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The Quantum Computer

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Matthias Christandl

on 1 December 2014

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Transcript of The Quantum Computer

The Quantum Computer
Matthias Christandl
Professor
Department of Mathematical Sciences
University of Copenhagen, Denmark

1600s
1920s
1930s
1980s
. . .
1996
today
?
0101
1100

First Quantum
Computer

Information
Classical Mechanics
abstract concept
independent of
physical implementation
Claude Shannon
Alan Turing
unit of information, the bit: 0 or 1
0101
1100
all physical information
can be abstracted this way
0 or 1
information theory
?
Quantum Mechanics
claim based on world being classical
position
measurement:
left or right?
position
measurement:
left or right?
particles have definite properties
location, velocity, color, ....
these can be measured (to arbitrary accuracy)
The Quantum Computer
single atoms (and other small objects)
they behave according to quantum mechanics
do not behave according to classical mechanics
spin of an electron
measurement:
up or down?
measurement:
left or right?
50%
50%
Particles have properties that only come into being through measurement
Quantum bits - Qubits
=
a
+ b
one qubit
. . .
Are several qubits described by several a´s and b´s?
No!
. . .
+
. . .
+ . . . +
. . .
Writing down the a´s of 100 qubits, we would need more bits than atoms in the universe! Qubits are very powerful!
number of a´s exponential
in number of particles
Computation
Entanglement
Einstein-Podolsky-Rosen pair
Schrödinger´s cat
. . .
. . .
achieved for 10 - 1000 particles
a real cat has 1000000000000000000000 atoms
Can this help us to compute faster?
Birth of the quantum computer
How many gates do we need? Depends on the function!
. . .
. . .
. . .
. . .
. . .
multiplication
factorisation
number of gates
x
y
x
x+y+1
number of digits (2n)
fast!
number of gates
exponential in number of digits
slow!
0
0
0
1
p*q=?
k=?*?
. . .
. . .
. . .
. . .
. . .
Idea: Compute function for all inputs simultaneously!
input
output
Problem: get all answers at the same time...
+
+ . . . +
. . .
. . .
. . .
+
+ . . . +
. . .
. . .
. . .
Peter Shor solved this problem for factoring in 1996
On a quantum computer factoring is as fast as multiplying!
Building a Quantum Computer
State of the art: ca. 10 -100 qubits, can factor 15
0
1
0
0
1
0
1
0
1
1
1
1
. . .
input
output
. . .
function
gate
gate
gate
gate
gate
gate
gate
gate
=
Any function can be computed with gates!
Challenges:
Need: Mega
qu
bits, even Giga
qu
bits
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
gate
gate
gate
keep atoms isolated
Blatt, Wineland
excellent control over many atoms
Experimentally difficult, no fundamental obstruction!
Conceptual Fabric
Classical Computer Quantum Computer
is not just an upgrade, it is a paradigm shift
underlying physical theory is quantum mechanics
all previous computation was based on Newtonian mechanics
quantum parallelism
exponential speedup possible!
no conventional hardware upgrade can achieve this
. . .
. . .
no such superposition seen in universe yet!
Planck, Heisenberg,
Bohr, Schrödinger,
Einstein, ...
Includes classical mechanics.
more than classical mechanics!
Deutsch, Feynman
particle
interaction
particle
interaction
particle
interaction
Input
Output
efficient simulation of quantum physics
universe quantum computer
Large and growing field of research
universities, ibm, microsoft, google...
Nobel prize 2012
area of my own research
try all pairs until you find the correct one
Full transcript