Quantum Computing - Object-Oriented Programming and Data Structures - Lecture Sl, Lecture notes of Object Oriented Programming

Download Quantum Computing - Object-Oriented Programming and Data Structures - Lecture Sl and more Lecture notes Object Oriented Programming in PDF only on Docsity!

Quantum

Computing

(and

other

shortcuts

for

solving

hard

problems)

The

world

isn’t

as

simple

as

it

seems!

Starting

as

early

as

the

Greek

philosophers,

people

have

wondered

what

the

world

is

“made

of”

Fire,

earth,

water

and

air?

Atoms?

Basic

particles:

electrons,

neutrons,

protons?

Quarks?

Or

perhaps…

m

branes?

Each

discovery

has

explained

things

a

bit

better

and

also

revealed

new

puzzles

What

is

an

elementary

particle?

This is an old question - Bohr visualized a nice hard nugget of matter with various properties - Heisenberg was convinced that when you look very closely, you see some form of waves, not particles Are elementary particles like the bullet, or like the wave?

Two

slit

experiment

We point a laser at a mask with two slits scratched on it - If the laser light is particles, we would expect to see two bright spots - Instead, see an interference pattern

A

really

peculiar

example

Wheeler suggested this diamond setup as an even simpler illustration of the two ‐ slit experiments - A laser beam will interfere with itself… even if the intensity is just one photon at a time laser mirror mirror Beamsplitter

A

really

peculiar

example

Suppose we add a “photon detector”? Now we can tell “which way” the particle went… - …. And it switches to classical behavior! laser mirror mirror Beamsplitter There it is!

Weird

science

How about… turn on detector but hide it in a box? - This destroys the information about which way the photon went… - and we see an interference pattern - … open the box and the system becomes classical again - What if we use electronics to destroy the reading after the photon has already passed the detector? - …. Guess what? Interference pattern reappears - Isn’t this “editing the past”?

Weird

science

In

some

sense

when

we

observe

a

system

we

force

it

to

behave

classically.

Even

if

our

observation

occurs

after

the

event

that

seems

to

determine

classical/quantum

behavior!

But

only

observations

that

actually

reach

the

observer

matter.

So

we

need

to

think

about

the

meaning

of

“information

reaching

an

observer”

Decoherence

When

a

quantum

state

collapses

into

a

classical

one

because

of

an

interaction

with

the

outside

world

we

say

it

has

decohered

And it won’t take long: outside of very careful experiments, most quantum superpositions collapse within 10 ‐^13 seconds

But

macro

scale

quantum

effects

do

arise

In superconductors and superfluids - In analogues of the “Schrödinger’s Cat” scenario

What

does

it

mean

to

say

“X

saw

Y”?

This is a statement about something that happened: a measurement - And it was made at some point in “time” - Pre ‐ Einstein it seemed obvious that we could do experiments that measure time. For example, could talk about simultaneous events occurring at different places - We would say “X happened, and O was watching. When the light from X reached O, O could see that (and when) X happened.” - We could even claim that “events X and Y happened simultaneously, because O saw them both at the same time.” - These statements seemed to make sense

Speed

of

light

limit

Time is best measured in terms of the “real” speed of light, and this speed is the hypotenuse of a triangle - This sheds light (groan) on our experiments - A photon (moves at the speed of light) sees no “time” stand still! Movement in time Movement in space

Things

we

can

say

Time per se may not have any absolute meaning at all. - When we talked about deciding whether to turn the detector on “before” or “after” the photon hit the splitter, that comfortable notion isn’t a very good way to understand the system - Better is to think of information moving from place A to place B and not worrying about “when” at all

How

can

a

photon

“interfere”

with

itself?

You might have several ideas for explaining this - Maybe you doubt the experimental setup. But we can really build experiments this sensitive - Perhaps photons are “pure waves”? - But this contradicts the single ‐ slit variation. And a famous experiment by Bell rules out some other versions of this idea - Our single experiment reveals that a photon behaves like both a solid little object and a probability wave, depending on circumstances

Modern

thinking:

the

experiments

aren’t

measuring

the

identical

thing…

What

is

the

universe?

Since

we

can’t

talk

about

time

except

in

a

relative

sense,

how

can

we

talk

about

the

universe?

Think

about

graphs.

We

can

model

the

quantum

universe

as

a

graph

of

“states”

connected

by

“state

transition”

edges.

From

each

state

there

are

other

reachable

states,

and

probabilities

of

reaching

them

Who

throws

the

dice?

Maybe

the

graph

is

“all

there

is”.

Or

maybe

God

does.

b s a t