


灨潴潮猠瑨慴⁤潮


浡m攠e琠t漠䉯戠慲攠湯琠灡牴映 桥h步y




Eve cannot

捬潮c


瑨攠灨潴潮


景牢楤f敮e批
basic quantum mechanics




Measurements by Eve necessarily have a
chance (
25
%
)
to disturb the quantum state




䅬楣A⁡湤 䉯B 捡渠摥瑥捴 敲牯牳 楮⁴桥i步y!


If the bit error rate is too high, they simply discard
the key. No message is ever compromised.

What about Eavesdropping?

Current Free
-
Space QKD Distance Record:

144
km between
LaPalma

and
Tenerife


Last week news item: they used the
entangled photons to teleport the
state of a photon between the
islands


world distance record for
quantum teleportation!

QKD Goes Commercial…

Since we can seemingly

see


without

looking


using quantum interrogation, does this mean an
eavesdropper could use it to defeat quantum
cryptography?

No! It turns out that even making the gentlest
measurement possible, if the eavesdropper gains
any information, she disturbs the state.

Or if she is so gentle so as not to disturb the state,
then she gets no information.

Quantum key distribution is secure against
any

attack allowed by the laws of physics!

Quantum Interrogation vs.

Quantum Cryptography

Imagination is more
important than knowledge

Source: Intel

Moore

猠䱡L

The first solid
-
state transistor

(Bardeen, Brattain & Shockley, 1947)

INTEL

Pentium 4

transistor

The Ant and

the Pentium

~100 million transistors

Size of an atom

~ 0.1nm

Superposition

Interference

Wave
-
particle
duality

Intrinsic
randomness in
measurement


Entanglement

2
-
level atom
:

g
 
e



spin
-
1/2
:

 

polarization:


H
 
V


Binary digit




Quantum bit



bit







qubit



0, 1





0
 
1
 
0
  
1


Physical realization of qubits


any 2 level system


All 2
-
level systems are created equal, but some are
more equal than others!

Quantum communication


photons

Quantum storage


atoms, spins

Scaleable

circuits


superconducting
systems



Quantum


phenomena



Entanglement

Ⱐ,湤n瑨攠獣慬楮朠瑨慴t牥獵汴猬l楳 瑨攠
key to the power of quantum computing.





Classically

, information is stored in a bit register: a 3
-
bit

register can store

one


number, from 0


7.












a

|

000




+ b

|

001





+ c

|

010




+ d

|

011




+ e

|

100




+ f

|

101




+ g

|

110




+ h

|

111







Result:

--



Classical:

one N
-
bit number

--


Quantum:

2

N


(all possible) N
-
bit numbers



N.B.

:


A 300
-

qubit


register can simultaneously store

2
300

~ 10
90

numbers

1

0

1

Quantum Mechanically
, a register of 3 entangled
qubits

can store all of these numbers in superposition:

That’s a BIG number

10
9
0

=

This is more than the total number of particles
in the Universe!



1,000,000,000,000,000,000,
000,000,000,000,000,000
,

000,000,000,000,000,000
,

000,000,000,000,000,000
,

000,000,000,000,000,000



Some important problems benefit from this
exponential scaling, enabling solutions of
otherwise insoluble problems.

A hard problem: factoring large integers
:

For example, it is hard to factor
167,659

But an elementary school student can
easily multiply

389 x 431 = 167,659

This asymmetry in the difficulty of factoring
vs. multiplying is the basis of public key
encryption, on which everything from on
-
line
transaction security to ensuring diplomatic
secrecy depends.

Quantum Computing

s

killer app.



RSA digits

PC

(1

GHz)

Blue

Waters

(10PF)

Quantum
Computer
(1

GHz)

129

4 months

1 sec

10 sec

225

300,000

yr

12 days

100 sec

300

10
16

yr

(>> universe)

20 million
yr

200 sec

The difficulty (impossibility) of factoring large numbers
(and the ease of creating a large number from its
factors) is the basis of public key encryption (which
nearly everyone uses for secure transmission today).

Quantum algorithms enable one to factor numbers
into their prime constituents MUCH faster:

state labels





,




Atom in different energy states:

atom

energy states:

atom in

state


atom in

state


atom in

superposition state

shorthand

wave function


representation




=




+


Probability of measuring , P


= |

|
2


Probability of measuring , P

= |

|
2

|0


|0


+ |1


|0


|0


|1


|rest


state of motion

Collective motion: the

quantum data bus


laser

|0


|0


|0


|0


|1


|rest


+ |moving


Science News


Quantum Computing Explored

Sep 12 2001 @ 08:10

American computer scientists are studying the possibility to
build a super fast computer based on quantum physics.


Technology requirements


Set of qubits isolated from environment.



Quantum information bus


to connect qubits.



Reliable read
-
out method.

Essential Dichotomy

Need WEAK coupling to
environment to avoid
decoherence
, but you also
need STRONG coupling to at
least some external modes in
order to ensure high speed and
reliability.

Why it might not work…

Quantum Information Timeline

0

5

10

~15

20?

25??

Time (years)

Difficulty/Complexity

Quantum

Measurement

Quantum

Communication

The known

Quantum

Computation

The expected

The unlikely


impossible?

Quantum

Sensors?

The as yet unimagined!!!

Quantum

Engineered
Photocells?

Quantum

Widgets

Quantum

Games & Toys


Why is it that nobody
understands me
, and
everybody likes me?














A.E.


Interconnected multi
-
trap
structure


Route ions by controlling
electrode potentials


Processor sympathetically
cooled


No individual optical
addressing during two
-
qubit
gates
(can do gates in strong
trap


晡f琩


One
-
qubit gates in subtrap


Readout in subtrap

Multiplexed Ion Trap
Architecture

control electrodes

0
200
400
600
800
1000
1
10
100
1000
1
10
4
1
10
5
1
10
6
1
10
7
1
10
8
1
10
9
1
10
10
1
10
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1
10
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1
10
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1
10
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1
10
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1
10
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1
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1
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1
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1
10
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1
10
24
Quantum factoring and cryptography

Classical
~ e
AL

# of instructions

# of bits, L, factored

Quantum
~
L
3

RSA129

~ 10
9

operations:

seconds

~ 10
17
instructions:
8 months

the RSA cryptosystem:


polynomial

work to
encrypt/decrypt


exponential
work to
break = factoring



BUT quantum factoring is
only
polynomial work



latency

㨠:楬氠楮景牭f瑩t渠
敮e特灴敤p瑯t慹 扥⁳b捵牥
慧a楮獴⁦畴s牥 煵慮瑵洠
捯浰畴敲c?