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Transcript 
Distributed Quantum Computing
Using the most precise description of our world
to solve some of the hardest problems
by Matthias Egli
Based on the paper „Distributed Quantum Computing“ by Harry Buhrman and Hein Röhrig
These slides are just an addition to the math
shown on the blackboard
Motivation
Communication Complexity
Alice
n
Bob
Communication Complexity
Alice
?
Bob
Communication Complexity
Classical Computer
Quantum Computer
Disjointness
n
n
Equality (Promise)
n
log(n)
Speedup with Quantum Computers
Classical Computer
Quantum Computer
log(n)
Factorization
an
Search
n
n
Deutsch-Jozsa
n
1
The qubit
Superposition
 
 0  1  
 
 00   01   10   11
1 1 
1  1


Quantum Gate
1
H
2
Entanglement
 00   11
Basics
Deutsch-Josza Algorithm
f : 0,1  0,1
n
Promise:
Function is constant or balanced
Deutsch-Josza Algorithm
n
Classcial Computer
Classical randomized
Quantum Computer
2
2
1
1
n
n
Log(n)
1
Communication
Communication
Qubit
Alice
 0  1
Bob
Communication
Entanglement
 00   11
Communication Types
Communication
Alice
Classical bits with EPR Pairs
0,1
Bob
Communication
Qubit with shared EPR Pairs
Alice
 0  1
Bob
Communication Types
Deutsch-Jozsa Communication
Alice
Bob
X: 00101100
Y: 00101100
Deutsch-Josza Communication
Alice
X: 00101100
Bob
X=Y?
Y: 00101100
Deutsch-Josza Communication
Alice
X: 00101100
n
Bob
X=Y?
Y: 00101100
Deutsch-Josza Communication
Alice
X: 00101100
?
Bob
X=Y?
Y: 00101100
Deutsch-Josza Communication
Alice
X: 00101100
Bob
X=Y?
Y: 00101100
Promise: Hamming Distance = n/2 or 0
Deutsch-Josza Communication
XOR
Alice
X: 00101100
Bob
X=Y?
Y: 00101100
Promise: Hamming Distance = n/2 or 0
Deutsch-Josza Communication
Alice
X: 00101100
Bob
X=Y?
Y: 00101100
Promise: Hamming Distance = n/2 or 0
Deutsch-Josza Communication
1
xi
(

1
)
i  Trick

n i0,1log( n )
Alice
1
xi
(

1
)
i  Trick

n i0,1log( n )
Alice
log(n)+1
Bob
1
xi
(

1
)
i  Trick

n i0,1log( n )
Bob
1
xi
(

1
)
i  Trick

n i0,1log( n )
1
xi  yi
(

1
)
i  Trick

n i0,1log( n )
Bob
1
xi
(

1
)
i  Trick

n i0,1log( n )
1
xi  yi
(

1
)
i  Trick

n i0,1log( n )
Bob
Deutsch-Jozsa Algorithm
What else is possible?
• Leader Election
• Disjointness
• […]
Sources
• Caltech Introduction to Quantum Computing
http://www.theory.caltech.edu/people/preskill/ph229/notes/chap1.pdf
• Distributed Quantum Computing
Harry Buhrmann and Hein Röhrig
• Can quantum mechanics help distributed computing?
Anne Broadbent and Alain Tapp
• Distributed Quantum Computing: A New Frontier in Distributed Systems
or Science Fiction?
Vasil S. Denchev and Gopal Pandurangan
Questions?
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